a scientific problem and a hypothesis

Have a language expert improve your writing

Run a free plagiarism check in 10 minutes, generate accurate citations for free.

• Knowledge Base

Methodology

• How to Write a Strong Hypothesis | Steps & Examples

How to Write a Strong Hypothesis | Steps & Examples

Published on May 6, 2022 by Shona McCombes . Revised on November 20, 2023.

A hypothesis is a statement that can be tested by scientific research. If you want to test a relationship between two or more variables, you need to write hypotheses before you start your experiment or data collection .

Example: Hypothesis

Daily apple consumption leads to fewer doctor’s visits.

Table of contents

What is a hypothesis, developing a hypothesis (with example), hypothesis examples, other interesting articles, frequently asked questions about writing hypotheses.

A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.

A hypothesis is not just a guess – it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).

Variables in hypotheses

Hypotheses propose a relationship between two or more types of variables .

• An independent variable is something the researcher changes or controls.
• A dependent variable is something the researcher observes and measures.

If there are any control variables , extraneous variables , or confounding variables , be sure to jot those down as you go to minimize the chances that research bias  will affect your results.

In this example, the independent variable is exposure to the sun – the assumed cause . The dependent variable is the level of happiness – the assumed effect .

Receive feedback on language, structure, and formatting

Professional editors proofread and edit your paper by focusing on:

• Academic style
• Vague sentences
• Style consistency

See an example

Step 1. Ask a question

Writing a hypothesis begins with a research question that you want to answer. The question should be focused, specific, and researchable within the constraints of your project.

Step 2. Do some preliminary research

Your initial answer to the question should be based on what is already known about the topic. Look for theories and previous studies to help you form educated assumptions about what your research will find.

At this stage, you might construct a conceptual framework to ensure that you’re embarking on a relevant topic . This can also help you identify which variables you will study and what you think the relationships are between them. Sometimes, you’ll have to operationalize more complex constructs.

Step 3. Formulate your hypothesis

Now you should have some idea of what you expect to find. Write your initial answer to the question in a clear, concise sentence.

4. Refine your hypothesis

You need to make sure your hypothesis is specific and testable. There are various ways of phrasing a hypothesis, but all the terms you use should have clear definitions, and the hypothesis should contain:

• The relevant variables
• The specific group being studied
• The predicted outcome of the experiment or analysis

5. Phrase your hypothesis in three ways

To identify the variables, you can write a simple prediction in  if…then form. The first part of the sentence states the independent variable and the second part states the dependent variable.

In academic research, hypotheses are more commonly phrased in terms of correlations or effects, where you directly state the predicted relationship between variables.

If you are comparing two groups, the hypothesis can state what difference you expect to find between them.

6. Write a null hypothesis

If your research involves statistical hypothesis testing , you will also have to write a null hypothesis . The null hypothesis is the default position that there is no association between the variables. The null hypothesis is written as H 0 , while the alternative hypothesis is H 1 or H a .

• H 0 : The number of lectures attended by first-year students has no effect on their final exam scores.
• H 1 : The number of lectures attended by first-year students has a positive effect on their final exam scores.

If you want to know more about the research process , methodology , research bias , or statistics , make sure to check out some of our other articles with explanations and examples.

• Sampling methods
• Simple random sampling
• Stratified sampling
• Cluster sampling
• Likert scales
• Reproducibility

 Statistics

• Null hypothesis
• Statistical power
• Probability distribution
• Effect size
• Poisson distribution

Research bias

• Optimism bias
• Cognitive bias
• Implicit bias
• Hawthorne effect
• Anchoring bias
• Explicit bias

Prevent plagiarism. Run a free check.

A hypothesis is not just a guess — it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).

Null and alternative hypotheses are used in statistical hypothesis testing . The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

Cite this Scribbr article

If you want to cite this source, you can copy and paste the citation or click the “Cite this Scribbr article” button to automatically add the citation to our free Citation Generator.

McCombes, S. (2023, November 20). How to Write a Strong Hypothesis | Steps & Examples. Scribbr. Retrieved June 7, 2024, from https://www.scribbr.com/methodology/hypothesis/

Is this article helpful?

Shona McCombes

Other students also liked, construct validity | definition, types, & examples, what is a conceptual framework | tips & examples, operationalization | a guide with examples, pros & cons, what is your plagiarism score.

What is a scientific hypothesis?

It's the initial building block in the scientific method.

Hypothesis basics

What makes a hypothesis testable.

• Types of hypotheses
• Hypothesis versus theory

Additional resources

Bibliography.

A scientific hypothesis is a tentative, testable explanation for a phenomenon in the natural world. It's the initial building block in the scientific method . Many describe it as an "educated guess" based on prior knowledge and observation. While this is true, a hypothesis is more informed than a guess. While an "educated guess" suggests a random prediction based on a person's expertise, developing a hypothesis requires active observation and background research. 

The basic idea of a hypothesis is that there is no predetermined outcome. For a solution to be termed a scientific hypothesis, it has to be an idea that can be supported or refuted through carefully crafted experimentation or observation. This concept, called falsifiability and testability, was advanced in the mid-20th century by Austrian-British philosopher Karl Popper in his famous book "The Logic of Scientific Discovery" (Routledge, 1959).

A key function of a hypothesis is to derive predictions about the results of future experiments and then perform those experiments to see whether they support the predictions.

A hypothesis is usually written in the form of an if-then statement, which gives a possibility (if) and explains what may happen because of the possibility (then). The statement could also include "may," according to California State University, Bakersfield .

Here are some examples of hypothesis statements:

• If garlic repels fleas, then a dog that is given garlic every day will not get fleas.
• If sugar causes cavities, then people who eat a lot of candy may be more prone to cavities.
• If ultraviolet light can damage the eyes, then maybe this light can cause blindness.

A useful hypothesis should be testable and falsifiable. That means that it should be possible to prove it wrong. A theory that can't be proved wrong is nonscientific, according to Karl Popper's 1963 book " Conjectures and Refutations ."

An example of an untestable statement is, "Dogs are better than cats." That's because the definition of "better" is vague and subjective. However, an untestable statement can be reworded to make it testable. For example, the previous statement could be changed to this: "Owning a dog is associated with higher levels of physical fitness than owning a cat." With this statement, the researcher can take measures of physical fitness from dog and cat owners and compare the two.

Types of scientific hypotheses

In an experiment, researchers generally state their hypotheses in two ways. The null hypothesis predicts that there will be no relationship between the variables tested, or no difference between the experimental groups. The alternative hypothesis predicts the opposite: that there will be a difference between the experimental groups. This is usually the hypothesis scientists are most interested in, according to the University of Miami .

For example, a null hypothesis might state, "There will be no difference in the rate of muscle growth between people who take a protein supplement and people who don't." The alternative hypothesis would state, "There will be a difference in the rate of muscle growth between people who take a protein supplement and people who don't."

If the results of the experiment show a relationship between the variables, then the null hypothesis has been rejected in favor of the alternative hypothesis, according to the book " Research Methods in Psychology " (​​BCcampus, 2015). 

There are other ways to describe an alternative hypothesis. The alternative hypothesis above does not specify a direction of the effect, only that there will be a difference between the two groups. That type of prediction is called a two-tailed hypothesis. If a hypothesis specifies a certain direction — for example, that people who take a protein supplement will gain more muscle than people who don't — it is called a one-tailed hypothesis, according to William M. K. Trochim , a professor of Policy Analysis and Management at Cornell University.

Sometimes, errors take place during an experiment. These errors can happen in one of two ways. A type I error is when the null hypothesis is rejected when it is true. This is also known as a false positive. A type II error occurs when the null hypothesis is not rejected when it is false. This is also known as a false negative, according to the University of California, Berkeley . 

A hypothesis can be rejected or modified, but it can never be proved correct 100% of the time. For example, a scientist can form a hypothesis stating that if a certain type of tomato has a gene for red pigment, that type of tomato will be red. During research, the scientist then finds that each tomato of this type is red. Though the findings confirm the hypothesis, there may be a tomato of that type somewhere in the world that isn't red. Thus, the hypothesis is true, but it may not be true 100% of the time.

Scientific theory vs. scientific hypothesis

The best hypotheses are simple. They deal with a relatively narrow set of phenomena. But theories are broader; they generally combine multiple hypotheses into a general explanation for a wide range of phenomena, according to the University of California, Berkeley . For example, a hypothesis might state, "If animals adapt to suit their environments, then birds that live on islands with lots of seeds to eat will have differently shaped beaks than birds that live on islands with lots of insects to eat." After testing many hypotheses like these, Charles Darwin formulated an overarching theory: the theory of evolution by natural selection.

"Theories are the ways that we make sense of what we observe in the natural world," Tanner said. "Theories are structures of ideas that explain and interpret facts." 

• Read more about writing a hypothesis, from the American Medical Writers Association.
• Find out why a hypothesis isn't always necessary in science, from The American Biology Teacher.
• Learn about null and alternative hypotheses, from Prof. Essa on YouTube .

Encyclopedia Britannica. Scientific Hypothesis. Jan. 13, 2022. https://www.britannica.com/science/scientific-hypothesis

Karl Popper, "The Logic of Scientific Discovery," Routledge, 1959.

California State University, Bakersfield, "Formatting a testable hypothesis." https://www.csub.edu/~ddodenhoff/Bio100/Bio100sp04/formattingahypothesis.htm  

Karl Popper, "Conjectures and Refutations," Routledge, 1963.

Price, P., Jhangiani, R., & Chiang, I., "Research Methods of Psychology — 2nd Canadian Edition," BCcampus, 2015.‌

University of Miami, "The Scientific Method" http://www.bio.miami.edu/dana/161/evolution/161app1_scimethod.pdf  

William M.K. Trochim, "Research Methods Knowledge Base," https://conjointly.com/kb/hypotheses-explained/  

University of California, Berkeley, "Multiple Hypothesis Testing and False Discovery Rate" https://www.stat.berkeley.edu/~hhuang/STAT141/Lecture-FDR.pdf  

University of California, Berkeley, "Science at multiple levels" https://undsci.berkeley.edu/article/0_0_0/howscienceworks_19

Sign up for the Live Science daily newsletter now

Get the world’s most fascinating discoveries delivered straight to your inbox.

100-foot 'walking tree' in New Zealand looks like an Ent from Lord of the Rings — and is the lone survivor of a lost forest

Earth from space: Shapeshifting rusty river winds through Madagascar's 'red lands'

'Increased evidence that we should be alert': H5N1 bird flu is adapting to mammals in 'new ways'

scientific method

Our editors will review what you’ve submitted and determine whether to revise the article.

• University of Nevada, Reno - College of Agriculture, Biotechnology and Natural Resources Extension - The Scientific Method
• World History Encyclopedia - Scientific Method
• LiveScience - What Is Science?
• Verywell Mind - Scientific Method Steps in Psychology Research
• WebMD - What is the Scientific Method?
• Chemistry LibreTexts - The Scientific Method
• Khan Academy - The scientific method
• Simply Psychology - What are the steps in the Scientific Method?
• Stanford Encyclopedia of Philosophy - Scientific Method

scientific method , mathematical and experimental technique employed in the sciences . More specifically, it is the technique used in the construction and testing of a scientific hypothesis .

The process of observing, asking questions, and seeking answers through tests and experiments is not unique to any one field of science. In fact, the scientific method is applied broadly in science, across many different fields. Many empirical sciences, especially the social sciences , use mathematical tools borrowed from probability theory and statistics , together with outgrowths of these, such as decision theory , game theory , utility theory, and operations research . Philosophers of science have addressed general methodological problems, such as the nature of scientific explanation and the justification of induction .

The scientific method is critical to the development of scientific theories , which explain empirical (experiential) laws in a scientifically rational manner. In a typical application of the scientific method, a researcher develops a hypothesis , tests it through various means, and then modifies the hypothesis on the basis of the outcome of the tests and experiments. The modified hypothesis is then retested, further modified, and tested again, until it becomes consistent with observed phenomena and testing outcomes. In this way, hypotheses serve as tools by which scientists gather data. From that data and the many different scientific investigations undertaken to explore hypotheses, scientists are able to develop broad general explanations, or scientific theories.

See also Mill’s methods ; hypothetico-deductive method .

• Bipolar Disorder
• Therapy Center
• When To See a Therapist
• Types of Therapy
• Best Online Therapy
• Best Couples Therapy
• Best Family Therapy
• Managing Stress
• Sleep and Dreaming
• Understanding Emotions
• Self-Improvement
• Healthy Relationships
• Student Resources
• Personality Types
• Guided Meditations
• Verywell Mind Insights
• 2024 Verywell Mind 25
• Mental Health in the Classroom
• Editorial Process
• Meet Our Review Board
• Crisis Support

How to Write a Great Hypothesis

Hypothesis Definition, Format, Examples, and Tips

Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Amy Morin, LCSW, is a psychotherapist and international bestselling author. Her books, including "13 Things Mentally Strong People Don't Do," have been translated into more than 40 languages. Her TEDx talk,  "The Secret of Becoming Mentally Strong," is one of the most viewed talks of all time.

Verywell / Alex Dos Diaz

• The Scientific Method

Hypothesis Format

Falsifiability of a hypothesis.

• Operationalization

Hypothesis Types

Hypotheses examples.

• Collecting Data

A hypothesis is a tentative statement about the relationship between two or more variables. It is a specific, testable prediction about what you expect to happen in a study. It is a preliminary answer to your question that helps guide the research process.

Consider a study designed to examine the relationship between sleep deprivation and test performance. The hypothesis might be: "This study is designed to assess the hypothesis that sleep-deprived people will perform worse on a test than individuals who are not sleep-deprived."

At a Glance

A hypothesis is crucial to scientific research because it offers a clear direction for what the researchers are looking to find. This allows them to design experiments to test their predictions and add to our scientific knowledge about the world. This article explores how a hypothesis is used in psychology research, how to write a good hypothesis, and the different types of hypotheses you might use.

The Hypothesis in the Scientific Method

In the scientific method , whether it involves research in psychology, biology, or some other area, a hypothesis represents what the researchers think will happen in an experiment. The scientific method involves the following steps:

• Forming a question
• Performing background research
• Creating a hypothesis
• Designing an experiment
• Collecting data
• Analyzing the results
• Drawing conclusions
• Communicating the results

The hypothesis is a prediction, but it involves more than a guess. Most of the time, the hypothesis begins with a question which is then explored through background research. At this point, researchers then begin to develop a testable hypothesis.

Unless you are creating an exploratory study, your hypothesis should always explain what you  expect  to happen.

In a study exploring the effects of a particular drug, the hypothesis might be that researchers expect the drug to have some type of effect on the symptoms of a specific illness. In psychology, the hypothesis might focus on how a certain aspect of the environment might influence a particular behavior.

Remember, a hypothesis does not have to be correct. While the hypothesis predicts what the researchers expect to see, the goal of the research is to determine whether this guess is right or wrong. When conducting an experiment, researchers might explore numerous factors to determine which ones might contribute to the ultimate outcome.

In many cases, researchers may find that the results of an experiment  do not  support the original hypothesis. When writing up these results, the researchers might suggest other options that should be explored in future studies.

In many cases, researchers might draw a hypothesis from a specific theory or build on previous research. For example, prior research has shown that stress can impact the immune system. So a researcher might hypothesize: "People with high-stress levels will be more likely to contract a common cold after being exposed to the virus than people who have low-stress levels."

In other instances, researchers might look at commonly held beliefs or folk wisdom. "Birds of a feather flock together" is one example of folk adage that a psychologist might try to investigate. The researcher might pose a specific hypothesis that "People tend to select romantic partners who are similar to them in interests and educational level."

Elements of a Good Hypothesis

So how do you write a good hypothesis? When trying to come up with a hypothesis for your research or experiments, ask yourself the following questions:

• Is your hypothesis based on your research on a topic?
• Can your hypothesis be tested?
• Does your hypothesis include independent and dependent variables?

Before you come up with a specific hypothesis, spend some time doing background research. Once you have completed a literature review, start thinking about potential questions you still have. Pay attention to the discussion section in the  journal articles you read . Many authors will suggest questions that still need to be explored.

How to Formulate a Good Hypothesis

To form a hypothesis, you should take these steps:

• Collect as many observations about a topic or problem as you can.
• Evaluate these observations and look for possible causes of the problem.
• Create a list of possible explanations that you might want to explore.
• After you have developed some possible hypotheses, think of ways that you could confirm or disprove each hypothesis through experimentation. This is known as falsifiability.

In the scientific method ,  falsifiability is an important part of any valid hypothesis. In order to test a claim scientifically, it must be possible that the claim could be proven false.

Students sometimes confuse the idea of falsifiability with the idea that it means that something is false, which is not the case. What falsifiability means is that  if  something was false, then it is possible to demonstrate that it is false.

One of the hallmarks of pseudoscience is that it makes claims that cannot be refuted or proven false.

The Importance of Operational Definitions

A variable is a factor or element that can be changed and manipulated in ways that are observable and measurable. However, the researcher must also define how the variable will be manipulated and measured in the study.

Operational definitions are specific definitions for all relevant factors in a study. This process helps make vague or ambiguous concepts detailed and measurable.

For example, a researcher might operationally define the variable " test anxiety " as the results of a self-report measure of anxiety experienced during an exam. A "study habits" variable might be defined by the amount of studying that actually occurs as measured by time.

These precise descriptions are important because many things can be measured in various ways. Clearly defining these variables and how they are measured helps ensure that other researchers can replicate your results.

Replicability

One of the basic principles of any type of scientific research is that the results must be replicable.

Replication means repeating an experiment in the same way to produce the same results. By clearly detailing the specifics of how the variables were measured and manipulated, other researchers can better understand the results and repeat the study if needed.

Some variables are more difficult than others to define. For example, how would you operationally define a variable such as aggression ? For obvious ethical reasons, researchers cannot create a situation in which a person behaves aggressively toward others.

To measure this variable, the researcher must devise a measurement that assesses aggressive behavior without harming others. The researcher might utilize a simulated task to measure aggressiveness in this situation.

Hypothesis Checklist

• Does your hypothesis focus on something that you can actually test?
• Does your hypothesis include both an independent and dependent variable?
• Can you manipulate the variables?
• Can your hypothesis be tested without violating ethical standards?

The hypothesis you use will depend on what you are investigating and hoping to find. Some of the main types of hypotheses that you might use include:

• Simple hypothesis : This type of hypothesis suggests there is a relationship between one independent variable and one dependent variable.
• Complex hypothesis : This type suggests a relationship between three or more variables, such as two independent and dependent variables.
• Null hypothesis : This hypothesis suggests no relationship exists between two or more variables.
• Alternative hypothesis : This hypothesis states the opposite of the null hypothesis.
• Statistical hypothesis : This hypothesis uses statistical analysis to evaluate a representative population sample and then generalizes the findings to the larger group.
• Logical hypothesis : This hypothesis assumes a relationship between variables without collecting data or evidence.

A hypothesis often follows a basic format of "If {this happens} then {this will happen}." One way to structure your hypothesis is to describe what will happen to the  dependent variable  if you change the  independent variable .

The basic format might be: "If {these changes are made to a certain independent variable}, then we will observe {a change in a specific dependent variable}."

A few examples of simple hypotheses:

• "Students who eat breakfast will perform better on a math exam than students who do not eat breakfast."
• "Students who experience test anxiety before an English exam will get lower scores than students who do not experience test anxiety."​
• "Motorists who talk on the phone while driving will be more likely to make errors on a driving course than those who do not talk on the phone."
• "Children who receive a new reading intervention will have higher reading scores than students who do not receive the intervention."

Examples of a complex hypothesis include:

• "People with high-sugar diets and sedentary activity levels are more likely to develop depression."
• "Younger people who are regularly exposed to green, outdoor areas have better subjective well-being than older adults who have limited exposure to green spaces."

Examples of a null hypothesis include:

• "There is no difference in anxiety levels between people who take St. John's wort supplements and those who do not."
• "There is no difference in scores on a memory recall task between children and adults."
• "There is no difference in aggression levels between children who play first-person shooter games and those who do not."

Examples of an alternative hypothesis:

• "People who take St. John's wort supplements will have less anxiety than those who do not."
• "Adults will perform better on a memory task than children."
• "Children who play first-person shooter games will show higher levels of aggression than children who do not." 

Collecting Data on Your Hypothesis

Once a researcher has formed a testable hypothesis, the next step is to select a research design and start collecting data. The research method depends largely on exactly what they are studying. There are two basic types of research methods: descriptive research and experimental research.

Descriptive Research Methods

Descriptive research such as  case studies ,  naturalistic observations , and surveys are often used when  conducting an experiment is difficult or impossible. These methods are best used to describe different aspects of a behavior or psychological phenomenon.

Once a researcher has collected data using descriptive methods, a  correlational study  can examine how the variables are related. This research method might be used to investigate a hypothesis that is difficult to test experimentally.

Experimental Research Methods

Experimental methods  are used to demonstrate causal relationships between variables. In an experiment, the researcher systematically manipulates a variable of interest (known as the independent variable) and measures the effect on another variable (known as the dependent variable).

Unlike correlational studies, which can only be used to determine if there is a relationship between two variables, experimental methods can be used to determine the actual nature of the relationship—whether changes in one variable actually  cause  another to change.

The hypothesis is a critical part of any scientific exploration. It represents what researchers expect to find in a study or experiment. In situations where the hypothesis is unsupported by the research, the research still has value. Such research helps us better understand how different aspects of the natural world relate to one another. It also helps us develop new hypotheses that can then be tested in the future.

Thompson WH, Skau S. On the scope of scientific hypotheses .  R Soc Open Sci . 2023;10(8):230607. doi:10.1098/rsos.230607

Taran S, Adhikari NKJ, Fan E. Falsifiability in medicine: what clinicians can learn from Karl Popper [published correction appears in Intensive Care Med. 2021 Jun 17;:].  Intensive Care Med . 2021;47(9):1054-1056. doi:10.1007/s00134-021-06432-z

Eyler AA. Research Methods for Public Health . 1st ed. Springer Publishing Company; 2020. doi:10.1891/9780826182067.0004

Nosek BA, Errington TM. What is replication ?  PLoS Biol . 2020;18(3):e3000691. doi:10.1371/journal.pbio.3000691

Aggarwal R, Ranganathan P. Study designs: Part 2 - Descriptive studies .  Perspect Clin Res . 2019;10(1):34-36. doi:10.4103/picr.PICR_154_18

Nevid J. Psychology: Concepts and Applications. Wadworth, 2013.

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

• Privacy Policy

Home » What is a Hypothesis – Types, Examples and Writing Guide

What is a Hypothesis – Types, Examples and Writing Guide

Table of Contents

Definition:

Hypothesis is an educated guess or proposed explanation for a phenomenon, based on some initial observations or data. It is a tentative statement that can be tested and potentially proven or disproven through further investigation and experimentation.

Hypothesis is often used in scientific research to guide the design of experiments and the collection and analysis of data. It is an essential element of the scientific method, as it allows researchers to make predictions about the outcome of their experiments and to test those predictions to determine their accuracy.

Types of Hypothesis

Types of Hypothesis are as follows:

Research Hypothesis

A research hypothesis is a statement that predicts a relationship between variables. It is usually formulated as a specific statement that can be tested through research, and it is often used in scientific research to guide the design of experiments.

Null Hypothesis

The null hypothesis is a statement that assumes there is no significant difference or relationship between variables. It is often used as a starting point for testing the research hypothesis, and if the results of the study reject the null hypothesis, it suggests that there is a significant difference or relationship between variables.

Alternative Hypothesis

An alternative hypothesis is a statement that assumes there is a significant difference or relationship between variables. It is often used as an alternative to the null hypothesis and is tested against the null hypothesis to determine which statement is more accurate.

Directional Hypothesis

A directional hypothesis is a statement that predicts the direction of the relationship between variables. For example, a researcher might predict that increasing the amount of exercise will result in a decrease in body weight.

Non-directional Hypothesis

A non-directional hypothesis is a statement that predicts the relationship between variables but does not specify the direction. For example, a researcher might predict that there is a relationship between the amount of exercise and body weight, but they do not specify whether increasing or decreasing exercise will affect body weight.

Statistical Hypothesis

A statistical hypothesis is a statement that assumes a particular statistical model or distribution for the data. It is often used in statistical analysis to test the significance of a particular result.

Composite Hypothesis

A composite hypothesis is a statement that assumes more than one condition or outcome. It can be divided into several sub-hypotheses, each of which represents a different possible outcome.

Empirical Hypothesis

An empirical hypothesis is a statement that is based on observed phenomena or data. It is often used in scientific research to develop theories or models that explain the observed phenomena.

Simple Hypothesis

A simple hypothesis is a statement that assumes only one outcome or condition. It is often used in scientific research to test a single variable or factor.

Complex Hypothesis

A complex hypothesis is a statement that assumes multiple outcomes or conditions. It is often used in scientific research to test the effects of multiple variables or factors on a particular outcome.

Applications of Hypothesis

Hypotheses are used in various fields to guide research and make predictions about the outcomes of experiments or observations. Here are some examples of how hypotheses are applied in different fields:

• Science : In scientific research, hypotheses are used to test the validity of theories and models that explain natural phenomena. For example, a hypothesis might be formulated to test the effects of a particular variable on a natural system, such as the effects of climate change on an ecosystem.
• Medicine : In medical research, hypotheses are used to test the effectiveness of treatments and therapies for specific conditions. For example, a hypothesis might be formulated to test the effects of a new drug on a particular disease.
• Psychology : In psychology, hypotheses are used to test theories and models of human behavior and cognition. For example, a hypothesis might be formulated to test the effects of a particular stimulus on the brain or behavior.
• Sociology : In sociology, hypotheses are used to test theories and models of social phenomena, such as the effects of social structures or institutions on human behavior. For example, a hypothesis might be formulated to test the effects of income inequality on crime rates.
• Business : In business research, hypotheses are used to test the validity of theories and models that explain business phenomena, such as consumer behavior or market trends. For example, a hypothesis might be formulated to test the effects of a new marketing campaign on consumer buying behavior.
• Engineering : In engineering, hypotheses are used to test the effectiveness of new technologies or designs. For example, a hypothesis might be formulated to test the efficiency of a new solar panel design.

How to write a Hypothesis

Here are the steps to follow when writing a hypothesis:

Identify the Research Question

The first step is to identify the research question that you want to answer through your study. This question should be clear, specific, and focused. It should be something that can be investigated empirically and that has some relevance or significance in the field.

Conduct a Literature Review

Before writing your hypothesis, it’s essential to conduct a thorough literature review to understand what is already known about the topic. This will help you to identify the research gap and formulate a hypothesis that builds on existing knowledge.

Determine the Variables

The next step is to identify the variables involved in the research question. A variable is any characteristic or factor that can vary or change. There are two types of variables: independent and dependent. The independent variable is the one that is manipulated or changed by the researcher, while the dependent variable is the one that is measured or observed as a result of the independent variable.

Formulate the Hypothesis

Based on the research question and the variables involved, you can now formulate your hypothesis. A hypothesis should be a clear and concise statement that predicts the relationship between the variables. It should be testable through empirical research and based on existing theory or evidence.

Write the Null Hypothesis

The null hypothesis is the opposite of the alternative hypothesis, which is the hypothesis that you are testing. The null hypothesis states that there is no significant difference or relationship between the variables. It is important to write the null hypothesis because it allows you to compare your results with what would be expected by chance.

Refine the Hypothesis

After formulating the hypothesis, it’s important to refine it and make it more precise. This may involve clarifying the variables, specifying the direction of the relationship, or making the hypothesis more testable.

Examples of Hypothesis

Here are a few examples of hypotheses in different fields:

• Psychology : “Increased exposure to violent video games leads to increased aggressive behavior in adolescents.”
• Biology : “Higher levels of carbon dioxide in the atmosphere will lead to increased plant growth.”
• Sociology : “Individuals who grow up in households with higher socioeconomic status will have higher levels of education and income as adults.”
• Education : “Implementing a new teaching method will result in higher student achievement scores.”
• Marketing : “Customers who receive a personalized email will be more likely to make a purchase than those who receive a generic email.”
• Physics : “An increase in temperature will cause an increase in the volume of a gas, assuming all other variables remain constant.”
• Medicine : “Consuming a diet high in saturated fats will increase the risk of developing heart disease.”

Purpose of Hypothesis

The purpose of a hypothesis is to provide a testable explanation for an observed phenomenon or a prediction of a future outcome based on existing knowledge or theories. A hypothesis is an essential part of the scientific method and helps to guide the research process by providing a clear focus for investigation. It enables scientists to design experiments or studies to gather evidence and data that can support or refute the proposed explanation or prediction.

The formulation of a hypothesis is based on existing knowledge, observations, and theories, and it should be specific, testable, and falsifiable. A specific hypothesis helps to define the research question, which is important in the research process as it guides the selection of an appropriate research design and methodology. Testability of the hypothesis means that it can be proven or disproven through empirical data collection and analysis. Falsifiability means that the hypothesis should be formulated in such a way that it can be proven wrong if it is incorrect.

In addition to guiding the research process, the testing of hypotheses can lead to new discoveries and advancements in scientific knowledge. When a hypothesis is supported by the data, it can be used to develop new theories or models to explain the observed phenomenon. When a hypothesis is not supported by the data, it can help to refine existing theories or prompt the development of new hypotheses to explain the phenomenon.

When to use Hypothesis

Here are some common situations in which hypotheses are used:

• In scientific research , hypotheses are used to guide the design of experiments and to help researchers make predictions about the outcomes of those experiments.
• In social science research , hypotheses are used to test theories about human behavior, social relationships, and other phenomena.
• I n business , hypotheses can be used to guide decisions about marketing, product development, and other areas. For example, a hypothesis might be that a new product will sell well in a particular market, and this hypothesis can be tested through market research.

Characteristics of Hypothesis

Here are some common characteristics of a hypothesis:

• Testable : A hypothesis must be able to be tested through observation or experimentation. This means that it must be possible to collect data that will either support or refute the hypothesis.
• Falsifiable : A hypothesis must be able to be proven false if it is not supported by the data. If a hypothesis cannot be falsified, then it is not a scientific hypothesis.
• Clear and concise : A hypothesis should be stated in a clear and concise manner so that it can be easily understood and tested.
• Based on existing knowledge : A hypothesis should be based on existing knowledge and research in the field. It should not be based on personal beliefs or opinions.
• Specific : A hypothesis should be specific in terms of the variables being tested and the predicted outcome. This will help to ensure that the research is focused and well-designed.
• Tentative: A hypothesis is a tentative statement or assumption that requires further testing and evidence to be confirmed or refuted. It is not a final conclusion or assertion.
• Relevant : A hypothesis should be relevant to the research question or problem being studied. It should address a gap in knowledge or provide a new perspective on the issue.

Advantages of Hypothesis

Hypotheses have several advantages in scientific research and experimentation:

• Guides research: A hypothesis provides a clear and specific direction for research. It helps to focus the research question, select appropriate methods and variables, and interpret the results.
• Predictive powe r: A hypothesis makes predictions about the outcome of research, which can be tested through experimentation. This allows researchers to evaluate the validity of the hypothesis and make new discoveries.
• Facilitates communication: A hypothesis provides a common language and framework for scientists to communicate with one another about their research. This helps to facilitate the exchange of ideas and promotes collaboration.
• Efficient use of resources: A hypothesis helps researchers to use their time, resources, and funding efficiently by directing them towards specific research questions and methods that are most likely to yield results.
• Provides a basis for further research: A hypothesis that is supported by data provides a basis for further research and exploration. It can lead to new hypotheses, theories, and discoveries.
• Increases objectivity: A hypothesis can help to increase objectivity in research by providing a clear and specific framework for testing and interpreting results. This can reduce bias and increase the reliability of research findings.

Limitations of Hypothesis

Some Limitations of the Hypothesis are as follows:

• Limited to observable phenomena: Hypotheses are limited to observable phenomena and cannot account for unobservable or intangible factors. This means that some research questions may not be amenable to hypothesis testing.
• May be inaccurate or incomplete: Hypotheses are based on existing knowledge and research, which may be incomplete or inaccurate. This can lead to flawed hypotheses and erroneous conclusions.
• May be biased: Hypotheses may be biased by the researcher’s own beliefs, values, or assumptions. This can lead to selective interpretation of data and a lack of objectivity in research.
• Cannot prove causation: A hypothesis can only show a correlation between variables, but it cannot prove causation. This requires further experimentation and analysis.
• Limited to specific contexts: Hypotheses are limited to specific contexts and may not be generalizable to other situations or populations. This means that results may not be applicable in other contexts or may require further testing.
• May be affected by chance : Hypotheses may be affected by chance or random variation, which can obscure or distort the true relationship between variables.

About the author

Muhammad Hassan

Researcher, Academic Writer, Web developer

You may also like

Problem Statement – Writing Guide, Examples and...

Thesis Format – Templates and Samples

Background of The Study – Examples and Writing...

Table of Contents – Types, Formats, Examples

Research Problem – Examples, Types and Guide

Context of the Study – Writing Guide and Examples

• school Campus Bookshelves
• menu_book Bookshelves
• perm_media Learning Objects
• login Login
• how_to_reg Request Instructor Account
• hub Instructor Commons

Margin Size

• Download Page (PDF)
• Download Full Book (PDF)
• Periodic Table
• Physics Constants
• Scientific Calculator
• Reference & Cite
• Tools expand_more
• Readability

selected template will load here

This action is not available.

4.14: Experiments and Hypotheses

• Last updated
• Save as PDF
• Page ID 43806

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)

( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)

\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)

\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

\( \newcommand{\Span}{\mathrm{span}}\)

\( \newcommand{\id}{\mathrm{id}}\)

\( \newcommand{\kernel}{\mathrm{null}\,}\)

\( \newcommand{\range}{\mathrm{range}\,}\)

\( \newcommand{\RealPart}{\mathrm{Re}}\)

\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

\( \newcommand{\Argument}{\mathrm{Arg}}\)

\( \newcommand{\norm}[1]{\| #1 \|}\)

\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)

\( \newcommand{\vectorA}[1]{\vec{#1}}      % arrow\)

\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}}      % arrow\)

\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

\( \newcommand{\vectorC}[1]{\textbf{#1}} \)

\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)

\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)

\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)

Now we’ll focus on the methods of scientific inquiry. Science often involves making observations and developing hypotheses. Experiments and further observations are often used to test the hypotheses.

A scientific experiment is a carefully organized procedure in which the scientist intervenes in a system to change something, then observes the result of the change. Scientific inquiry often involves doing experiments, though not always. For example, a scientist studying the mating behaviors of ladybugs might begin with detailed observations of ladybugs mating in their natural habitats. While this research may not be experimental, it is scientific: it involves careful and verifiable observation of the natural world. The same scientist might then treat some of the ladybugs with a hormone hypothesized to trigger mating and observe whether these ladybugs mated sooner or more often than untreated ones. This would qualify as an experiment because the scientist is now making a change in the system and observing the effects.

Forming a Hypothesis

When conducting scientific experiments, researchers develop hypotheses to guide experimental design. A hypothesis is a suggested explanation that is both testable and falsifiable. You must be able to test your hypothesis, and it must be possible to prove your hypothesis true or false.

For example, Michael observes that maple trees lose their leaves in the fall. He might then propose a possible explanation for this observation: “cold weather causes maple trees to lose their leaves in the fall.” This statement is testable. He could grow maple trees in a warm enclosed environment such as a greenhouse and see if their leaves still dropped in the fall. The hypothesis is also falsifiable. If the leaves still dropped in the warm environment, then clearly temperature was not the main factor in causing maple leaves to drop in autumn.

In the Try It below, you can practice recognizing scientific hypotheses. As you consider each statement, try to think as a scientist would: can I test this hypothesis with observations or experiments? Is the statement falsifiable? If the answer to either of these questions is “no,” the statement is not a valid scientific hypothesis.

Practice Questions

Determine whether each following statement is a scientific hypothesis.

• No. This statement is not testable or falsifiable.
• No. This statement is not testable.
• No. This statement is not falsifiable.
• Yes. This statement is testable and falsifiable.

[reveal-answer q=”429550″] Show Answers [/reveal-answer] [hidden-answer a=”429550″]

• d: Yes. This statement is testable and falsifiable. This could be tested with a number of different kinds of observations and experiments, and it is possible to gather evidence that indicates that air pollution is not linked with asthma.
• a: No. This statement is not testable or falsifiable. “Bad thoughts and behaviors” are excessively vague and subjective variables that would be impossible to measure or agree upon in a reliable way. The statement might be “falsifiable” if you came up with a counterexample: a “wicked” place that was not punished by a natural disaster. But some would question whether the people in that place were really wicked, and others would continue to predict that a natural disaster was bound to strike that place at some point. There is no reason to suspect that people’s immoral behavior affects the weather unless you bring up the intervention of a supernatural being, making this idea even harder to test.

[/hidden-answer]

Testing a Vaccine

Let’s examine the scientific process by discussing an actual scientific experiment conducted by researchers at the University of Washington. These researchers investigated whether a vaccine may reduce the incidence of the human papillomavirus (HPV). The experimental process and results were published in an article titled, “ A controlled trial of a human papillomavirus type 16 vaccine .”

Preliminary observations made by the researchers who conducted the HPV experiment are listed below:

• Human papillomavirus (HPV) is the most common sexually transmitted virus in the United States.
• There are about 40 different types of HPV. A significant number of people that have HPV are unaware of it because many of these viruses cause no symptoms.
• Some types of HPV can cause cervical cancer.
• About 4,000 women a year die of cervical cancer in the United States.

Practice Question

Researchers have developed a potential vaccine against HPV and want to test it. What is the first testable hypothesis that the researchers should study?

• HPV causes cervical cancer.
• People should not have unprotected sex with many partners.
• People who get the vaccine will not get HPV.
• The HPV vaccine will protect people against cancer.

[reveal-answer q=”20917″] Show Answer [/reveal-answer] [hidden-answer a=”20917″]Hypothesis A is not the best choice because this information is already known from previous studies. Hypothesis B is not testable because scientific hypotheses are not value statements; they do not include judgments like “should,” “better than,” etc. Scientific evidence certainly might support this value judgment, but a hypothesis would take a different form: “Having unprotected sex with many partners increases a person’s risk for cervical cancer.” Before the researchers can test if the vaccine protects against cancer (hypothesis D), they want to test if it protects against the virus. This statement will make an excellent hypothesis for the next study. The researchers should first test hypothesis C—whether or not the new vaccine can prevent HPV.[/hidden-answer]

Experimental Design

You’ve successfully identified a hypothesis for the University of Washington’s study on HPV: People who get the HPV vaccine will not get HPV.

The next step is to design an experiment that will test this hypothesis. There are several important factors to consider when designing a scientific experiment. First, scientific experiments must have an experimental group. This is the group that receives the experimental treatment necessary to address the hypothesis.

The experimental group receives the vaccine, but how can we know if the vaccine made a difference? Many things may change HPV infection rates in a group of people over time. To clearly show that the vaccine was effective in helping the experimental group, we need to include in our study an otherwise similar control group that does not get the treatment. We can then compare the two groups and determine if the vaccine made a difference. The control group shows us what happens in the absence of the factor under study.

However, the control group cannot get “nothing.” Instead, the control group often receives a placebo. A placebo is a procedure that has no expected therapeutic effect—such as giving a person a sugar pill or a shot containing only plain saline solution with no drug. Scientific studies have shown that the “placebo effect” can alter experimental results because when individuals are told that they are or are not being treated, this knowledge can alter their actions or their emotions, which can then alter the results of the experiment.

Moreover, if the doctor knows which group a patient is in, this can also influence the results of the experiment. Without saying so directly, the doctor may show—through body language or other subtle cues—his or her views about whether the patient is likely to get well. These errors can then alter the patient’s experience and change the results of the experiment. Therefore, many clinical studies are “double blind.” In these studies, neither the doctor nor the patient knows which group the patient is in until all experimental results have been collected.

Both placebo treatments and double-blind procedures are designed to prevent bias. Bias is any systematic error that makes a particular experimental outcome more or less likely. Errors can happen in any experiment: people make mistakes in measurement, instruments fail, computer glitches can alter data. But most such errors are random and don’t favor one outcome over another. Patients’ belief in a treatment can make it more likely to appear to “work.” Placebos and double-blind procedures are used to level the playing field so that both groups of study subjects are treated equally and share similar beliefs about their treatment.

The scientists who are researching the effectiveness of the HPV vaccine will test their hypothesis by separating 2,392 young women into two groups: the control group and the experimental group. Answer the following questions about these two groups.

• This group is given a placebo.
• This group is deliberately infected with HPV.
• This group is given nothing.
• This group is given the HPV vaccine.

[reveal-answer q=”918962″] Show Answers [/reveal-answer] [hidden-answer a=”918962″]

• a: This group is given a placebo. A placebo will be a shot, just like the HPV vaccine, but it will have no active ingredient. It may change peoples’ thinking or behavior to have such a shot given to them, but it will not stimulate the immune systems of the subjects in the same way as predicted for the vaccine itself.
• d: This group is given the HPV vaccine. The experimental group will receive the HPV vaccine and researchers will then be able to see if it works, when compared to the control group.

Experimental Variables

A variable is a characteristic of a subject (in this case, of a person in the study) that can vary over time or among individuals. Sometimes a variable takes the form of a category, such as male or female; often a variable can be measured precisely, such as body height. Ideally, only one variable is different between the control group and the experimental group in a scientific experiment. Otherwise, the researchers will not be able to determine which variable caused any differences seen in the results. For example, imagine that the people in the control group were, on average, much more sexually active than the people in the experimental group. If, at the end of the experiment, the control group had a higher rate of HPV infection, could you confidently determine why? Maybe the experimental subjects were protected by the vaccine, but maybe they were protected by their low level of sexual contact.

To avoid this situation, experimenters make sure that their subject groups are as similar as possible in all variables except for the variable that is being tested in the experiment. This variable, or factor, will be deliberately changed in the experimental group. The one variable that is different between the two groups is called the independent variable. An independent variable is known or hypothesized to cause some outcome. Imagine an educational researcher investigating the effectiveness of a new teaching strategy in a classroom. The experimental group receives the new teaching strategy, while the control group receives the traditional strategy. It is the teaching strategy that is the independent variable in this scenario. In an experiment, the independent variable is the variable that the scientist deliberately changes or imposes on the subjects.

Dependent variables are known or hypothesized consequences; they are the effects that result from changes or differences in an independent variable. In an experiment, the dependent variables are those that the scientist measures before, during, and particularly at the end of the experiment to see if they have changed as expected. The dependent variable must be stated so that it is clear how it will be observed or measured. Rather than comparing “learning” among students (which is a vague and difficult to measure concept), an educational researcher might choose to compare test scores, which are very specific and easy to measure.

In any real-world example, many, many variables MIGHT affect the outcome of an experiment, yet only one or a few independent variables can be tested. Other variables must be kept as similar as possible between the study groups and are called control variables . For our educational research example, if the control group consisted only of people between the ages of 18 and 20 and the experimental group contained people between the ages of 30 and 35, we would not know if it was the teaching strategy or the students’ ages that played a larger role in the results. To avoid this problem, a good study will be set up so that each group contains students with a similar age profile. In a well-designed educational research study, student age will be a controlled variable, along with other possibly important factors like gender, past educational achievement, and pre-existing knowledge of the subject area.

What is the independent variable in this experiment?

• Sex (all of the subjects will be female)
• Presence or absence of the HPV vaccine
• Presence or absence of HPV (the virus)

[reveal-answer q=”68680″]Show Answer[/reveal-answer] [hidden-answer a=”68680″]Answer b. Presence or absence of the HPV vaccine. This is the variable that is different between the control and the experimental groups. All the subjects in this study are female, so this variable is the same in all groups. In a well-designed study, the two groups will be of similar age. The presence or absence of the virus is what the researchers will measure at the end of the experiment. Ideally the two groups will both be HPV-free at the start of the experiment.

List three control variables other than age.

[practice-area rows=”3″][/practice-area] [reveal-answer q=”903121″]Show Answer[/reveal-answer] [hidden-answer a=”903121″]Some possible control variables would be: general health of the women, sexual activity, lifestyle, diet, socioeconomic status, etc.

What is the dependent variable in this experiment?

• Sex (male or female)
• Rates of HPV infection
• Age (years)

[reveal-answer q=”907103″]Show Answer[/reveal-answer] [hidden-answer a=”907103″]Answer b. Rates of HPV infection. The researchers will measure how many individuals got infected with HPV after a given period of time.[/hidden-answer]

Contributors and Attributions

• Revision and adaptation. Authored by : Shelli Carter and Lumen Learning. Provided by : Lumen Learning. License : CC BY-NC-SA: Attribution-NonCommercial-ShareAlike
• Scientific Inquiry. Provided by : Open Learning Initiative. Located at : https://oli.cmu.edu/jcourse/workbook/activity/page?context=434a5c2680020ca6017c03488572e0f8 . Project : Introduction to Biology (Open + Free). License : CC BY-NC-SA: Attribution-NonCommercial-ShareAlike

• school Campus Bookshelves
• menu_book Bookshelves
• perm_media Learning Objects
• login Login
• how_to_reg Request Instructor Account
• hub Instructor Commons

Margin Size

• Download Page (PDF)
• Download Full Book (PDF)
• Periodic Table
• Physics Constants
• Scientific Calculator
• Reference & Cite
• Tools expand_more
• Readability

selected template will load here

This action is not available.

1.1.6: Scientific Problem Solving

• Last updated
• Save as PDF
• Page ID 419240

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)

( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)

\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)

\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

\( \newcommand{\Span}{\mathrm{span}}\)

\( \newcommand{\id}{\mathrm{id}}\)

\( \newcommand{\kernel}{\mathrm{null}\,}\)

\( \newcommand{\range}{\mathrm{range}\,}\)

\( \newcommand{\RealPart}{\mathrm{Re}}\)

\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

\( \newcommand{\Argument}{\mathrm{Arg}}\)

\( \newcommand{\norm}[1]{\| #1 \|}\)

\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)

\( \newcommand{\vectorA}[1]{\vec{#1}}      % arrow\)

\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}}      % arrow\)

\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

\( \newcommand{\vectorC}[1]{\textbf{#1}} \)

\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)

\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)

\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)

How can we use problem solving in our everyday routines?

One day you wake up and realize your clock radio did not turn on to get you out of bed. You are puzzled, so you decide to find out what happened. You list three possible explanations:

• There was a power failure and your radio cannot turn on.
• Your little sister turned it off as a joke.
• You did not set the alarm last night.

Upon investigation, you find that the clock is on, so there is no power failure. Your little sister was spending the night with a friend and could not have turned the alarm off. You notice that the alarm is not set—your forgetfulness made you late. You have used the scientific method to answer a question.

Scientific Problem Solving

Humans have always wondered about the world around them. One of the questions of interest was (and still is): what is this world made of? Chemistry has been defined in various ways as the study of matter. What matter consists of has been a source of debate over the centuries. One of the key areas for this debate in the Western world was Greek philosophy.

The basic approach of the Greek philosophers was to discuss and debate the questions they had about the world. There was no gathering of information to speak of, just talking. As a result, several ideas about matter were put forth, but never resolved. The first philosopher to carry out the gathering of data was Aristotle (384-322 B.C.). He recorded many observations on the weather, on plant and animal life and behavior, on physical motions, and a number of other topics. Aristotle could probably be considered the first "real" scientist, because he made systematic observations of nature and tried to understand what he was seeing.

Inductive and Deductive Reasoning

Two approaches to logical thinking developed over the centuries. These two methods are inductive reasoning and deductive reasoning . Inductive reasoning involves getting a collection of specific examples and drawing a general conclusion from them. Deductive reasoning takes a general principle and then draws a specific conclusion from the general concept. Both are used in the development of scientific ideas.

Inductive reasoning first involves the collection of data: "If I add sodium metal to water, I observe a very violent reaction. Every time I repeat the process, I see the same thing happen." A general conclusion is drawn from these observations: the addition of sodium to water results in a violent reaction.

In deductive reasoning, a specific prediction is made based on a general principle. One general principle is that acids turn blue litmus paper red. Using the deductive reasoning process, one might predict: "If I have a bottle of liquid labeled 'acid', I expect the litmus paper to turn red when I immerse it in the liquid."

The Idea of the Experiment

Inductive reasoning is at the heart of what is now called the " scientific method ." In European culture, this approach was developed mainly by Francis Bacon (1561-1626), a British scholar. He advocated the use of inductive reasoning in every area of life, not just science. The scientific method, as developed by Bacon and others, involves several steps:

• Ask a question - identify the problem to be considered.
• Make observations - gather data that pertains to the question.
• Propose an explanation (a hypothesis) for the observations.
• Make new observations to test the hypothesis further.

Note that this should not be considered a "cookbook" for scientific research. Scientists do not sit down with their daily "to do" list and write down these steps. The steps may not necessarily be followed in order. But this does provide a general idea of how scientific research is usually done.

When a hypothesis is confirmed repeatedly, it eventually becomes a theory—a general principle that is offered to explain natural phenomena. Note a key word— explain , or  explanation . A theory offers a description of why something happens. A law, on the other hand, is a statement that is always true, but offers no explanation as to why. The law of gravity says a rock will fall when dropped, but does not explain why (gravitational theory is very complex and incomplete at present). The kinetic molecular theory of gases, on the other hand, states what happens when a gas is heated in a closed container (the pressure increases), but also explains why (the motions of the gas molecules are increased due to the change in temperature). Theories do not get "promoted" to laws, because laws do not answer the "why" question.

• The early Greek philosophers spent their time talking about nature, but did little or no actual exploration or investigation.
• Inductive reasoning - to develop a general conclusion from a collection of observations.
• Deductive reasoning - to make a specific statement based on a general principle.
• Scientific method - a process of observation, developing a hypothesis, and testing that hypothesis.
• What was the basic shortcoming of the Greek philosophers approach to studying the material world?
• How did Aristotle improve the approach?
• Define “inductive reasoning” and give an example.
• Define “deductive reasoning” and give an example.
• What is the difference between a hypothesis and a theory?
• What is the difference between a theory and a law?

Theories, Hypotheses, and Laws: Definitions, examples, and their roles in science

by Anthony Carpi, Ph.D., Anne E. Egger, Ph.D.

Listen to this reading

Did you know that the idea of evolution had been part of Western thought for more than 2,000 years before Charles Darwin was born? Like many theories, the theory of evolution was the result of the work of many different scientists working in different disciplines over a period of time.

A scientific theory is an explanation inferred from multiple lines of evidence for some broad aspect of the natural world and is logical, testable, and predictive.

As new evidence comes to light, or new interpretations of existing data are proposed, theories may be revised and even change; however, they are not tenuous or speculative.

A scientific hypothesis is an inferred explanation of an observation or research finding; while more exploratory in nature than a theory, it is based on existing scientific knowledge.

A scientific law is an expression of a mathematical or descriptive relationship observed in nature.

Imagine yourself shopping in a grocery store with a good friend who happens to be a chemist. Struggling to choose between the many different types of tomatoes in front of you, you pick one up, turn to your friend, and ask her if she thinks the tomato is organic . Your friend simply chuckles and replies, "Of course it's organic!" without even looking at how the fruit was grown. Why the amused reaction? Your friend is highlighting a simple difference in vocabulary. To a chemist, the term organic refers to any compound in which hydrogen is bonded to carbon. Tomatoes (like all plants) are abundant in organic compounds – thus your friend's laughter. In modern agriculture, however, organic has come to mean food items grown or raised without the use of chemical fertilizers, pesticides, or other additives.

So who is correct? You both are. Both uses of the word are correct, though they mean different things in different contexts. There are, of course, lots of words that have more than one meaning (like bat , for example), but multiple meanings can be especially confusing when two meanings convey very different ideas and are specific to one field of study.

• Scientific theories

The term theory also has two meanings, and this double meaning often leads to confusion. In common language, the term theory generally refers to speculation or a hunch or guess. You might have a theory about why your favorite sports team isn't playing well, or who ate the last cookie from the cookie jar. But these theories do not fit the scientific use of the term. In science, a theory is a well-substantiated and comprehensive set of ideas that explains a phenomenon in nature. A scientific theory is based on large amounts of data and observations that have been collected over time. Scientific theories can be tested and refined by additional research , and they allow scientists to make predictions. Though you may be correct in your hunch, your cookie jar conjecture doesn't fit this more rigorous definition.

All scientific disciplines have well-established, fundamental theories . For example, atomic theory describes the nature of matter and is supported by multiple lines of evidence from the way substances behave and react in the world around us (see our series on Atomic Theory ). Plate tectonic theory describes the large scale movement of the outer layer of the Earth and is supported by evidence from studies about earthquakes , magnetic properties of the rocks that make up the seafloor , and the distribution of volcanoes on Earth (see our series on Plate Tectonic Theory ). The theory of evolution by natural selection , which describes the mechanism by which inherited traits that affect survivability or reproductive success can cause changes in living organisms over generations , is supported by extensive studies of DNA , fossils , and other types of scientific evidence (see our Charles Darwin series for more information). Each of these major theories guides and informs modern research in those fields, integrating a broad, comprehensive set of ideas.

So how are these fundamental theories developed, and why are they considered so well supported? Let's take a closer look at some of the data and research supporting the theory of natural selection to better see how a theory develops.

Comprehension Checkpoint

• The development of a scientific theory: Evolution and natural selection

The theory of evolution by natural selection is sometimes maligned as Charles Darwin 's speculation on the origin of modern life forms. However, evolutionary theory is not speculation. While Darwin is rightly credited with first articulating the theory of natural selection, his ideas built on more than a century of scientific research that came before him, and are supported by over a century and a half of research since.

• The Fixity Notion: Linnaeus

Figure 1: Cover of the 1760 edition of Systema Naturae .

Research about the origins and diversity of life proliferated in the 18th and 19th centuries. Carolus Linnaeus , a Swedish botanist and the father of modern taxonomy (see our module Taxonomy I for more information), was a devout Christian who believed in the concept of Fixity of Species , an idea based on the biblical story of creation. The Fixity of Species concept said that each species is based on an ideal form that has not changed over time. In the early stages of his career, Linnaeus traveled extensively and collected data on the structural similarities and differences between different species of plants. Noting that some very different plants had similar structures, he began to piece together his landmark work, Systema Naturae, in 1735 (Figure 1). In Systema , Linnaeus classified organisms into related groups based on similarities in their physical features. He developed a hierarchical classification system , even drawing relationships between seemingly disparate species (for example, humans, orangutans, and chimpanzees) based on the physical similarities that he observed between these organisms. Linnaeus did not explicitly discuss change in organisms or propose a reason for his hierarchy, but by grouping organisms based on physical characteristics, he suggested that species are related, unintentionally challenging the Fixity notion that each species is created in a unique, ideal form.

• The age of Earth: Leclerc and Hutton

Also in the early 1700s, Georges-Louis Leclerc, a French naturalist, and James Hutton , a Scottish geologist, began to develop new ideas about the age of the Earth. At the time, many people thought of the Earth as 6,000 years old, based on a strict interpretation of the events detailed in the Christian Old Testament by the influential Scottish Archbishop Ussher. By observing other planets and comets in the solar system , Leclerc hypothesized that Earth began as a hot, fiery ball of molten rock, mostly consisting of iron. Using the cooling rate of iron, Leclerc calculated that Earth must therefore be at least 70,000 years old in order to have reached its present temperature.

Hutton approached the same topic from a different perspective, gathering observations of the relationships between different rock formations and the rates of modern geological processes near his home in Scotland. He recognized that the relatively slow processes of erosion and sedimentation could not create all of the exposed rock layers in only a few thousand years (see our module The Rock Cycle ). Based on his extensive collection of data (just one of his many publications ran to 2,138 pages), Hutton suggested that the Earth was far older than human history – hundreds of millions of years old.

While we now know that both Leclerc and Hutton significantly underestimated the age of the Earth (by about 4 billion years), their work shattered long-held beliefs and opened a window into research on how life can change over these very long timescales.

• Fossil studies lead to the development of a theory of evolution: Cuvier

Figure 2: Illustration of an Indian elephant jaw and a mammoth jaw from Cuvier's 1796 paper.

With the age of Earth now extended by Leclerc and Hutton, more researchers began to turn their attention to studying past life. Fossils are the main way to study past life forms, and several key studies on fossils helped in the development of a theory of evolution . In 1795, Georges Cuvier began to work at the National Museum in Paris as a naturalist and anatomist. Through his work, Cuvier became interested in fossils found near Paris, which some claimed were the remains of the elephants that Hannibal rode over the Alps when he invaded Rome in 218 BCE . In studying both the fossils and living species , Cuvier documented different patterns in the dental structure and number of teeth between the fossils and modern elephants (Figure 2) (Horner, 1843). Based on these data , Cuvier hypothesized that the fossil remains were not left by Hannibal, but were from a distinct species of animal that once roamed through Europe and had gone extinct thousands of years earlier: the mammoth. The concept of species extinction had been discussed by a few individuals before Cuvier, but it was in direct opposition to the Fixity of Species concept – if every organism were based on a perfectly adapted, ideal form, how could any cease to exist? That would suggest it was no longer ideal.

While his work provided critical evidence of extinction , a key component of evolution , Cuvier was highly critical of the idea that species could change over time. As a result of his extensive studies of animal anatomy, Cuvier had developed a holistic view of organisms , stating that the

number, direction, and shape of the bones that compose each part of an animal's body are always in a necessary relation to all the other parts, in such a way that ... one can infer the whole from any one of them ...

In other words, Cuvier viewed each part of an organism as a unique, essential component of the whole organism. If one part were to change, he believed, the organism could not survive. His skepticism about the ability of organisms to change led him to criticize the whole idea of evolution , and his prominence in France as a scientist played a large role in discouraging the acceptance of the idea in the scientific community.

• Studies of invertebrates support a theory of change in species: Lamarck

Jean Baptiste Lamarck, a contemporary of Cuvier's at the National Museum in Paris, studied invertebrates like insects and worms. As Lamarck worked through the museum's large collection of invertebrates, he was impressed by the number and variety of organisms . He became convinced that organisms could, in fact, change through time, stating that

... time and favorable conditions are the two principal means which nature has employed in giving existence to all her productions. We know that for her time has no limit, and that consequently she always has it at her disposal.

This was a radical departure from both the fixity concept and Cuvier's ideas, and it built on the long timescale that geologists had recently established. Lamarck proposed that changes that occurred during an organism 's lifetime could be passed on to their offspring, suggesting, for example, that a body builder's muscles would be inherited by their children.

As it turned out, the mechanism by which Lamarck proposed that organisms change over time was wrong, and he is now often referred to disparagingly for his "inheritance of acquired characteristics" idea. Yet despite the fact that some of his ideas were discredited, Lamarck established a support for evolutionary theory that others would build on and improve.

• Rock layers as evidence for evolution: Smith

In the early 1800s, a British geologist and canal surveyor named William Smith added another component to the accumulating evidence for evolution . Smith observed that rock layers exposed in different parts of England bore similarities to one another: These layers (or strata) were arranged in a predictable order, and each layer contained distinct groups of fossils . From this series of observations , he developed a hypothesis that specific groups of animals followed one another in a definite sequence through Earth's history, and this sequence could be seen in the rock layers. Smith's hypothesis was based on his knowledge of geological principles , including the Law of Superposition.

The Law of Superposition states that sediments are deposited in a time sequence, with the oldest sediments deposited first, or at the bottom, and newer layers deposited on top. The concept was first expressed by the Persian scientist Avicenna in the 11th century, but was popularized by the Danish scientist Nicolas Steno in the 17th century. Note that the law does not state how sediments are deposited; it simply describes the relationship between the ages of deposited sediments.

Figure 3: Engraving from William Smith's 1815 monograph on identifying strata by fossils.

Smith backed up his hypothesis with extensive drawings of fossils uncovered during his research (Figure 3), thus allowing other scientists to confirm or dispute his findings. His hypothesis has, in fact, been confirmed by many other scientists and has come to be referred to as the Law of Faunal Succession. His work was critical to the formation of evolutionary theory as it not only confirmed Cuvier's work that organisms have gone extinct , but it also showed that the appearance of life does not date to the birth of the planet. Instead, the fossil record preserves a timeline of the appearance and disappearance of different organisms in the past, and in doing so offers evidence for change in organisms over time.

• The theory of evolution by natural selection: Darwin and Wallace

It was into this world that Charles Darwin entered: Linnaeus had developed a taxonomy of organisms based on their physical relationships, Leclerc and Hutton demonstrated that there was sufficient time in Earth's history for organisms to change, Cuvier showed that species of organisms have gone extinct , Lamarck proposed that organisms change over time, and Smith established a timeline of the appearance and disappearance of different organisms in the geological record .

Figure 4: Title page of the 1859 Murray edition of the Origin of Species by Charles Darwin.

Charles Darwin collected data during his work as a naturalist on the HMS Beagle starting in 1831. He took extensive notes on the geology of the places he visited; he made a major find of fossils of extinct animals in Patagonia and identified an extinct giant ground sloth named Megatherium . He experienced an earthquake in Chile that stranded beds of living mussels above water, where they would be preserved for years to come.

Perhaps most famously, he conducted extensive studies of animals on the Galápagos Islands, noting subtle differences in species of mockingbird, tortoise, and finch that were isolated on different islands with different environmental conditions. These subtle differences made the animals highly adapted to their environments .

This broad spectrum of data led Darwin to propose an idea about how organisms change "by means of natural selection" (Figure 4). But this idea was not based only on his work, it was also based on the accumulation of evidence and ideas of many others before him. Because his proposal encompassed and explained many different lines of evidence and previous work, they formed the basis of a new and robust scientific theory regarding change in organisms – the theory of evolution by natural selection .

Darwin's ideas were grounded in evidence and data so compelling that if he had not conceived them, someone else would have. In fact, someone else did. Between 1858 and 1859, Alfred Russel Wallace , a British naturalist, wrote a series of letters to Darwin that independently proposed natural selection as the means for evolutionary change. The letters were presented to the Linnean Society of London, a prominent scientific society at the time (see our module on Scientific Institutions and Societies ). This long chain of research highlights that theories are not just the work of one individual. At the same time, however, it often takes the insight and creativity of individuals to put together all of the pieces and propose a new theory . Both Darwin and Wallace were experienced naturalists who were familiar with the work of others. While all of the work leading up to 1830 contributed to the theory of evolution , Darwin's and Wallace's theory changed the way that future research was focused by presenting a comprehensive, well-substantiated set of ideas, thus becoming a fundamental theory of biological research.

• Expanding, testing, and refining scientific theories
• Genetics and evolution: Mendel and Dobzhansky

Since Darwin and Wallace first published their ideas, extensive research has tested and expanded the theory of evolution by natural selection . Darwin had no concept of genes or DNA or the mechanism by which characteristics were inherited within a species . A contemporary of Darwin's, the Austrian monk Gregor Mendel , first presented his own landmark study, Experiments in Plant Hybridization, in 1865 in which he provided the basic patterns of genetic inheritance , describing which characteristics (and evolutionary changes) can be passed on in organisms (see our Genetics I module for more information). Still, it wasn't until much later that a "gene" was defined as the heritable unit.

In 1937, the Ukrainian born geneticist Theodosius Dobzhansky published Genetics and the Origin of Species , a seminal work in which he described genes themselves and demonstrated that it is through mutations in genes that change occurs. The work defined evolution as "a change in the frequency of an allele within a gene pool" ( Dobzhansky, 1982 ). These studies and others in the field of genetics have added to Darwin's work, expanding the scope of the theory .

• Evolution under a microscope: Lenski

More recently, Dr. Richard Lenski, a scientist at Michigan State University, isolated a single Escherichia coli bacterium in 1989 as the first step of the longest running experimental test of evolutionary theory to date – a true test meant to replicate evolution and natural selection in the lab.

After the single microbe had multiplied, Lenski isolated the offspring into 12 different strains , each in their own glucose-supplied culture, predicting that the genetic make-up of each strain would change over time to become more adapted to their specific culture as predicted by evolutionary theory . These 12 lines have been nurtured for over 40,000 bacterial generations (luckily bacterial generations are much shorter than human generations) and exposed to different selective pressures such as heat , cold, antibiotics, and infection with other microorganisms. Lenski and colleagues have studied dozens of aspects of evolutionary theory with these genetically isolated populations . In 1999, they published a paper that demonstrated that random genetic mutations were common within the populations and highly diverse across different individual bacteria . However, "pivotal" mutations that are associated with beneficial changes in the group are shared by all descendants in a population and are much rarer than random mutations, as predicted by the theory of evolution by natural selection (Papadopoulos et al., 1999).

• Punctuated equilibrium: Gould and Eldredge

While established scientific theories like evolution have a wealth of research and evidence supporting them, this does not mean that they cannot be refined as new information or new perspectives on existing data become available. For example, in 1972, biologist Stephen Jay Gould and paleontologist Niles Eldredge took a fresh look at the existing data regarding the timing by which evolutionary change takes place. Gould and Eldredge did not set out to challenge the theory of evolution; rather they used it as a guiding principle and asked more specific questions to add detail and nuance to the theory. This is true of all theories in science: they provide a framework for additional research. At the time, many biologists viewed evolution as occurring gradually, causing small incremental changes in organisms at a relatively steady rate. The idea is referred to as phyletic gradualism , and is rooted in the geological concept of uniformitarianism . After reexamining the available data, Gould and Eldredge came to a different explanation, suggesting that evolution consists of long periods of stability that are punctuated by occasional instances of dramatic change – a process they called punctuated equilibrium .

Like Darwin before them, their proposal is rooted in evidence and research on evolutionary change, and has been supported by multiple lines of evidence. In fact, punctuated equilibrium is now considered its own theory in evolutionary biology. Punctuated equilibrium is not as broad of a theory as natural selection . In science, some theories are broad and overarching of many concepts, such as the theory of evolution by natural selection; others focus on concepts at a smaller, or more targeted, scale such as punctuated equilibrium. And punctuated equilibrium does not challenge or weaken the concept of natural selection; rather, it represents a change in our understanding of the timing by which change occurs in organisms , and a theory within a theory. The theory of evolution by natural selection now includes both gradualism and punctuated equilibrium to describe the rate at which change proceeds.

• Hypotheses and laws: Other scientific concepts

One of the challenges in understanding scientific terms like theory is that there is not a precise definition even within the scientific community. Some scientists debate over whether certain proposals merit designation as a hypothesis or theory , and others mistakenly use the terms interchangeably. But there are differences in these terms. A hypothesis is a proposed explanation for an observable phenomenon. Hypotheses , just like theories , are based on observations from research . For example, LeClerc did not hypothesize that Earth had cooled from a molten ball of iron as a random guess; rather, he developed this hypothesis based on his observations of information from meteorites.

A scientist often proposes a hypothesis before research confirms it as a way of predicting the outcome of study to help better define the parameters of the research. LeClerc's hypothesis allowed him to use known parameters (the cooling rate of iron) to do additional work. A key component of a formal scientific hypothesis is that it is testable and falsifiable. For example, when Richard Lenski first isolated his 12 strains of bacteria , he likely hypothesized that random mutations would cause differences to appear within a period of time in the different strains of bacteria. But when a hypothesis is generated in science, a scientist will also make an alternative hypothesis , an explanation that explains a study if the data do not support the original hypothesis. If the different strains of bacteria in Lenski's work did not diverge over the indicated period of time, perhaps the rate of mutation was slower than first thought.

So you might ask, if theories are so well supported, do they eventually become laws? The answer is no – not because they aren't well-supported, but because theories and laws are two very different things. Laws describe phenomena, often mathematically. Theories, however, explain phenomena. For example, in 1687 Isaac Newton proposed a Theory of Gravitation, describing gravity as a force of attraction between two objects. As part of this theory, Newton developed a Law of Universal Gravitation that explains how this force operates. This law states that the force of gravity between two objects is inversely proportional to the square of the distance between those objects. Newton 's Law does not explain why this is true, but it describes how gravity functions (see our Gravity: Newtonian Relationships module for more detail). In 1916, Albert Einstein developed his theory of general relativity to explain the mechanism by which gravity has its effect. Einstein's work challenges Newton's theory, and has been found after extensive testing and research to more accurately describe the phenomenon of gravity. While Einstein's work has replaced Newton's as the dominant explanation of gravity in modern science, Newton's Law of Universal Gravitation is still used as it reasonably (and more simply) describes the force of gravity under many conditions. Similarly, the Law of Faunal Succession developed by William Smith does not explain why organisms follow each other in distinct, predictable ways in the rock layers, but it accurately describes the phenomenon.

Theories, hypotheses , and laws drive scientific progress

Theories, hypotheses , and laws are not simply important components of science, they drive scientific progress. For example, evolutionary biology now stands as a distinct field of science that focuses on the origins and descent of species . Geologists now rely on plate tectonics as a conceptual model and guiding theory when they are studying processes at work in Earth's crust . And physicists refer to atomic theory when they are predicting the existence of subatomic particles yet to be discovered. This does not mean that science is "finished," or that all of the important theories have been discovered already. Like evolution , progress in science happens both gradually and in short, dramatic bursts. Both types of progress are critical for creating a robust knowledge base with data as the foundation and scientific theories giving structure to that knowledge.

Table of Contents

• Theories, hypotheses, and laws drive scientific progress

Activate glossary term highlighting to easily identify key terms within the module. Once highlighted, you can click on these terms to view their definitions.

Activate NGSS annotations to easily identify NGSS standards within the module. Once highlighted, you can click on them to view these standards.

If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

Mechanics (Essentials) - Class 11th

Course: mechanics (essentials) - class 11th   >   unit 2.

• Introduction to physics
• What is physics?

The scientific method

• Models and Approximations in Physics

Introduction

• Make an observation.
• Ask a question.
• Form a hypothesis , or testable explanation.
• Make a prediction based on the hypothesis.
• Test the prediction.
• Iterate: use the results to make new hypotheses or predictions.

Scientific method example: Failure to toast

1. make an observation., 2. ask a question., 3. propose a hypothesis., 4. make predictions., 5. test the predictions..

• If the toaster does toast, then the hypothesis is supported—likely correct.
• If the toaster doesn't toast, then the hypothesis is not supported—likely wrong.

Logical possibility

Practical possibility, building a body of evidence, 6. iterate..

• If the hypothesis was supported, we might do additional tests to confirm it, or revise it to be more specific. For instance, we might investigate why the outlet is broken.
• If the hypothesis was not supported, we would come up with a new hypothesis. For instance, the next hypothesis might be that there's a broken wire in the toaster.

Want to join the conversation?

• Skip to primary navigation
• Skip to main content
• Skip to primary sidebar
• Skip to footer

Understanding Science

How science REALLY works...

• Understanding Science 101
• Misconceptions
• Testing ideas with evidence from the natural world is at the core of science.
• Scientific testing involves figuring out what we would  expect  to observe if an idea were correct and comparing that expectation to what we  actually  observe.
• Scientific arguments are built from an idea and the evidence relevant to that idea.
• Scientific arguments can be built in any order. Sometimes a scientific idea precedes any evidence relevant to it, and other times the evidence helps inspire the idea.

Misconception:  Science proves ideas.

Misconception:  Science can only disprove ideas.

Correction:  Science neither proves nor disproves. It accepts or rejects ideas based on supporting and refuting evidence, but may revise those conclusions if warranted by new evidence or perspectives.  Read more about it.

The core of science: Relating evidence and ideas

In this case, the term  argument  refers not to a disagreement between two people, but to an evidence-based line of reasoning — so scientific arguments are more like the closing argument in a court case (a logical description of what we think and why we think it) than they are like the fights you may have had with siblings. Scientific arguments involve three components: the idea (a  hypothesis  or theory), the  expectations  generated by that idea (frequently called predictions), and the actual observations relevant to those expectations (the evidence). These components are always related in the same logical way:

• What would we expect to see if this idea were true (i.e., what is our expected observation)?
• What do we actually observe?
• Do our expectations match our observations?

PREDICTIONS OR EXPECTATIONS?

When scientists describe their arguments, they frequently talk about their expectations in terms of what a hypothesis or theory predicts: “If it were the case that smoking causes lung cancer, then we’d  predict  that countries with higher rates of smoking would have higher rates of lung cancer.” At first, it might seem confusing to talk about a prediction that doesn’t deal with the future, but that refers to something going on right now or that may have already happened. In fact, this is just another way of discussing the expectations that the hypothesis or theory generates. So when a scientist talks about the  predicted  rates of lung cancer, he or she really means something like “the rates that we’d expect to see if our hypothesis were correct.”

If the idea generates expectations that hold true (are actually observed), then the idea is more likely to be accurate. If the idea generates expectations that don’t hold true (are not observed), then we are less likely to  accept  the idea. For example, consider the idea that cells are the building blocks of life. If that idea were true, we’d expect to see cells in all kinds of living tissues observed under a microscope — that’s our expected observation. In fact, we do observe this (our actual observation), so evidence supports the idea that living things are built from cells.

Though the structure of this argument is consistent (hypothesis, then expectation, then actual observation), its pieces may be assembled in different orders. For example, the first observations of cells were made in the 1600s, but cell theory was not postulated until 200 years later — so in this case, the evidence actually helped inspire the idea. Whether the idea comes first or the evidence comes first, the logic relating them remains the same.

Here, we’ll explore scientific arguments and how to build them. You can investigate:

Putting the pieces together: The hard work of building arguments

• Predicting the past
• Arguments with legs to stand on

Or just click the  Next  button to dive right in!

• Take a sidetrip
• Teaching resources

Scientific arguments rely on testable ideas. To learn what makes an idea testable, review our  Science Checklist .

• Forming hypotheses — scientific explanations — can be difficult for students. It is often easier for students to generate an expectation (what they think will happen or what they expect to observe) based on prior experience than to formulate a potential explanation for that phenomena. You can help students go beyond expectations to generate real, explanatory hypotheses by providing sentence stems for them to fill in: “I expect to observe A because B.” Once students have filled in this sentence you can explain that B is a hypothesis and A is the expectation generated by that hypothesis.
• You can help students learn to distinguish between hypotheses and the expectations generated by them by regularly asking students to analyze lecture material, text, or video. Students should try to figure out which aspects of the content were hypotheses and which were expectations.

Summing up the process

Subscribe to our newsletter

• The science flowchart
• Science stories
• Grade-level teaching guides
• Teaching resource database
• Journaling tool

Get Your ALL ACCESS Shop Pass here →

Scientific Method For Kids With Examples

Kids have questions about the world around them every day, and there is so much to learn through experimentation with simple materials. You can begin using the scientific method with elementary kids. Below we’ll share with you how and when to introduce the scientific method, the steps of the scientific method, and some easy scientific method experiments. There are so many great ways to enjoy science projects with kids!

What Is The Scientific Method?

The scientific method is a process or method of research. A problem is identified, information about the problem is gathered, a hypothesis or question is formulated from the information, and the hypothesis is put to the test with an experiment to prove or disprove its validity.

Sounds heavy… What in the world does that mean?!? It means you don’t need to try and solve the world’s biggest science questions! The scientific method is all about studying and learning things right around you.

As children develop practices that involve creating, gathering data evaluating, analyzing, and communicating, they can apply these critical thinking skills to any situation.

Note: The use of the best Science and Engineering Practices is also relevant to the topic of using the scientific method. Read more here and see if it fits your science planning needs.

Can Young Kids Use the Scientific Method?

Kids are great scientists at any age, and can use the scientific method in context to what they are learning. It can be adapted for any age!

The scientific method is a valuable tool for introducing kids to a logical way to solve scientific problems. Scientists use the scientific method to study, learn, and come up with an answer!

The scientific method is a process that helps double-check that answers are correct and the correct results are obtained through careful planning. Sometimes the guesses and questions change as you run your experiments.

Kids can use the scientific method too on questions that are relevant to them!

Let’s break the scientific method for kids down into six parts, and you can quickly see how each can be incorporated into your next science experiment.

What Are The Steps In The Scientific Method?

• Make initial observations.
• Come up with a question of interest that is based on the observations.
• Develop a hypothesis or prediction to go along with the question.
• Experiment and test.
• Gather and record results of tests and experiments and draw conclusions.
• Share and discuss results.

Whoa… Wait A  Minute! That sounds like a lot for a young kid!

You are correct. Depending on your kid’s abilities, following all the scientific method steps precisely will not go well. Someone will get frustrated, bored, and turned off by just how cool science can be. We do not want that to happen!

Using The Scientific Method For Preschool and Kindergarten

Use the scientific method steps as a guideline in the back of your mind. You can cover most of the steps by talking with your kids about…

• What do they think will happen?
• What is happening ?
• What happened compared to what they thought would happen ?

No writing is required! It’s also best to pick pretty straightforward ideas that aren’t overly involved or complicated to set up and test. Kids always have burning questions and “what ifs.”

See if you can tackle their next “what if” using the scientific method by listening carefully to their conversations. You can even have them keep a journal with their “what if” questions for your next science time.

Learn more about Science Activities For Preschoolers and Kindergarten Science Experiments .

Now on to how to apply the scientific method for elementary kiddos and beyond.

Scientific Method Steps In Action

Learn more about the steps of the scientific method below, which are great for science at home with your kids or in the classroom! We have also included some simple scientific method experiments for you to enjoy.

Ice Science Experiments are perfect for this! Try these 3 today !

STEP 1: Make Observations

Tons of everyday activities would make for cool science experiments using the scientific method. Listen to what your kids talk about and see happening. My son noticed that ice melted pretty fast in his water.

Observation is simply noticing what’s happening through our senses or with tools like a magnifying glass. Observation is used to collect and record data, enabling scientists to construct and test hypotheses and theories.

Learn more about observations in science.

STEP 2: Come Up With A Question 

Your kids’ observations should lead to some sort of question. For my son and his ice observations, he came up with questions. Does ice melt faster in different liquids? His curiosity about what happens to the ice in liquids is a simple science experiment perfect for using the scientific method.

Next! Do some research and come up with ideas!

STEP 3: Develop A Prediction or Hypothesis

You have made your observations, you have your question, and now you need to make a prediction about what you think will happen.

A prediction is a guess at what might happen in an experiment based on observation or other information.

A hypothesis is not simply a guess! It’s a statement of what you believe will happen based on the information you have gathered.

My son hypothesizes that ice will melt faster in juice than in water.

STEP 4: Conduct An Experiment

We made a prediction that ice will melt faster in juice than it will in water, and now we have to test our hypothesis. We set up an experiment with a glass of juice, a glass of water, and an ice cube for each.

For the best experiments, only one thing should change! All the things that can be changed in a science experiment are called variables. There are three types of variables; independent, dependent, and controlled.

The independent variable is the one that is changed in the experiment and will affect the dependent variable. Here we will use different types of liquids to melt our ice cube in.

The dependent variable is the factor that is observed or measured in the experiment. This will be the melting of the ice cubes. Set up a stopwatch or set a time limit to observe the changes!

The controlled variable stays constant in the experiment. The liquids should be roughly the same temperature (as close as possible) for our ice melting experiment and measured to the same amount. So we left them out to come to room temperature. They could also be tested right out of the fridge!

You can find simple science experiments here with dependent and controlled variables.

STEP 5: Record Results and Draw Conclusions

Make sure to record what is happening as well as the results—note changes at specific time intervals or after one set time interval.

For example…

• Record when each ice cube is completely melted.
• Add drawings if you wish of the setup up and the end results.
• Was your prediction accurate? If it was inaccurate, record why.
• Write out a final conclusion to your experiment.

STEP 6: Communicate Your Results

This is the opportunity to talk about your hypothesis, experiment, results, and conclusion!

ALTERNATIVE IDEAS: Switch out an ice cube for a lollipop or change the liquids using vinegar and cooking oil.

Now you have gone through the steps of the scientific method, read on for more fun scientific method experiments to try!

Free printable scientific method worksheets!

Fun Scientific Method Experiments

Sink or float experiment.

A Sink or Float experiment is great for practicing the steps of the scientific method with younger kids.

Grab this FREE printable sink or float experiment

Here are a few of our favorite scientific method experiments, which are great for elementary-age kids . Of course, you can find tons more awesome and doable science projects for kids here!

Magic Milk Experiment

Start with demonstrating this delightful magic milk experiment. Then get kids to apply the steps of the scientific method by coming up with a question to investigate. What happens when you change the type of milk used?

What Dissolves In Water

Investigate  what solids dissolve in water  and what do not. Here’s a super fun science experiment for kids that’s very easy to set up! Learn about solutions, solutes, and solvents through experimenting with water and common kitchen ingredients.

Apple Browning Experiment

Investigate how to keep apples from turning brown with this apple oxidation experiment . What can you add to cut apples to stop or slow the oxidation process?

Freezing Water Experiment

Will it freeze? What happens to the freezing point of water when you add salt?

Viscosity Experiment

Learn about the viscosity of fluids with a simple  viscosity experiment . Grab some marbles and add them to different household liquids to find out which one will fall to the bottom first. 

Seed Germination Experiment

Set up a simple seed germination experiment .

Catapult Experiment

Make a simple popsicle stick catapult and use one of our experiment ideas to investigate from rubber band tension to changes in launch angle and more. How far can you fling your objects? Take measurements and find out.

Floating Orange

Investigate whether an orange floats or sinks in water, and what happens if you use different types of oranges. Learn about buoyancy and density with a simple ingredient from the kitchen, an orange.

Bread Mold Experiment

Grow mold on bread for science, and investigate how factors such as moisture, temperature, and air affect mold growth. 

Eggshell Strength Experiment

Test how strong an egg is with this eggshell strength experiment . Grab some eggs, and find out how much weight an egg can support.

Free Printable Science Fair Starter Guide

Are you looking to plan a science fair project, make a science fair board, or want an easy guide to set up science experiments?

Learn more about prepping for a science fair and grab this free printable science fair project pack here!

If you want a variety of science fair experiments with instructions, make sure to pick up a copy of our Science Project Pack in the shop.

Bonus STEM Projects For Kids

STEM activities include science, technology, engineering, and mathematics. As well as our kids science experiments, we have lots of fun STEM activities for you to try. Check out these STEM ideas below…

• Building Activities
• Engineering Projects For Kids
• What Is Engineering For Kids?
• LEGO Engineering Projects
• Coding Activities For Kids
• STEM Worksheets
• Top 10 STEM Challenges For Kids

Printable Science Projects Pack

If you’re looking to grab all of our printable science projects in one convenient place plus exclusive worksheets and bonuses like a STEAM Project pack, our Science Project Pack is what you need! Over 300+ Pages!

• 90+ classic science activities  with journal pages, supply lists, set up and process, and science information.  NEW! Activity-specific observation pages!
• Best science practices posters  and our original science method process folders for extra alternatives!
• Be a Collector activities pack  introduces kids to the world of making collections through the eyes of a scientist. What will they collect first?
• Know the Words Science vocabulary pack  includes flashcards, crosswords, and word searches that illuminate keywords in the experiments!
• My science journal writing prompts  explore what it means to be a scientist!!
• Bonus STEAM Project Pack:  Art meets science with doable projects!
• Bonus Quick Grab Packs for Biology, Earth Science, Chemistry, and Physics

19 Comments

A great post and sure to help extend children’s thinking! I would like to download the 6 steps but the blue download button doesn’t seem to be working for me.

Thank you! All fixed. You should be able to download now!

• Pingback: Popsicle Stick Catapult Ideas for Kids STEM Activity
• Pingback: Magical Dancing Corn Thanksgiving Science Experiment
• Pingback: Shadow Science Physics Activity With Animal Puppets (FREE Printable)
• Pingback: Books to inspire your young scientists! – Mom Read It
• Pingback: Seed Jar Science Experiment for Spring STEM Activities with Kids
• Pingback: Magic Milk Classic Science Experiment Kids Science
• Pingback: Earth Day Science Activity and Homemade Liquid Density Lava Lamp
• Pingback: Dissolving Candy Hearts Science Experiment for Valentine's Day
• Pingback: Seashells With Vinegar Ocean Experiment | Little Bins for Little Hands
• Pingback: DIY Snow Globe For Kids | Little Bins for Little Hands
• Pingback: Science Project Ideas with Usable Tips From a Teacher!
• Pingback: Drops Of Water On A Penny | Little Bins for Little Hands
• Pingback: The BEST Very Simple Science Experiments for Kids to Try Anywhere

it is so great, thanks a lot.

This helped for a science project.Thanks so much.

Comments are closed.

Subscribe to receive a free 5-Day STEM Challenge Guide

~ projects to try now ~.

What is The Null Hypothesis & When Do You Reject The Null Hypothesis

Julia Simkus

Editor at Simply Psychology

BA (Hons) Psychology, Princeton University

Julia Simkus is a graduate of Princeton University with a Bachelor of Arts in Psychology. She is currently studying for a Master's Degree in Counseling for Mental Health and Wellness in September 2023. Julia's research has been published in peer reviewed journals.

Learn about our Editorial Process

Saul Mcleod, PhD

Editor-in-Chief for Simply Psychology

BSc (Hons) Psychology, MRes, PhD, University of Manchester

Saul Mcleod, PhD., is a qualified psychology teacher with over 18 years of experience in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.

Olivia Guy-Evans, MSc

Associate Editor for Simply Psychology

BSc (Hons) Psychology, MSc Psychology of Education

Olivia Guy-Evans is a writer and associate editor for Simply Psychology. She has previously worked in healthcare and educational sectors.

On This Page:

A null hypothesis is a statistical concept suggesting no significant difference or relationship between measured variables. It’s the default assumption unless empirical evidence proves otherwise.

The null hypothesis states no relationship exists between the two variables being studied (i.e., one variable does not affect the other).

The null hypothesis is the statement that a researcher or an investigator wants to disprove.

Testing the null hypothesis can tell you whether your results are due to the effects of manipulating ​ the dependent variable or due to random chance. 

How to Write a Null Hypothesis

Null hypotheses (H0) start as research questions that the investigator rephrases as statements indicating no effect or relationship between the independent and dependent variables.

It is a default position that your research aims to challenge or confirm.

For example, if studying the impact of exercise on weight loss, your null hypothesis might be:

There is no significant difference in weight loss between individuals who exercise daily and those who do not.

Examples of Null Hypotheses

When Do We Reject The Null Hypothesis? 

We reject the null hypothesis when the data provide strong enough evidence to conclude that it is likely incorrect. This often occurs when the p-value (probability of observing the data given the null hypothesis is true) is below a predetermined significance level.

If the collected data does not meet the expectation of the null hypothesis, a researcher can conclude that the data lacks sufficient evidence to back up the null hypothesis, and thus the null hypothesis is rejected. 

Rejecting the null hypothesis means that a relationship does exist between a set of variables and the effect is statistically significant ( p > 0.05).

If the data collected from the random sample is not statistically significance , then the null hypothesis will be accepted, and the researchers can conclude that there is no relationship between the variables. 

You need to perform a statistical test on your data in order to evaluate how consistent it is with the null hypothesis. A p-value is one statistical measurement used to validate a hypothesis against observed data.

Calculating the p-value is a critical part of null-hypothesis significance testing because it quantifies how strongly the sample data contradicts the null hypothesis.

The level of statistical significance is often expressed as a  p  -value between 0 and 1. The smaller the p-value, the stronger the evidence that you should reject the null hypothesis.

Usually, a researcher uses a confidence level of 95% or 99% (p-value of 0.05 or 0.01) as general guidelines to decide if you should reject or keep the null.

When your p-value is less than or equal to your significance level, you reject the null hypothesis.

In other words, smaller p-values are taken as stronger evidence against the null hypothesis. Conversely, when the p-value is greater than your significance level, you fail to reject the null hypothesis.

In this case, the sample data provides insufficient data to conclude that the effect exists in the population.

Because you can never know with complete certainty whether there is an effect in the population, your inferences about a population will sometimes be incorrect.

When you incorrectly reject the null hypothesis, it’s called a type I error. When you incorrectly fail to reject it, it’s called a type II error.

Why Do We Never Accept The Null Hypothesis?

The reason we do not say “accept the null” is because we are always assuming the null hypothesis is true and then conducting a study to see if there is evidence against it. And, even if we don’t find evidence against it, a null hypothesis is not accepted.

A lack of evidence only means that you haven’t proven that something exists. It does not prove that something doesn’t exist. 

It is risky to conclude that the null hypothesis is true merely because we did not find evidence to reject it. It is always possible that researchers elsewhere have disproved the null hypothesis, so we cannot accept it as true, but instead, we state that we failed to reject the null. 

One can either reject the null hypothesis, or fail to reject it, but can never accept it.

Why Do We Use The Null Hypothesis?

We can never prove with 100% certainty that a hypothesis is true; We can only collect evidence that supports a theory. However, testing a hypothesis can set the stage for rejecting or accepting this hypothesis within a certain confidence level.

The null hypothesis is useful because it can tell us whether the results of our study are due to random chance or the manipulation of a variable (with a certain level of confidence).

A null hypothesis is rejected if the measured data is significantly unlikely to have occurred and a null hypothesis is accepted if the observed outcome is consistent with the position held by the null hypothesis.

Rejecting the null hypothesis sets the stage for further experimentation to see if a relationship between two variables exists. 

Hypothesis testing is a critical part of the scientific method as it helps decide whether the results of a research study support a particular theory about a given population. Hypothesis testing is a systematic way of backing up researchers’ predictions with statistical analysis.

It helps provide sufficient statistical evidence that either favors or rejects a certain hypothesis about the population parameter. 

Purpose of a Null Hypothesis 

• The primary purpose of the null hypothesis is to disprove an assumption. 
• Whether rejected or accepted, the null hypothesis can help further progress a theory in many scientific cases.
• A null hypothesis can be used to ascertain how consistent the outcomes of multiple studies are.

Do you always need both a Null Hypothesis and an Alternative Hypothesis?

The null (H0) and alternative (Ha or H1) hypotheses are two competing claims that describe the effect of the independent variable on the dependent variable. They are mutually exclusive, which means that only one of the two hypotheses can be true. 

While the null hypothesis states that there is no effect in the population, an alternative hypothesis states that there is statistical significance between two variables. 

The goal of hypothesis testing is to make inferences about a population based on a sample. In order to undertake hypothesis testing, you must express your research hypothesis as a null and alternative hypothesis. Both hypotheses are required to cover every possible outcome of the study. 

What is the difference between a null hypothesis and an alternative hypothesis?

The alternative hypothesis is the complement to the null hypothesis. The null hypothesis states that there is no effect or no relationship between variables, while the alternative hypothesis claims that there is an effect or relationship in the population.

It is the claim that you expect or hope will be true. The null hypothesis and the alternative hypothesis are always mutually exclusive, meaning that only one can be true at a time.

What are some problems with the null hypothesis?

One major problem with the null hypothesis is that researchers typically will assume that accepting the null is a failure of the experiment. However, accepting or rejecting any hypothesis is a positive result. Even if the null is not refuted, the researchers will still learn something new.

Why can a null hypothesis not be accepted?

We can either reject or fail to reject a null hypothesis, but never accept it. If your test fails to detect an effect, this is not proof that the effect doesn’t exist. It just means that your sample did not have enough evidence to conclude that it exists.

We can’t accept a null hypothesis because a lack of evidence does not prove something that does not exist. Instead, we fail to reject it.

Failing to reject the null indicates that the sample did not provide sufficient enough evidence to conclude that an effect exists.

If the p-value is greater than the significance level, then you fail to reject the null hypothesis.

Is a null hypothesis directional or non-directional?

A hypothesis test can either contain an alternative directional hypothesis or a non-directional alternative hypothesis. A directional hypothesis is one that contains the less than (“<“) or greater than (“>”) sign.

A nondirectional hypothesis contains the not equal sign (“≠”).  However, a null hypothesis is neither directional nor non-directional.

A null hypothesis is a prediction that there will be no change, relationship, or difference between two variables.

The directional hypothesis or nondirectional hypothesis would then be considered alternative hypotheses to the null hypothesis.

Gill, J. (1999). The insignificance of null hypothesis significance testing.  Political research quarterly ,  52 (3), 647-674.

Krueger, J. (2001). Null hypothesis significance testing: On the survival of a flawed method.  American Psychologist ,  56 (1), 16.

Masson, M. E. (2011). A tutorial on a practical Bayesian alternative to null-hypothesis significance testing.  Behavior research methods ,  43 , 679-690.

Nickerson, R. S. (2000). Null hypothesis significance testing: a review of an old and continuing controversy.  Psychological methods ,  5 (2), 241.

Rozeboom, W. W. (1960). The fallacy of the null-hypothesis significance test.  Psychological bulletin ,  57 (5), 416.

Related Articles

Research Methodology

Qualitative Data Coding

What Is a Focus Group?

Cross-Cultural Research Methodology In Psychology

What Is Internal Validity In Research?

Research Methodology , Statistics

What Is Face Validity In Research? Importance & How To Measure

Criterion Validity: Definition & Examples

10 Hard Math Problems That Continue to Stump Even the Brightest Minds

Maybe you’ll have better luck.

For now, you can take a crack at the hardest math problems known to man, woman, and machine. For more puzzles and brainteasers, check out Puzzmo . ✅ More from Popular Mechanics :

• To Create His Geometric Artwork, M.C. Escher Had to Learn Math the Hard Way
• Fourier Transforms: The Math That Made Color TV Possible
• The Game of Trees is a Mad Math Theory That Is Impossible to Prove

The Collatz Conjecture

In September 2019, news broke regarding progress on this 82-year-old question, thanks to prolific mathematician Terence Tao. And while the story of Tao’s breakthrough is promising, the problem isn’t fully solved yet.

A refresher on the Collatz Conjecture : It’s all about that function f(n), shown above, which takes even numbers and cuts them in half, while odd numbers get tripled and then added to 1. Take any natural number, apply f, then apply f again and again. You eventually land on 1, for every number we’ve ever checked. The Conjecture is that this is true for all natural numbers (positive integers from 1 through infinity).

✅ Down the Rabbit Hole: The Math That Helps the James Webb Space Telescope Sit Steady in Space

Tao’s recent work is a near-solution to the Collatz Conjecture in some subtle ways. But he most likely can’t adapt his methods to yield a complete solution to the problem, as Tao subsequently explained. So, we might be working on it for decades longer.

The Conjecture lives in the math discipline known as Dynamical Systems , or the study of situations that change over time in semi-predictable ways. It looks like a simple, innocuous question, but that’s what makes it special. Why is such a basic question so hard to answer? It serves as a benchmark for our understanding; once we solve it, then we can proceed onto much more complicated matters.

The study of dynamical systems could become more robust than anyone today could imagine. But we’ll need to solve the Collatz Conjecture for the subject to flourish.

Goldbach’s Conjecture

One of the greatest unsolved mysteries in math is also very easy to write. Goldbach’s Conjecture is, “Every even number (greater than two) is the sum of two primes.” You check this in your head for small numbers: 18 is 13+5, and 42 is 23+19. Computers have checked the Conjecture for numbers up to some magnitude. But we need proof for all natural numbers.

Goldbach’s Conjecture precipitated from letters in 1742 between German mathematician Christian Goldbach and legendary Swiss mathematician Leonhard Euler , considered one of the greatest in math history. As Euler put it, “I regard [it] as a completely certain theorem, although I cannot prove it.”

✅ Dive In: The Math Behind Our Current Theory of Human Color Perception Is Wrong

Euler may have sensed what makes this problem counterintuitively hard to solve. When you look at larger numbers, they have more ways of being written as sums of primes, not less. Like how 3+5 is the only way to break 8 into two primes, but 42 can broken into 5+37, 11+31, 13+29, and 19+23. So it feels like Goldbach’s Conjecture is an understatement for very large numbers.

Still, a proof of the conjecture for all numbers eludes mathematicians to this day. It stands as one of the oldest open questions in all of math.

The Twin Prime Conjecture

Together with Goldbach’s, the Twin Prime Conjecture is the most famous in Number Theory—or the study of natural numbers and their properties, frequently involving prime numbers. Since you've known these numbers since grade school, stating the conjectures is easy.

When two primes have a difference of 2, they’re called twin primes. So 11 and 13 are twin primes, as are 599 and 601. Now, it's a Day 1 Number Theory fact that there are infinitely many prime numbers. So, are there infinitely many twin primes? The Twin Prime Conjecture says yes.

Let’s go a bit deeper. The first in a pair of twin primes is, with one exception, always 1 less than a multiple of 6. And so the second twin prime is always 1 more than a multiple of 6. You can understand why, if you’re ready to follow a bit of heady Number Theory.

✅ Keep Learning: If We Draw Graphs Like This, We Can Change Computers Forever

All primes after 2 are odd. Even numbers are always 0, 2, or 4 more than a multiple of 6, while odd numbers are always 1, 3, or 5 more than a multiple of 6. Well, one of those three possibilities for odd numbers causes an issue. If a number is 3 more than a multiple of 6, then it has a factor of 3. Having a factor of 3 means a number isn’t prime (with the sole exception of 3 itself). And that's why every third odd number can't be prime.

How’s your head after that paragraph? Now imagine the headaches of everyone who has tried to solve this problem in the last 170 years.

The good news is that we’ve made some promising progress in the last decade. Mathematicians have managed to tackle closer and closer versions of the Twin Prime Conjecture. This was their idea: Trouble proving there are infinitely many primes with a difference of 2? How about proving there are infinitely many primes with a difference of 70,000,000? That was cleverly proven in 2013 by Yitang Zhang at the University of New Hampshire.

For the last six years, mathematicians have been improving that number in Zhang’s proof, from millions down to hundreds. Taking it down all the way to 2 will be the solution to the Twin Prime Conjecture. The closest we’ve come —given some subtle technical assumptions—is 6. Time will tell if the last step from 6 to 2 is right around the corner, or if that last part will challenge mathematicians for decades longer.

The Riemann Hypothesis

Today’s mathematicians would probably agree that the Riemann Hypothesis is the most significant open problem in all of math. It’s one of the seven Millennium Prize Problems , with $1 million reward for its solution. It has implications deep into various branches of math, but it’s also simple enough that we can explain the basic idea right here.

There is a function, called the Riemann zeta function, written in the image above.

For each s, this function gives an infinite sum, which takes some basic calculus to approach for even the simplest values of s. For example, if s=2, then 𝜁(s) is the well-known series 1 + 1/4 + 1/9 + 1/16 + …, which strangely adds up to exactly 𝜋²/6. When s is a complex number—one that looks like a+b𝑖, using the imaginary number 𝑖—finding 𝜁(s) gets tricky.

So tricky, in fact, that it’s become the ultimate math question. Specifically, the Riemann Hypothesis is about when 𝜁(s)=0; the official statement is, “Every nontrivial zero of the Riemann zeta function has real part 1/2.” On the plane of complex numbers, this means the function has a certain behavior along a special vertical line. The hypothesis is that the behavior continues along that line infinitely.

✅ Stay Curious: How to Paint a Room Using Math

The Hypothesis and the zeta function come from German mathematician Bernhard Riemann, who described them in 1859. Riemann developed them while studying prime numbers and their distribution. Our understanding of prime numbers has flourished in the 160 years since, and Riemann would never have imagined the power of supercomputers. But lacking a solution to the Riemann Hypothesis is a major setback.

If the Riemann Hypothesis were solved tomorrow, it would unlock an avalanche of further progress. It would be huge news throughout the subjects of Number Theory and Analysis. Until then, the Riemann Hypothesis remains one of the largest dams to the river of math research.

The Birch and Swinnerton-Dyer Conjecture

The Birch and Swinnerton-Dyer Conjecture is another of the six unsolved Millennium Prize Problems, and it’s the only other one we can remotely describe in plain English. This Conjecture involves the math topic known as Elliptic Curves.

When we recently wrote about the toughest math problems that have been solved , we mentioned one of the greatest achievements in 20th-century math: the solution to Fermat’s Last Theorem. Sir Andrew Wiles solved it using Elliptic Curves. So, you could call this a very powerful new branch of math.

✅ The Latest: Mathematicians Discovered Something Mind-Blowing About the Number 15

In a nutshell, an elliptic curve is a special kind of function. They take the unthreatening-looking form y²=x³+ax+b. It turns out functions like this have certain properties that cast insight into math topics like Algebra and Number Theory.

British mathematicians Bryan Birch and Peter Swinnerton-Dyer developed their conjecture in the 1960s. Its exact statement is very technical, and has evolved over the years. One of the main stewards of this evolution has been none other than Wiles. To see its current status and complexity, check out this famous update by Wells in 2006.

The Kissing Number Problem

A broad category of problems in math are called the Sphere Packing Problems. They range from pure math to practical applications, generally putting math terminology to the idea of stacking many spheres in a given space, like fruit at the grocery store. Some questions in this study have full solutions, while some simple ones leave us stumped, like the Kissing Number Problem.

When a bunch of spheres are packed in some region, each sphere has a Kissing Number, which is the number of other spheres it’s touching; if you’re touching 6 neighboring spheres, then your kissing number is 6. Nothing tricky. A packed bunch of spheres will have an average kissing number, which helps mathematically describe the situation. But a basic question about the kissing number stands unanswered.

✅ Miracles Happen: Mathematicians Finally Make a Breakthrough on the Ramsey Number

First, a note on dimensions. Dimensions have a specific meaning in math: they’re independent coordinate axes. The x-axis and y-axis show the two dimensions of a coordinate plane. When a character in a sci-fi show says they’re going to a different dimension, that doesn’t make mathematical sense. You can’t go to the x-axis.

A 1-dimensional thing is a line, and 2-dimensional thing is a plane. For these low numbers, mathematicians have proven the maximum possible kissing number for spheres of that many dimensions. It’s 2 when you’re on a 1-D line—one sphere to your left and the other to your right. There’s proof of an exact number for 3 dimensions, although that took until the 1950s.

Beyond 3 dimensions, the Kissing Problem is mostly unsolved. Mathematicians have slowly whittled the possibilities to fairly narrow ranges for up to 24 dimensions, with a few exactly known, as you can see on this chart . For larger numbers, or a general form, the problem is wide open. There are several hurdles to a full solution, including computational limitations. So expect incremental progress on this problem for years to come.

The Unknotting Problem

The simplest version of the Unknotting Problem has been solved, so there’s already some success with this story. Solving the full version of the problem will be an even bigger triumph.

You probably haven’t heard of the math subject Knot Theory . It ’s taught in virtually no high schools, and few colleges. The idea is to try and apply formal math ideas, like proofs, to knots, like … well, what you tie your shoes with.

For example, you might know how to tie a “square knot” and a “granny knot.” They have the same steps except that one twist is reversed from the square knot to the granny knot. But can you prove that those knots are different? Well, knot theorists can.

✅ Up Next: The Amazing Math Inside the Rubik’s Cube

Knot theorists’ holy grail problem was an algorithm to identify if some tangled mess is truly knotted, or if it can be disentangled to nothing. The cool news is that this has been accomplished! Several computer algorithms for this have been written in the last 20 years, and some of them even animate the process .

But the Unknotting Problem remains computational. In technical terms, it’s known that the Unknotting Problem is in NP, while we don ’ t know if it’s in P. That roughly means that we know our algorithms are capable of unknotting knots of any complexity, but that as they get more complicated, it starts to take an impossibly long time. For now.

If someone comes up with an algorithm that can unknot any knot in what’s called polynomial time, that will put the Unknotting Problem fully to rest. On the flip side, someone could prove that isn’t possible, and that the Unknotting Problem’s computational intensity is unavoidably profound. Eventually, we’ll find out.

The Large Cardinal Project

If you’ve never heard of Large Cardinals , get ready to learn. In the late 19th century, a German mathematician named Georg Cantor figured out that infinity comes in different sizes. Some infinite sets truly have more elements than others in a deep mathematical way, and Cantor proved it.

There is the first infinite size, the smallest infinity , which gets denoted ℵ₀. That’s a Hebrew letter aleph; it reads as “aleph-zero.” It’s the size of the set of natural numbers, so that gets written |ℕ|=ℵ₀.

Next, some common sets are larger than size ℵ₀. The major example Cantor proved is that the set of real numbers is bigger, written |ℝ|>ℵ₀. But the reals aren’t that big; we’re just getting started on the infinite sizes.

✅ More Mind-Blowing Stuff: Mathematicians Discovered a New 13-Sided Shape That Can Do Remarkable Things

For the really big stuff, mathematicians keep discovering larger and larger sizes, or what we call Large Cardinals. It’s a process of pure math that goes like this: Someone says, “I thought of a definition for a cardinal, and I can prove this cardinal is bigger than all the known cardinals.” Then, if their proof is good, that’s the new largest known cardinal. Until someone else comes up with a larger one.

Throughout the 20th century, the frontier of known large cardinals was steadily pushed forward. There’s now even a beautiful wiki of known large cardinals , named in honor of Cantor. So, will this ever end? The answer is broadly yes, although it gets very complicated.

In some senses, the top of the large cardinal hierarchy is in sight. Some theorems have been proven, which impose a sort of ceiling on the possibilities for large cardinals. But many open questions remain, and new cardinals have been nailed down as recently as 2019. It’s very possible we will be discovering more for decades to come. Hopefully we’ll eventually have a comprehensive list of all large cardinals.

What’s the Deal with 𝜋+e?

Given everything we know about two of math’s most famous constants, 𝜋 and e , it’s a bit surprising how lost we are when they’re added together.

This mystery is all about algebraic real numbers . The definition: A real number is algebraic if it’s the root of some polynomial with integer coefficients. For example, x²-6 is a polynomial with integer coefficients, since 1 and -6 are integers. The roots of x²-6=0 are x=√6 and x=-√6, so that means √6 and -√6 are algebraic numbers.

✅ Try It Yourself: Can You Solve This Viral Brain Teaser From TikTok?

All rational numbers, and roots of rational numbers, are algebraic. So it might feel like “most” real numbers are algebraic. Turns out, it’s actually the opposite. The antonym to algebraic is transcendental, and it turns out almost all real numbers are transcendental—for certain mathematical meanings of “almost all.” So who’s algebraic , and who’s transcendental?

The real number 𝜋 goes back to ancient math, while the number e has been around since the 17th century. You’ve probably heard of both, and you’d think we know the answer to every basic question to be asked about them, right?

Well, we do know that both 𝜋 and e are transcendental. But somehow it’s unknown whether 𝜋+e is algebraic or transcendental. Similarly, we don’t know about 𝜋e, 𝜋/e, and other simple combinations of them. So there are incredibly basic questions about numbers we’ve known for millennia that still remain mysterious.

Is 𝛾 Rational?

Here’s another problem that’s very easy to write, but hard to solve. All you need to recall is the definition of rational numbers.

Rational numbers can be written in the form p/q, where p and q are integers. So, 42 and -11/3 are rational, while 𝜋 and √2 are not. It’s a very basic property, so you’d think we can easily tell when a number is rational or not, right?

Meet the Euler-Mascheroni constant 𝛾, which is a lowercase Greek gamma. It’s a real number, approximately 0.5772, with a closed form that’s not terribly ugly; it looks like the image above.

✅ One More Thing: Teens Have Proven the Pythagorean Theorem With Trigonometry. That Should Be Impossible

The sleek way of putting words to those symbols is “gamma is the limit of the difference of the harmonic series and the natural log.” So, it’s a combination of two very well-understood mathematical objects. It has other neat closed forms, and appears in hundreds of formulas.

But somehow, we don’t even know if 𝛾 is rational. We’ve calculated it to half a trillion digits, yet nobody can prove if it’s rational or not. The popular prediction is that 𝛾 is irrational. Along with our previous example 𝜋+e, we have another question of a simple property for a well-known number, and we can’t even answer it.

Dave Linkletter is a Ph.D. candidate in Pure Mathematics at the University of Nevada, Las Vegas. His research is in Large Cardinal Set Theory. He also teaches undergrad classes, and enjoys breaking down popular math topics for wide audiences.

.css-cuqpxl:before{padding-right:0.3125rem;content:'//';display:inline;} Pop Mech Pro .css-xtujxj:before{padding-left:0.3125rem;content:'//';display:inline;}

North Korea Sends “Poop Balloons” Into South Korea

Plane Flown by 'Ace of Aces' Pilot Finally Found

The F-35 Is Still One of the Safest Planes

The Air Force’s Upcoming “Doomsday Plane” Replacem

Meet the Marines' New Kamikaze Drone

Did Russia Launch a Weapon Near a U.S. Satellite?

A Groundbreaking Discovery For Interstellar Travel

America's Missile Defense Has Entered a New Era

The Army’s Laser Isn’t All It’s Cracked Up To Be

What We Know About Russia’s Mystery Radio Signal

Corpses Found Under Hitler's Lair

April 5, 2024

AI Chatbots Will Never Stop Hallucinating

Some amount of chatbot hallucination is inevitable. But there are ways to minimize it

By Lauren Leffer

Moor Studio/Getty Images

Last summer a federal judge fined a New York City law firm $5,000 after a lawyer used the artificial intelligence tool ChatGPT to draft a brief for a personal injury case. The text was full of falsehoods —including more than six entirely fabricated past cases meant to establish precedent for the personal injury suit. Similar errors are rampant across AI-generated legal outputs, researchers at Stanford University and Yale University found in a recent preprint study of three popular large language models (LLMs). There’s a term for when generative AI models produce responses that don’t match reality: “hallucination.”

Hallucination is usually framed as a technical problem with AI—one that hardworking developers will eventually solve. But many machine-learning experts don’t view hallucination as fixable because it stems from LLMs doing exactly what they were developed and trained to do: respond, however they can, to user prompts. The real problem, according to some AI researchers, lies in our collective ideas about what these models are and how we’ve decided to use them. To mitigate hallucinations, the researchers say, generative AI tools must be paired with fact-checking systems that leave no chatbot unsupervised.

Many conflicts related to AI hallucinations have roots in marketing and hype. Tech companies have portrayed their LLMs as digital Swiss Army knives, capable of solving myriad problems or replacing human work. But applied in the wrong setting, these tools simply fail. Chatbots have offered users incorrect and potentially harmful medical advice, media outlets have published AI-generated articles that included inaccurate financial guidance , and search engines with AI interfaces have invented fake citations . As more people and businesses rely on chatbots for factual information, their tendency to make things up becomes even more apparent and disruptive.

On supporting science journalism

If you're enjoying this article, consider supporting our award-winning journalism by subscribing . By purchasing a subscription you are helping to ensure the future of impactful stories about the discoveries and ideas shaping our world today.

But today’s LLMs were never designed to be purely accurate. They were created to create—to generate —says Subbarao Kambhampati , a computer science professor who researches artificial intelligence at Arizona State University. “The reality is: there’s no way to guarantee the factuality of what is generated,” he explains, adding that all computer-generated “creativity is hallucination, to some extent.”

In a preprint study released in January, three machine-learning researchers at the National University of Singapore presented a proof that hallucination is inevitable in large language models. The proof applies some classic results in learning theory, such as Cantor’s diagonalization argument , to demonstrate that that LLMs simply cannot learn all computable functions. In other words, it shows that there will always be solvable problems beyond a model’s abilities. “For any LLM, there is a part of the real world that it cannot learn, where it will inevitably hallucinate,” wrote study co-authors Ziwei Xu, Sanjay Jain and Mohan Kankanhalli in a joint e-mail to Scientific American .

Although the proof appears to be accurate, Kambhampati says, the argument it makes—that certain difficult problems will always stump computers—is too broad to provide much insight into why specific confabulations happen. And, he continues, the issue is more widespread than the proof shows because LLMs hallucinate even when faced with simple requests.

One main reason AI chatbots routinely hallucinate stems from their fundamental construction, says Dilek Hakkani-Tür , a computer science professor who studies natural language and speech processing at the University of Illinois at Urbana-Champaign. LLMs are basically hyperadvanced autocomplete tools; they are trained to predict what should come next in a sequence such as a string of text. If a model’s training data include lots of information on a certain subject, it might produce accurate outputs. But LLMs are built to always produce an answer, even on topics that don’t appear in their training data. Hakkani-Tür says this increases the chance errors will emerge.

Adding more factually grounded training data might seem like an obvious solution. But there are practical and physical limits to how much information an LLM can hold, says computer scientist Amr Awadallah , co-founder and CEO of the AI platform Vectara, which tracks hallucination rates among LLMs on a leaderboard. (The lowest hallucination rates among tracked AI models are around 3 to 5 percent .) To achieve their language fluency, these massive models are trained on orders of magnitude more data than they can store—and data compression is the inevitable result. When LLMs cannot “recall everything exactly like it was in their training, they make up stuff and fill in the blanks,” Awadallah says. And, he adds, these models already operate at the edge of our computing capacity; trying to avoid hallucinations by making LLMs larger would produce slower models that are more expensive and more environmentally harmful to operate.

Another cause of hallucination is calibration, says Santosh Vempala , a computer science professor at the Georgia Institute of Technology. Calibration is the process by which LLMs are adjusted to favor certain outputs over others (to match the statistics of training data or to generate more realistically human-sounding phrases).* In a preprint paper first released last November, Vempala and a coauthor suggest that any calibrated language model will hallucinate —because accuracy itself is sometimes at odds with text that flows naturally and seems original. Reducing calibration can boost factuality while simultaneously introducing other flaws in LLM-generated text. Uncalibrated models might write formulaically, repeating words and phrases more often than a person would, Vempala says. The problem is that users expect AI chatbots to be both factual and fluid.

Accepting that LLMs may never be able to produce completely accurate outputs means reconsidering when, where and how we deploy these generative tools, Kambhampati says. They are wonderful idea generators, he adds, but they are not independent problem solvers. “You can leverage them by putting them into an architecture with verifiers,” he explains—whether that means putting more humans in the loop or using other automated programs.

At Vectara, Awadallah is working on exactly that. His team’s leaderboard project is an early proof of concept for a hallucination detector—and detecting hallucinations is the first step to being able to fix them, he says. A future detector might be paired with an automated AI editor that corrects errors before they reach an end user. His company is also working on a hybrid chatbot and news database called AskNews, which combines an LLM with a retrieval engine that picks the most relevant facts from recently published articles to answer a user’s question. Awadallah says AskNews provides descriptions of current events that are significantly more accurate than what an LLM alone could produce because the chatbot bases its responses only on the sources dredged up by the database search tool.

Hakkani-Tür, too, is researching factually grounded systems that pair specialized language models with relatively reliable information sources such as corporate documents, verified product reviews, medical literature or Wikipedia posts to boost accuracy. She hopes that—once all the kinks are ironed out—these grounded networks could one day be useful tools for things like health access and educational equity. “I do see the strength of language models as tools for making our lives better, more productive and more fair,” she says.

In a future where specialized systems verify LLM outputs, AI tools designed for specific contexts would partially replace today’s all-purpose models. Each application of an AI text generator (be it a customer service chatbot, a news summary service or even a legal adviser) would be part of a custom-built architecture that would enable its utility. Meanwhile less- grounded generalist chatbots would be able to respond to anything you ask but with no guarantee of truth. They would continue to be powerful creative partners or sources of inspiration and entertainment—yet not oracles or encyclopedias—exactly as designed.

* Editor’s Note (4/5/24): This sentence was edited after posting. It previously stated that mitigating bias in a large language model’s output is an example of calibration. That is instead a separate process known as alignment.

The science refresher you need before diving into Netflix's hit sci-fi series '3 Body Problem'

• Netflix's " 3 Body Problem " is based on a science-fiction trilogy and follows a group of physicists.
• We asked an astronomer and an aerospace engineer to explain some of the show's scientific concepts.
• It might help to have a bit of background on the Fermi paradox and the Wow! signal before you watch.

The upcoming Netflix show "3 Body Problem" is a sci-fi story about a group of physicists grappling with the discovery of an alien civilization .

Taking its name from a tricky bit of orbital mechanics — three celestial bodies moving around each other — the show is based on the science-fiction trilogy " Remembrance of Earth's Past " by Liu Cixin.

In the show, several of the main characters studied physics at Oxford University . Luckily, you don't need to have the same background to enjoy the show.

However, there are a few scientific concepts that might be helpful to know before you tune in on March 21.

The three-body problem is unsolvable and chaotic

Some of the show's action takes place in a virtual world that's orbited by three suns. The celestial mechanics of such a planet have long perplexed scientists in the real world.

"This is a centuries-old problem," Shane Ross, an aerospace and ocean engineering professor at Virginia Tech, told Business Insider.

Isaac Newton was able to figure out the two-body problem, how a pair of massive objects like stars or planets move when affected by each other's gravity.

"The two-body problem is sort of the paradigm of stability," Ross said. Adding in a third body, though, makes everything topsy-turvy.

From a mathematical perspective , "it's unsolvable," Ross said of the three-body problem. "You can't write out the solution for all time as some algebraic formula."

It's a bit like the butterfly effect: a small change can vastly alter the outcome. "Any uncertainty we have in the initial conditions grows exponentially, to the point where the future state of the system is essentially unpredictable."

Alpha Centauri is the closest star system to Earth

The three-body system in the story is based on a real neighboring star system called Alpha Centauri.

At about 4 light-years from Earth, it's the closest star system to our own and contains three stars: Alpha Centauri A, Alpha Centauri B, and Proxima Centauri, which has two planets orbiting around it.

"We're talking about something super close to us," Franck Marchis, a senior planetary astronomer with the SETI Institute, said. "It's like looking at the backyard of neighbors, basically."

However, it would take special conditions for life, at least as we know it, to survive, on either planet around Proxima Centauri. "The conditions for life are extremely rare," Ross said. "I think the Earth is a very special planet," adding that "there could be life that takes some other form that we don't know about."

If a civilization from Alpha Centauri evolved at a similar pace to our own, then "they're probably more advanced than us," Marchis said because the system is estimated to be between 5 and 7 billion years old whereas Earth's solar system formed 4.5 billion years ago.

The Fermi paradox poses the question, where are all the aliens?

If there are highly evolved beings on other planets, why haven't they gotten in touch? That's the question astrophysicist Ye Wenjie is asking when she brings up the Fermi paradox in the show.

In 1950, Nobel prize-winning physicist Enrico Fermi wondered where all the extraterrestrials were. Decades later, other scientists picked up the question. If other civilizations existed, they must have left some evidence.

To Marchis, what became known as the Fermi paradox is an outdated way of thinking. "The idea is that because we are a civilization that's become technologically advanced, the first thing that we do is to travel through the galaxy, 'Star Trek'-like," he said.

Instead, he prefers the "zoo hypothesis."

If they are truly advanced, he said, "they probably reached a certain level of sentientness or consciousness that makes them more respectful of other civilizations which are progressing."

In short, they're purposefully avoiding contact with our planet .

Aliens could have communicated through the Wow! signal

One of the most mysterious potential alien communications is known as the Wow! signal. In the show, Clarence (Benedict Wong) describes how the strange signal was picked up in Ohio and China.

During the 1970s, researchers at Ohio State University really were involved in the Search for Extraterrestrial Intelligence, or SETI . They used a radio observatory nicknamed "Big Ear" to try and pick up extraterrestrial communications.

Related stories

In 1977, volunteer Jerry Ehman was looking at a computer printout of a signal Big Ear had picked up three days earlier. He circled the numbers and wrote "Wow!" alongside them. The 72-second signal was strong and located at a frequency known as the hydrogen line.

At the time, researchers thought aliens would communicate via that frequency "because it's the easiest way to send signals through the galaxy," Marchis said.

The signal has never repeated or been detected again Marchis said. (And no other observatories reported picking up the signal, in China or anywhere else.)

Since the signal itself wasn't saved, there's no way of knowing if it contained a message, Marchis said. Some more mundane explanations for the signal have been suggested, like the radio transmission reflecting off a passing comet.

SETI has come a long way since the '70s, with many researchers using newer technology and a broader range of signals, Marchis said. "We assume that if aliens will communicate with us," he said, "they're slightly more advanced than the people from the 1970s."

Occam's razor suggests simple explanations are often better

Like many other sci-fi movies and shows before it, including "Contact" and "Fringe," "3 Body Problem" makes a reference to Occam's razor.

In 1852, philosopher Sir William Hamilton coined the term "Occam's razor," attributing the idea to 14th-century theologian William of Ockham.

William of Ockham had written, "Numquam ponenda est pluralitas sine necessitate," or "Plurality must never be posited without necessity." It's an idea that Aristotle and Ptolemy also stated.

Today, the well-known concept is usually stated as "the simplest solution is usually correct." The often-cited example is, if you hear the sound of hoofbeats, think horses, not zebras (provided you're not on the savanna).

Particle accelerators move particles at almost the speed of light

The bizarre, illogical behavior of subatomic particles inside particle accelerator experiments spurs a major plot point in the show.

Often located in large facilities, particle accelerators like the Large Hadron Collider have been used in lots of different ways, from medical research to industrial applications like sealing chip bags.

Many of these devices use magnets and magnetic fields to speed up and collide charged particles, which then release energy. Particles move at almost the speed of light. In this unique environment, scientists can try to solve some of the biggest questions in physics.

For example, in 2012, the LHC helped researchers observe the Higgs boson , the "God particle" that helps explain why our universe has mass.

Neutrino detectors are built deep underground

The trailer for the show includes a dramatic shot of one of the characters stepping into what looks like a neutrino detector and falling, presumably to her death.

Neutrinos, also known as ghost particles, are subatomic particles that the sun and  supernovae  create. Billions pass through your body at any given time.

Much like particle accelerators, the devices may help unlock some of the universe's secrets. They're often built underground to shield them from cosmic rays that can interfere with the data.

Three celestial bodies lined up is known as syzygy

During the show's third episode, the three suns in the virtual world all line up in a triple eclipse.

Ross pointed out that the show debuts around a "cosmically significant day," the vernal equinox . "That's the day when all across the world it's equal daylight and nighttime," he said.

It's also close to the upcoming solar eclipse that has a path of totality through a large portion of North America.

"That's the sun, moon, and Earth all in a line," Ross said. "It's called syzygy, when three celestial bodies are exactly in a line."

Protons are subatomic particles

In one of the show's more science-fiction moments, tiny supercomputers called sophons cause all sorts of unusual activity.

A sophon is completely fiction. However, it's described as a proton that the aliens have transformed into a sentient supercomputer. And protons, at least, are real.

In real life, protons are positively charged particles found in atomic nuclei, usually alongside neutrons.

The periodic table is arranged by increasing atomic number, which is equal to the number of protons in an element's nucleus.

• Main content

What Are Examples of a Hypothesis?

• Scientific Method
• Chemical Laws
• Periodic Table
• Projects & Experiments
• Biochemistry
• Physical Chemistry
• Medical Chemistry
• Chemistry In Everyday Life
• Famous Chemists
• Activities for Kids
• Abbreviations & Acronyms
• Weather & Climate
• Ph.D., Biomedical Sciences, University of Tennessee at Knoxville
• B.A., Physics and Mathematics, Hastings College

A hypothesis is an explanation for a set of observations. Here are examples of a scientific hypothesis.

Although you could state a scientific hypothesis in various ways, most hypotheses are either "If, then" statements or forms of the null hypothesis . The null hypothesis is sometimes called the "no difference" hypothesis. The null hypothesis is good for experimentation because it's simple to disprove. If you disprove a null hypothesis, that is evidence for a relationship between the variables you are examining.

Examples of Null Hypotheses

• Hyperactivity is unrelated to eating sugar.
• All daisies have the same number of petals.
• The number of pets in a household is unrelated to the number of people living in it.
• A person's preference for a shirt is unrelated to its color.

Examples of If, Then Hypotheses

• If you get at least 6 hours of sleep, you will do better on tests than if you get less sleep.
• If you drop a ball, it will fall toward the ground.
• If you drink coffee before going to bed, then it will take longer to fall asleep.
• If you cover a wound with a bandage, then it will heal with less scarring.

Improving a Hypothesis to Make It Testable

You may wish to revise your first hypothesis in order to make it easier to design an experiment to test. For example, let's say you have a bad breakout the morning after eating a lot of greasy food. You may wonder if there is a correlation between eating greasy food and getting pimples. You propose the hypothesis:

Eating greasy food causes pimples.

Next, you need to design an experiment to test this hypothesis. Let's say you decide to eat greasy food every day for a week and record the effect on your face. Then, as a control, you'll avoid greasy food for the next week and see what happens. Now, this is not a good experiment because it does not take into account other factors such as hormone levels, stress, sun exposure, exercise, or any number of other variables that might conceivably affect your skin.

The problem is that you cannot assign cause to your effect . If you eat french fries for a week and suffer a breakout, can you definitely say it was the grease in the food that caused it? Maybe it was the salt. Maybe it was the potato. Maybe it was unrelated to diet. You can't prove your hypothesis. It's much easier to disprove a hypothesis.

So, let's restate the hypothesis to make it easier to evaluate the data:

Getting pimples is unaffected by eating greasy food.

So, if you eat fatty food every day for a week and suffer breakouts and then don't break out the week that you avoid greasy food, you can be pretty sure something is up. Can you disprove the hypothesis? Probably not, since it is so hard to assign cause and effect. However, you can make a strong case that there is some relationship between diet and acne.

If your skin stays clear for the entire test, you may decide to accept your hypothesis . Again, you didn't prove or disprove anything, which is fine

• Null Hypothesis Examples
• Difference Between Independent and Dependent Variables
• Examples of Independent and Dependent Variables
• What Is a Hypothesis? (Science)
• Null Hypothesis Definition and Examples
• The 10 Most Important Lab Safety Rules
• What Are the Elements of a Good Hypothesis?
• Understanding Simple vs Controlled Experiments
• What Is a Testable Hypothesis?
• What 'Fail to Reject' Means in a Hypothesis Test
• Scientific Method Vocabulary Terms
• Scientific Hypothesis Examples
• How To Design a Science Fair Experiment
• Six Steps of the Scientific Method
• An Example of a Hypothesis Test

Review of the analytical network-averaging: part I — theoretical foundation

• Itskov, Mikhail
• Khiêm, Vu Ngoc

The analytical network-averaging, an elegant homogenization scheme, has been proposed in Khiêm and Itskov (J. Mech. Phys. Solids 95:254-269, 2016) to capture a wide range of mechanical phenomena in soft materials. These phenomena include nonlinear elasticity observed in unfilled rubbers, anisotropic damage behaviors in mechanoresponsive elastomers, phase transition occurring in natural rubbers, cross-effect of damage in double-network hydrogels, and irreversible fiber sliding in textile reinforcements. While the effectiveness of the analytical network-averaging has been evidenced through various illustrative examples, a thorough exposition of the theory remains elusive, primarily due to the concise nature preferred in conventional scientific articles and the specific thematic emphasis of individual publications. In the first part of this review series, an exhaustive theoretical examination of the analytical network-averaging concept is provided. Such theory postulates the presence of an orientational distribution function of material directions, such as fibers or polymer chains. Utilizing this distribution function, microscopic strain measures essential for solving homogenized boundary value problems can be obtained by averaging of macroscopic strain measures. It is interesting that in all scenarios, analytical derivation of the microscopic strain measures can always be obtained. Thus, such analytical homogenization scheme offers physically based invariants that automatically guarantee realistic behaviors (such as non-affine deformation, material objectivity and material symmetry) in stress response functions. This is particularly important in the age of data science and machine learning as it allows for the choice of stress hypothesis without limitations, while ensuring a priori interpretability of results.

• Analytical network-averaging;
• Homogenization;
• Non-affine deformation;
• Interpretability;
• Internal variables;
• Nonlinear elasticity