null hypothesis is also known as research hypothesis

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• Null and Alternative Hypotheses | Definitions & Examples

Null & Alternative Hypotheses | Definitions, Templates & Examples

Published on May 6, 2022 by Shaun Turney . Revised on June 22, 2023.

The null and alternative hypotheses are two competing claims that researchers weigh evidence for and against using a statistical test :

• Null hypothesis ( H 0 ): There’s no effect in the population .
• Alternative hypothesis ( H a or H 1 ) : There’s an effect in the population.

Table of contents

Answering your research question with hypotheses, what is a null hypothesis, what is an alternative hypothesis, similarities and differences between null and alternative hypotheses, how to write null and alternative hypotheses, other interesting articles, frequently asked questions.

The null and alternative hypotheses offer competing answers to your research question . When the research question asks “Does the independent variable affect the dependent variable?”:

• The null hypothesis ( H 0 ) answers “No, there’s no effect in the population.”
• The alternative hypothesis ( H a ) answers “Yes, there is an effect in the population.”

The null and alternative are always claims about the population. That’s because the goal of hypothesis testing is to make inferences about a population based on a sample . Often, we infer whether there’s an effect in the population by looking at differences between groups or relationships between variables in the sample. It’s critical for your research to write strong hypotheses .

You can use a statistical test to decide whether the evidence favors the null or alternative hypothesis. Each type of statistical test comes with a specific way of phrasing the null and alternative hypothesis. However, the hypotheses can also be phrased in a general way that applies to any test.

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The null hypothesis is the claim that there’s no effect in the population.

If the sample provides enough evidence against the claim that there’s no effect in the population ( p ≤ α), then we can reject the null hypothesis . Otherwise, we fail to reject the null hypothesis.

Although “fail to reject” may sound awkward, it’s the only wording that statisticians accept . Be careful not to say you “prove” or “accept” the null hypothesis.

Null hypotheses often include phrases such as “no effect,” “no difference,” or “no relationship.” When written in mathematical terms, they always include an equality (usually =, but sometimes ≥ or ≤).

You can never know with complete certainty whether there is an effect in the population. Some percentage of the time, your inference about the population will 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 a type II error.

Examples of null hypotheses

The table below gives examples of research questions and null hypotheses. There’s always more than one way to answer a research question, but these null hypotheses can help you get started.

*Note that some researchers prefer to always write the null hypothesis in terms of “no effect” and “=”. It would be fine to say that daily meditation has no effect on the incidence of depression and p 1 = p 2 .

The alternative hypothesis ( H a ) is the other answer to your research question . It claims that there’s an effect in the population.

Often, your alternative hypothesis is the same as your research hypothesis. In other words, it’s the claim that you expect or hope will be true.

The alternative hypothesis is the complement to the null hypothesis. Null and alternative hypotheses are exhaustive, meaning that together they cover every possible outcome. They are also mutually exclusive, meaning that only one can be true at a time.

Alternative hypotheses often include phrases such as “an effect,” “a difference,” or “a relationship.” When alternative hypotheses are written in mathematical terms, they always include an inequality (usually ≠, but sometimes < or >). As with null hypotheses, there are many acceptable ways to phrase an alternative hypothesis.

Examples of alternative hypotheses

The table below gives examples of research questions and alternative hypotheses to help you get started with formulating your own.

Null and alternative hypotheses are similar in some ways:

• They’re both answers to the research question.
• They both make claims about the population.
• They’re both evaluated by statistical tests.

However, there are important differences between the two types of hypotheses, summarized in the following table.

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To help you write your hypotheses, you can use the template sentences below. If you know which statistical test you’re going to use, you can use the test-specific template sentences. Otherwise, you can use the general template sentences.

General template sentences

The only thing you need to know to use these general template sentences are your dependent and independent variables. To write your research question, null hypothesis, and alternative hypothesis, fill in the following sentences with your variables:

Does independent variable affect dependent variable ?

• Null hypothesis ( H 0 ): Independent variable does not affect dependent variable.
• Alternative hypothesis ( H a ): Independent variable affects dependent variable.

Test-specific template sentences

Once you know the statistical test you’ll be using, you can write your hypotheses in a more precise and mathematical way specific to the test you chose. The table below provides template sentences for common statistical tests.

Note: The template sentences above assume that you’re performing one-tailed tests . One-tailed tests are appropriate for most studies.

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

• Normal distribution
• Descriptive statistics
• Measures of central tendency
• Correlation coefficient

Methodology

• Cluster sampling
• Stratified sampling
• Types of interviews
• Cohort study
• Thematic analysis

Research bias

• Implicit bias
• Cognitive bias
• Survivorship bias
• Availability heuristic
• Nonresponse bias
• Regression to the mean

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.

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.

The null hypothesis is often abbreviated as H 0 . When the null hypothesis is written using mathematical symbols, it always includes an equality symbol (usually =, but sometimes ≥ or ≤).

The alternative hypothesis is often abbreviated as H a or H 1 . When the alternative hypothesis is written using mathematical symbols, it always includes an inequality symbol (usually ≠, but sometimes < or >).

A research hypothesis is your proposed answer to your research question. The research hypothesis usually includes an explanation (“ x affects y because …”).

A statistical hypothesis, on the other hand, is a mathematical statement about a population parameter. Statistical hypotheses always come in pairs: the null and alternative hypotheses . In a well-designed study , the statistical hypotheses correspond logically to the research hypothesis.

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Turney, S. (2023, June 22). Null & Alternative Hypotheses | Definitions, Templates & Examples. Scribbr. Retrieved September 27, 2024, from https://www.scribbr.com/statistics/null-and-alternative-hypotheses/

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Statistics By Jim

Making statistics intuitive

Null Hypothesis: Definition, Rejecting & Examples

By Jim Frost 6 Comments

What is a Null Hypothesis?

The null hypothesis in statistics states that there is no difference between groups or no relationship between variables. It is one of two mutually exclusive hypotheses about a population in a hypothesis test.

• Null Hypothesis H 0 : No effect exists in the population.
• Alternative Hypothesis H A : The effect exists in the population.

In every study or experiment, researchers assess an effect or relationship. This effect can be the effectiveness of a new drug, building material, or other intervention that has benefits. There is a benefit or connection that the researchers hope to identify. Unfortunately, no effect may exist. In statistics, we call this lack of an effect the null hypothesis. Researchers assume that this notion of no effect is correct until they have enough evidence to suggest otherwise, similar to how a trial presumes innocence.

In this context, the analysts don’t necessarily believe the null hypothesis is correct. In fact, they typically want to reject it because that leads to more exciting finds about an effect or relationship. The new vaccine works!

You can think of it as the default theory that requires sufficiently strong evidence to reject. Like a prosecutor, researchers must collect sufficient evidence to overturn the presumption of no effect. Investigators must work hard to set up a study and a data collection system to obtain evidence that can reject the null hypothesis.

Related post : What is an Effect in Statistics?

Null Hypothesis Examples

Null hypotheses start as research questions that the investigator rephrases as a statement indicating there is no effect or relationship.

After reading these examples, you might think they’re a bit boring and pointless. However, the key is to remember that the null hypothesis defines the condition that the researchers need to discredit before suggesting an effect exists.

Let’s see how you reject the null hypothesis and get to those more exciting findings!

When to Reject the Null Hypothesis

So, you want to reject the null hypothesis, but how and when can you do that? To start, you’ll need to perform a statistical test on your data. The following is an overview of performing a study that uses a hypothesis test.

The first step is to devise a research question and the appropriate null hypothesis. After that, the investigators need to formulate an experimental design and data collection procedures that will allow them to gather data that can answer the research question. Then they collect the data. For more information about designing a scientific study that uses statistics, read my post 5 Steps for Conducting Studies with Statistics .

After data collection is complete, statistics and hypothesis testing enter the picture. Hypothesis testing takes your sample data and evaluates how consistent they are with the null hypothesis. The p-value is a crucial part of the statistical results because it quantifies how strongly the sample data contradict the null hypothesis.

When the sample data provide sufficient evidence, you can reject the null hypothesis. In a hypothesis test, this process involves comparing the p-value to your significance level .

Rejecting the Null Hypothesis

Reject the null hypothesis when the p-value is less than or equal to your significance level. Your sample data favor the alternative hypothesis, which suggests that the effect exists in the population. For a mnemonic device, remember—when the p-value is low, the null must go!

When you can reject the null hypothesis, your results are statistically significant. Learn more about Statistical Significance: Definition & Meaning .

Failing to Reject the Null Hypothesis

Conversely, when the p-value is greater than your significance level, you fail to reject the null hypothesis. The sample data provides insufficient data to conclude that the effect exists in the population. When the p-value is high, the null must fly!

Note that failing to reject the null is not the same as proving it. For more information about the difference, read my post about Failing to Reject the Null .

That’s a very general look at the process. But I hope you can see how the path to more exciting findings depends on being able to rule out the less exciting null hypothesis that states there’s nothing to see here!

Let’s move on to learning how to write the null hypothesis for different types of effects, relationships, and tests.

Related posts : How Hypothesis Tests Work and Interpreting P-values

How to Write a Null Hypothesis

The null hypothesis varies by the type of statistic and hypothesis test. Remember that inferential statistics use samples to draw conclusions about populations. Consequently, when you write a null hypothesis, it must make a claim about the relevant population parameter . Further, that claim usually indicates that the effect does not exist in the population. Below are typical examples of writing a null hypothesis for various parameters and hypothesis tests.

Related posts : Descriptive vs. Inferential Statistics and Populations, Parameters, and Samples in Inferential Statistics

Group Means

T-tests and ANOVA assess the differences between group means. For these tests, the null hypothesis states that there is no difference between group means in the population. In other words, the experimental conditions that define the groups do not affect the mean outcome. Mu (µ) is the population parameter for the mean, and you’ll need to include it in the statement for this type of study.

For example, an experiment compares the mean bone density changes for a new osteoporosis medication. The control group does not receive the medicine, while the treatment group does. The null states that the mean bone density changes for the control and treatment groups are equal.

• Null Hypothesis H 0 : Group means are equal in the population: µ 1 = µ 2 , or µ 1 – µ 2 = 0
• Alternative Hypothesis H A : Group means are not equal in the population: µ 1 ≠ µ 2 , or µ 1 – µ 2 ≠ 0.

Group Proportions

Proportions tests assess the differences between group proportions. For these tests, the null hypothesis states that there is no difference between group proportions. Again, the experimental conditions did not affect the proportion of events in the groups. P is the population proportion parameter that you’ll need to include.

For example, a vaccine experiment compares the infection rate in the treatment group to the control group. The treatment group receives the vaccine, while the control group does not. The null states that the infection rates for the control and treatment groups are equal.

• Null Hypothesis H 0 : Group proportions are equal in the population: p 1 = p 2 .
• Alternative Hypothesis H A : Group proportions are not equal in the population: p 1 ≠ p 2 .

Correlation and Regression Coefficients

Some studies assess the relationship between two continuous variables rather than differences between groups.

In these studies, analysts often use either correlation or regression analysis . For these tests, the null states that there is no relationship between the variables. Specifically, it says that the correlation or regression coefficient is zero. As one variable increases, there is no tendency for the other variable to increase or decrease. Rho (ρ) is the population correlation parameter and beta (β) is the regression coefficient parameter.

For example, a study assesses the relationship between screen time and test performance. The null states that there is no correlation between this pair of variables. As screen time increases, test performance does not tend to increase or decrease.

• Null Hypothesis H 0 : The correlation in the population is zero: ρ = 0.
• Alternative Hypothesis H A : The correlation in the population is not zero: ρ ≠ 0.

For all these cases, the analysts define the hypotheses before the study. After collecting the data, they perform a hypothesis test to determine whether they can reject the null hypothesis.

The preceding examples are all for two-tailed hypothesis tests. To learn about one-tailed tests and how to write a null hypothesis for them, read my post One-Tailed vs. Two-Tailed Tests .

Related post : Understanding Correlation

Neyman, J; Pearson, E. S. (January 1, 1933).  On the Problem of the most Efficient Tests of Statistical Hypotheses .  Philosophical Transactions of the Royal Society A .  231  (694–706): 289–337.

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Reader Interactions

January 11, 2024 at 2:57 pm

Thanks for the reply.

January 10, 2024 at 1:23 pm

Hi Jim, In your comment you state that equivalence test null and alternate hypotheses are reversed. For hypothesis tests of data fits to a probability distribution, the null hypothesis is that the probability distribution fits the data. Is this correct?

January 10, 2024 at 2:15 pm

Those two separate things, equivalence testing and normality tests. But, yes, you’re correct for both.

Hypotheses are switched for equivalence testing. You need to “work” (i.e., collect a large sample of good quality data) to be able to reject the null that the groups are different to be able to conclude they’re the same.

With typical hypothesis tests, if you have low quality data and a low sample size, you’ll fail to reject the null that they’re the same, concluding they’re equivalent. But that’s more a statement about the low quality and small sample size than anything to do with the groups being equal.

So, equivalence testing make you work to obtain a finding that the groups are the same (at least within some amount you define as a trivial difference).

For normality testing, and other distribution tests, the null states that the data follow the distribution (normal or whatever). If you reject the null, you have sufficient evidence to conclude that your sample data don’t follow the probability distribution. That’s a rare case where you hope to fail to reject the null. And it suffers from the problem I describe above where you might fail to reject the null simply because you have a small sample size. In that case, you’d conclude the data follow the probability distribution but it’s more that you don’t have enough data for the test to register the deviation. In this scenario, if you had a larger sample size, you’d reject the null and conclude it doesn’t follow that distribution.

I don’t know of any equivalence testing type approach for distribution fit tests where you’d need to work to show the data follow a distribution, although I haven’t looked for one either!

February 20, 2022 at 9:26 pm

Is a null hypothesis regularly (always) stated in the negative? “there is no” or “does not”

February 23, 2022 at 9:21 pm

Typically, the null hypothesis includes an equal sign. The null hypothesis states that the population parameter equals a particular value. That value is usually one that represents no effect. In the case of a one-sided hypothesis test, the null still contains an equal sign but it’s “greater than or equal to” or “less than or equal to.” If you wanted to translate the null hypothesis from its native mathematical expression, you could use the expression “there is no effect.” But the mathematical form more specifically states what it’s testing.

It’s the alternative hypothesis that typically contains does not equal.

There are some exceptions. For example, in an equivalence test where the researchers want to show that two things are equal, the null hypothesis states that they’re not equal.

In short, the null hypothesis states the condition that the researchers hope to reject. They need to work hard to set up an experiment and data collection that’ll gather enough evidence to be able to reject the null condition.

February 15, 2022 at 9:32 am

Dear sir I always read your notes on Research methods.. Kindly tell is there any available Book on all these..wonderfull Urgent

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• Knowledge Base
• Null and Alternative Hypotheses | Definitions & Examples

Null and Alternative Hypotheses | Definitions & Examples

Published on 5 October 2022 by Shaun Turney . Revised on 6 December 2022.

The null and alternative hypotheses are two competing claims that researchers weigh evidence for and against using a statistical test :

• Null hypothesis (H 0 ): There’s no effect in the population .
• Alternative hypothesis (H A ): There’s an effect in the population.

The effect is usually the effect of the independent variable on the dependent variable .

Table of contents

Answering your research question with hypotheses, what is a null hypothesis, what is an alternative hypothesis, differences between null and alternative hypotheses, how to write null and alternative hypotheses, frequently asked questions about null and alternative hypotheses.

The null and alternative hypotheses offer competing answers to your research question . When the research question asks “Does the independent variable affect the dependent variable?”, the null hypothesis (H 0 ) answers “No, there’s no effect in the population.” On the other hand, the alternative hypothesis (H A ) answers “Yes, there is an effect in the population.”

The null and alternative are always claims about the population. That’s because the goal of hypothesis testing is to make inferences about a population based on a sample . Often, we infer whether there’s an effect in the population by looking at differences between groups or relationships between variables in the sample.

You can use a statistical test to decide whether the evidence favors the null or alternative hypothesis. Each type of statistical test comes with a specific way of phrasing the null and alternative hypothesis. However, the hypotheses can also be phrased in a general way that applies to any test.

The null hypothesis is the claim that there’s no effect in the population.

If the sample provides enough evidence against the claim that there’s no effect in the population ( p ≤ α), then we can reject the null hypothesis . Otherwise, we fail to reject the null hypothesis.

Although “fail to reject” may sound awkward, it’s the only wording that statisticians accept. Be careful not to say you “prove” or “accept” the null hypothesis.

Null hypotheses often include phrases such as “no effect”, “no difference”, or “no relationship”. When written in mathematical terms, they always include an equality (usually =, but sometimes ≥ or ≤).

Examples of null hypotheses

The table below gives examples of research questions and null hypotheses. There’s always more than one way to answer a research question, but these null hypotheses can help you get started.

*Note that some researchers prefer to always write the null hypothesis in terms of “no effect” and “=”. It would be fine to say that daily meditation has no effect on the incidence of depression and p 1 = p 2 .

The alternative hypothesis (H A ) is the other answer to your research question . It claims that there’s an effect in the population.

Often, your alternative hypothesis is the same as your research hypothesis. In other words, it’s the claim that you expect or hope will be true.

The alternative hypothesis is the complement to the null hypothesis. Null and alternative hypotheses are exhaustive, meaning that together they cover every possible outcome. They are also mutually exclusive, meaning that only one can be true at a time.

Alternative hypotheses often include phrases such as “an effect”, “a difference”, or “a relationship”. When alternative hypotheses are written in mathematical terms, they always include an inequality (usually ≠, but sometimes > or <). As with null hypotheses, there are many acceptable ways to phrase an alternative hypothesis.

Examples of alternative hypotheses

The table below gives examples of research questions and alternative hypotheses to help you get started with formulating your own.

Null and alternative hypotheses are similar in some ways:

• They’re both answers to the research question
• They both make claims about the population
• They’re both evaluated by statistical tests.

However, there are important differences between the two types of hypotheses, summarized in the following table.

To help you write your hypotheses, you can use the template sentences below. If you know which statistical test you’re going to use, you can use the test-specific template sentences. Otherwise, you can use the general template sentences.

The only thing you need to know to use these general template sentences are your dependent and independent variables. To write your research question, null hypothesis, and alternative hypothesis, fill in the following sentences with your variables:

Does independent variable affect dependent variable ?

• Null hypothesis (H 0 ): Independent variable does not affect dependent variable .
• Alternative hypothesis (H A ): Independent variable affects dependent variable .

Test-specific

Once you know the statistical test you’ll be using, you can write your hypotheses in a more precise and mathematical way specific to the test you chose. The table below provides template sentences for common statistical tests.

Note: The template sentences above assume that you’re performing one-tailed tests . One-tailed tests are appropriate for most studies.

The null hypothesis is often abbreviated as H 0 . When the null hypothesis is written using mathematical symbols, it always includes an equality symbol (usually =, but sometimes ≥ or ≤).

The alternative hypothesis is often abbreviated as H a or H 1 . When the alternative hypothesis is written using mathematical symbols, it always includes an inequality symbol (usually ≠, but sometimes < or >).

A research hypothesis is your proposed answer to your research question. The research hypothesis usually includes an explanation (‘ x affects y because …’).

A statistical hypothesis, on the other hand, is a mathematical statement about a population parameter. Statistical hypotheses always come in pairs: the null and alternative hypotheses. In a well-designed study , the statistical hypotheses correspond logically to the research hypothesis.

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Turney, S. (2022, December 06). Null and Alternative Hypotheses | Definitions & Examples. Scribbr. Retrieved 27 September 2024, from https://www.scribbr.co.uk/stats/null-and-alternative-hypothesis/

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An Introduction to Statistics: Understanding Hypothesis Testing and Statistical Errors

Priya ranganathan.

1 Department of Anesthesiology, Critical Care and Pain, Tata Memorial Hospital, Mumbai, Maharashtra, India

2 Department of Surgical Oncology, Tata Memorial Centre, Mumbai, Maharashtra, India

The second article in this series on biostatistics covers the concepts of sample, population, research hypotheses and statistical errors.

How to cite this article

Ranganathan P, Pramesh CS. An Introduction to Statistics: Understanding Hypothesis Testing and Statistical Errors. Indian J Crit Care Med 2019;23(Suppl 3):S230–S231.

Two papers quoted in this issue of the Indian Journal of Critical Care Medicine report. The results of studies aim to prove that a new intervention is better than (superior to) an existing treatment. In the ABLE study, the investigators wanted to show that transfusion of fresh red blood cells would be superior to standard-issue red cells in reducing 90-day mortality in ICU patients. 1 The PROPPR study was designed to prove that transfusion of a lower ratio of plasma and platelets to red cells would be superior to a higher ratio in decreasing 24-hour and 30-day mortality in critically ill patients. 2 These studies are known as superiority studies (as opposed to noninferiority or equivalence studies which will be discussed in a subsequent article).

SAMPLE VERSUS POPULATION

A sample represents a group of participants selected from the entire population. Since studies cannot be carried out on entire populations, researchers choose samples, which are representative of the population. This is similar to walking into a grocery store and examining a few grains of rice or wheat before purchasing an entire bag; we assume that the few grains that we select (the sample) are representative of the entire sack of grains (the population).

The results of the study are then extrapolated to generate inferences about the population. We do this using a process known as hypothesis testing. This means that the results of the study may not always be identical to the results we would expect to find in the population; i.e., there is the possibility that the study results may be erroneous.

HYPOTHESIS TESTING

A clinical trial begins with an assumption or belief, and then proceeds to either prove or disprove this assumption. In statistical terms, this belief or assumption is known as a hypothesis. Counterintuitively, what the researcher believes in (or is trying to prove) is called the “alternate” hypothesis, and the opposite is called the “null” hypothesis; every study has a null hypothesis and an alternate hypothesis. For superiority studies, the alternate hypothesis states that one treatment (usually the new or experimental treatment) is superior to the other; the null hypothesis states that there is no difference between the treatments (the treatments are equal). For example, in the ABLE study, we start by stating the null hypothesis—there is no difference in mortality between groups receiving fresh RBCs and standard-issue RBCs. We then state the alternate hypothesis—There is a difference between groups receiving fresh RBCs and standard-issue RBCs. It is important to note that we have stated that the groups are different, without specifying which group will be better than the other. This is known as a two-tailed hypothesis and it allows us to test for superiority on either side (using a two-sided test). This is because, when we start a study, we are not 100% certain that the new treatment can only be better than the standard treatment—it could be worse, and if it is so, the study should pick it up as well. One tailed hypothesis and one-sided statistical testing is done for non-inferiority studies, which will be discussed in a subsequent paper in this series.

STATISTICAL ERRORS

There are two possibilities to consider when interpreting the results of a superiority study. The first possibility is that there is truly no difference between the treatments but the study finds that they are different. This is called a Type-1 error or false-positive error or alpha error. This means falsely rejecting the null hypothesis.

The second possibility is that there is a difference between the treatments and the study does not pick up this difference. This is called a Type 2 error or false-negative error or beta error. This means falsely accepting the null hypothesis.

The power of the study is the ability to detect a difference between groups and is the converse of the beta error; i.e., power = 1-beta error. Alpha and beta errors are finalized when the protocol is written and form the basis for sample size calculation for the study. In an ideal world, we would not like any error in the results of our study; however, we would need to do the study in the entire population (infinite sample size) to be able to get a 0% alpha and beta error. These two errors enable us to do studies with realistic sample sizes, with the compromise that there is a small possibility that the results may not always reflect the truth. The basis for this will be discussed in a subsequent paper in this series dealing with sample size calculation.

Conventionally, type 1 or alpha error is set at 5%. This means, that at the end of the study, if there is a difference between groups, we want to be 95% certain that this is a true difference and allow only a 5% probability that this difference has occurred by chance (false positive). Type 2 or beta error is usually set between 10% and 20%; therefore, the power of the study is 90% or 80%. This means that if there is a difference between groups, we want to be 80% (or 90%) certain that the study will detect that difference. For example, in the ABLE study, sample size was calculated with a type 1 error of 5% (two-sided) and power of 90% (type 2 error of 10%) (1).

Table 1 gives a summary of the two types of statistical errors with an example

Statistical errors

In the next article in this series, we will look at the meaning and interpretation of ‘ p ’ value and confidence intervals for hypothesis testing.

Source of support: Nil

Conflict of interest: None

Null Hypothesis Definition and Examples

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• Ph.D., Biomedical Sciences, University of Tennessee at Knoxville
• B.A., Physics and Mathematics, Hastings College

In a scientific experiment, the null hypothesis is the proposition that there is no effect or no relationship between phenomena or populations. If the null hypothesis is true, any observed difference in phenomena or populations would be due to sampling error (random chance) or experimental error. The null hypothesis is useful because it can be tested and found to be false, which then implies that there is a relationship between the observed data. It may be easier to think of it as a nullifiable hypothesis or one that the researcher seeks to nullify. The null hypothesis is also known as the H 0, or no-difference hypothesis.

The alternate hypothesis, H A or H 1 , proposes that observations are influenced by a non-random factor. In an experiment, the alternate hypothesis suggests that the experimental or independent variable has an effect on the dependent variable .

How to State a Null Hypothesis

There are two ways to state a null hypothesis. One is to state it as a declarative sentence, and the other is to present it as a mathematical statement.

For example, say a researcher suspects that exercise is correlated to weight loss, assuming diet remains unchanged. The average length of time to achieve a certain amount of weight loss is six weeks when a person works out five times a week. The researcher wants to test whether weight loss takes longer to occur if the number of workouts is reduced to three times a week.

The first step to writing the null hypothesis is to find the (alternate) hypothesis. In a word problem like this, you're looking for what you expect to be the outcome of the experiment. In this case, the hypothesis is "I expect weight loss to take longer than six weeks."

This can be written mathematically as: H 1 : μ > 6

In this example, μ is the average.

Now, the null hypothesis is what you expect if this hypothesis does not happen. In this case, if weight loss isn't achieved in greater than six weeks, then it must occur at a time equal to or less than six weeks. This can be written mathematically as:

H 0 : μ ≤ 6

The other way to state the null hypothesis is to make no assumption about the outcome of the experiment. In this case, the null hypothesis is simply that the treatment or change will have no effect on the outcome of the experiment. For this example, it would be that reducing the number of workouts would not affect the time needed to achieve weight loss:

H 0 : μ = 6

Null Hypothesis Examples

"Hyperactivity is unrelated to eating sugar " is an example of a null hypothesis. If the hypothesis is tested and found to be false, using statistics, then a connection between hyperactivity and sugar ingestion may be indicated. A significance test is the most common statistical test used to establish confidence in a null hypothesis.

Another example of a null hypothesis is "Plant growth rate is unaffected by the presence of cadmium in the soil ." A researcher could test the hypothesis by measuring the growth rate of plants grown in a medium lacking cadmium, compared with the growth rate of plants grown in mediums containing different amounts of cadmium. Disproving the null hypothesis would set the groundwork for further research into the effects of different concentrations of the element in soil.

Why Test a Null Hypothesis?

You may be wondering why you would want to test a hypothesis just to find it false. Why not just test an alternate hypothesis and find it true? The short answer is that it is part of the scientific method. In science, propositions are not explicitly "proven." Rather, science uses math to determine the probability that a statement is true or false. It turns out it's much easier to disprove a hypothesis than to positively prove one. Also, while the null hypothesis may be simply stated, there's a good chance the alternate hypothesis is incorrect.

For example, if your null hypothesis is that plant growth is unaffected by duration of sunlight, you could state the alternate hypothesis in several different ways. Some of these statements might be incorrect. You could say plants are harmed by more than 12 hours of sunlight or that plants need at least three hours of sunlight, etc. There are clear exceptions to those alternate hypotheses, so if you test the wrong plants, you could reach the wrong conclusion. The null hypothesis is a general statement that can be used to develop an alternate hypothesis, which may or may not be correct.

• Kelvin Temperature Scale Definition
• Independent Variable Definition and Examples
• Theory Definition in Science
• Hypothesis Definition (Science)
• de Broglie Equation Definition
• Law of Combining Volumes Definition
• Chemical Definition
• Pure Substance Definition in Chemistry
• Acid Definition and Examples
• Extensive Property Definition (Chemistry)
• Radiation Definition and Examples
• Valence Definition in Chemistry
• Atomic Solid Definition
• Weak Base Definition and Examples
• Oxidation Definition and Example in Chemistry
• Definition of Binary Compound

9.1 Null and Alternative Hypotheses

The actual test begins by considering two hypotheses . They are called the null hypothesis and the alternative hypothesis . These hypotheses contain opposing viewpoints.

H 0 , the — null hypothesis: a statement of no difference between sample means or proportions or no difference between a sample mean or proportion and a population mean or proportion. In other words, the difference equals 0.

H a —, the alternative hypothesis: a claim about the population that is contradictory to H 0 and what we conclude when we reject H 0 .

Since the null and alternative hypotheses are contradictory, you must examine evidence to decide if you have enough evidence to reject the null hypothesis or not. The evidence is in the form of sample data.

After you have determined which hypothesis the sample supports, you make a decision. There are two options for a decision. They are reject H 0 if the sample information favors the alternative hypothesis or do not reject H 0 or decline to reject H 0 if the sample information is insufficient to reject the null hypothesis.

Mathematical Symbols Used in H 0 and H a :

H 0 always has a symbol with an equal in it. H a never has a symbol with an equal in it. The choice of symbol depends on the wording of the hypothesis test. However, be aware that many researchers use = in the null hypothesis, even with > or < as the symbol in the alternative hypothesis. This practice is acceptable because we only make the decision to reject or not reject the null hypothesis.

Example 9.1

H 0 : No more than 30 percent of the registered voters in Santa Clara County voted in the primary election. p ≤ 30 H a : More than 30 percent of the registered voters in Santa Clara County voted in the primary election. p > 30

A medical trial is conducted to test whether or not a new medicine reduces cholesterol by 25 percent. State the null and alternative hypotheses.

Example 9.2

We want to test whether the mean GPA of students in American colleges is different from 2.0 (out of 4.0). The null and alternative hypotheses are the following: H 0 : μ = 2.0 H a : μ ≠ 2.0

We want to test whether the mean height of eighth graders is 66 inches. State the null and alternative hypotheses. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.

• H 0 : μ __ 66
• H a : μ __ 66

Example 9.3

We want to test if college students take fewer than five years to graduate from college, on the average. The null and alternative hypotheses are the following: H 0 : μ ≥ 5 H a : μ < 5

We want to test if it takes fewer than 45 minutes to teach a lesson plan. State the null and alternative hypotheses. Fill in the correct symbol ( =, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.

• H 0 : μ __ 45
• H a : μ __ 45

Example 9.4

An article on school standards stated that about half of all students in France, Germany, and Israel take advanced placement exams and a third of the students pass. The same article stated that 6.6 percent of U.S. students take advanced placement exams and 4.4 percent pass. Test if the percentage of U.S. students who take advanced placement exams is more than 6.6 percent. State the null and alternative hypotheses. H 0 : p ≤ 0.066 H a : p > 0.066

On a state driver’s test, about 40 percent pass the test on the first try. We want to test if more than 40 percent pass on the first try. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.

• H 0 : p __ 0.40
• H a : p __ 0.40

Collaborative Exercise

Bring to class a newspaper, some news magazines, and some internet articles. In groups, find articles from which your group can write null and alternative hypotheses. Discuss your hypotheses with the rest of the class.

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Access for free at https://openstax.org/books/statistics/pages/1-introduction

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• Publication date: Mar 27, 2020
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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.

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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.

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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.

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Once you have developed a clear and focused research question or set of research questions, you’ll be ready to conduct further research, a literature review, on the topic to help you make an educated guess about the answer to your question(s). This educated guess is called a hypothesis.

In research, there are two types of hypotheses: null and alternative. They work as a complementary pair, each stating that the other is wrong.

• Null Hypothesis (H 0 ) – This can be thought of as the implied hypothesis. “Null” meaning “nothing.”  This hypothesis states that there is no difference between groups or no relationship between variables. The null hypothesis is a presumption of status quo or no change.
• Alternative Hypothesis (H a ) – This is also known as the claim. This hypothesis should state what you expect the data to show, based on your research on the topic. This is your answer to your research question.

Null Hypothesis:   H 0 : There is no difference in the salary of factory workers based on gender. Alternative Hypothesis :  H a : Male factory workers have a higher salary than female factory workers.

Null Hypothesis :  H 0 : There is no relationship between height and shoe size. Alternative Hypothesis :  H a : There is a positive relationship between height and shoe size.

Null Hypothesis :  H 0 : Experience on the job has no impact on the quality of a brick mason’s work. Alternative Hypothesis :  H a : The quality of a brick mason’s work is influenced by on-the-job experience.

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Null Hypothesis vs. Hypothesis: What’s the Difference?

Updated: September 25, 2024 by Liam Frady

Null hypothesis vs. hypothesis, which is the right choice? When you get into the different methods of analyzing data, there is no shortage of tools at your disposal. Understanding the difference between a null hypothesis and a hypothesis can make or break your testing and analysis stages. Let’s dive into both of these tools and clarify which is best suited for a given application.

What Is the Null Hypothesis?

A null hypothesis is a prediction that there is no statistical relationship between two variables or two sets of data. Essentially, a null hypothesis assumes that any measured differences are the result of randomness and that the two possibilities are the same until proven otherwise.

The Benefits of a Null Hypothesis

A null hypothesis is commonly used in research to determine whether there is a real relationship between two measured phenomena. To this end, it offers the ability to distinguish between results that are the result of random chance or if there is a legitimate statistical relationship.

How to Create a Null Hypothesis

To create a null hypothesis, start by asking a few questions about the set of data or experiments. Then rephrase those questions into a statement that assumes no relationship. Subsequently, null hypotheses usually include phrases such as “no relationship,” “no effect,” etc.

For example, let’s say you are looking at some data about whether the number of people on a project affects the overall ability of the team to accomplish its goals.

A question might look like this:

“Does the number of people working on a team project impact the ability of the team to achieve the goals of the project?”

However, rephrasing this into a null hypothesis that assumes no relationship would look like this:

“The number of people working on a team project does not impact the ability of the team to achieve the goals of the project.”

The null hypothesis is assumed true until proven otherwise.

What Is a Hypothesis?

A hypothesis, also known as an alternative hypothesis, is an educated theory or “guess” based on limited evidence that requires further testing to be proven true or false. It is used in an experiment to define a relationship between two variables.

The Benefits of a Hypothesis

A hypothesis helps a researcher prove or disprove their theories, or guesses, using limited data and knowledge. In effect, researchers and scientists will create a formalized hypothesis based on past data or experiments. This hypothesis forces them to think about what they should be looking for in their experiments.

How to Create a Hypothesis

The best way to create a hypothesis is first to create a null hypothesis. Once you have your null hypothesis that states there is no relationship, you can then revise the statement that implies a relationship does exist. This is the reason it is referred to as an “alternative hypothesis.”

As an example:

Null hypothesis: There is no relationship between mediation and the reduction of depression. Alternative hypothesis: The practice of meditation reduces depression.

In this example, the research wants to disprove that there is no relationship between meditation and the reduction of depression and prove that meditation does reduce depression. Specifically, the researcher’s goal is to prove their hypothesis through statistical data.

Null Hypothesis vs. Hypothesis: What’s the Difference?

In the simplest terms, a hypothesis is something that a researcher tries to prove, while a null hypothesis is something that a researcher tries to disprove. Both are used when performing research and evaluating data.

There are two variables in a hypothesis. The first is called the independent variable. This is the driving force of the experiment or research. The second is called the dependent variable, which is the measurable result.

However, the biggest difference between the two is that a null hypothesis cannot be proven; it can only be rejected.

Null Hypothesis vs. Hypothesis: Who Would Use Null Hypothesis and/or Hypothesis?

Having both a null hypothesis and hypothesis is beneficial and required in nearly all fields of research. Having both null and alternative hypotheses offers competing views in your research. Researchers weigh the evidence for and against the two hypotheses using a statistical test.

The statistical data is used to prove or disprove the alternative hypothesis. Additionally, If an alternative hypothesis is disproved, researchers can then modify their alternative hypothesis and look at their experimentation method(s) to achieve their goals and improve the accuracy of their experiments.

Choosing Between Null Hypothesis and Hypothesis: Real World Scenarios

Null and alternative hypotheses are used extensively in medical research. As such, let’s say a team of researchers is trying to determine if flossing decreases the number of cavities a person might experience.

Their null hypothesis might look like this:

“There is no relationship between tooth flossing and the number of cavities a person experiences.”

Their alternative hypothesis might be:

“Tooth flossing reduces the number of cavities a person experiences.”

In the world of investing, a null hypothesis is frequently used in the quantitative analysis of data to test theories about economies, investing strategies, and other financial markets.

An example of a null hypothesis: The mean annual return of a stock option is 3%.

An example of an alternative hypothesis: The mean annual return of a stock option is NOT 3%.

Essentially, the theories are the alternative hypothesis you are trying to prove, and the null hypothesis is the statement you are trying to disprove.

The bottom line is that both types of hypotheses are required for proper research and data evaluation. Create a null hypothesis to disprove and an alternative hypothesis to prove. Collect and evaluate the data to determine which hypothesis is favored.

About the Author

What Is A Research Hypothesis?

A Plain-Language Explainer + Practical Examples

Research Hypothesis 101

• What is a hypothesis ?
• What is a research hypothesis (scientific hypothesis)?
• Requirements for a research hypothesis
• Definition of a research hypothesis
• The null hypothesis

What is a hypothesis?

Let’s start with the general definition of a hypothesis (not a research hypothesis or scientific hypothesis), according to the Cambridge Dictionary:

Hypothesis: an idea or explanation for something that is based on known facts but has not yet been proved.

In other words, it’s a statement that provides an explanation for why or how something works, based on facts (or some reasonable assumptions), but that has not yet been specifically tested . For example, a hypothesis might look something like this:

Hypothesis: sleep impacts academic performance.

This statement predicts that academic performance will be influenced by the amount and/or quality of sleep a student engages in – sounds reasonable, right? It’s based on reasonable assumptions , underpinned by what we currently know about sleep and health (from the existing literature). So, loosely speaking, we could call it a hypothesis, at least by the dictionary definition.

But that’s not good enough…

Unfortunately, that’s not quite sophisticated enough to describe a research hypothesis (also sometimes called a scientific hypothesis), and it wouldn’t be acceptable in a dissertation, thesis or research paper . In the world of academic research, a statement needs a few more criteria to constitute a true research hypothesis .

What is a research hypothesis?

A research hypothesis (also called a scientific hypothesis) is a statement about the expected outcome of a study (for example, a dissertation or thesis). To constitute a quality hypothesis, the statement needs to have three attributes – specificity , clarity and testability .

Let’s take a look at these more closely.

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Hypothesis Essential #1: Specificity & Clarity

A good research hypothesis needs to be extremely clear and articulate about both what’ s being assessed (who or what variables are involved ) and the expected outcome (for example, a difference between groups, a relationship between variables, etc.).

Let’s stick with our sleepy students example and look at how this statement could be more specific and clear.

Hypothesis: Students who sleep at least 8 hours per night will, on average, achieve higher grades in standardised tests than students who sleep less than 8 hours a night.

As you can see, the statement is very specific as it identifies the variables involved (sleep hours and test grades), the parties involved (two groups of students), as well as the predicted relationship type (a positive relationship). There’s no ambiguity or uncertainty about who or what is involved in the statement, and the expected outcome is clear.

Contrast that to the original hypothesis we looked at – “Sleep impacts academic performance” – and you can see the difference. “Sleep” and “academic performance” are both comparatively vague , and there’s no indication of what the expected relationship direction is (more sleep or less sleep). As you can see, specificity and clarity are key.

Hypothesis Essential #2: Testability (Provability)

A statement must be testable to qualify as a research hypothesis. In other words, there needs to be a way to prove (or disprove) the statement. If it’s not testable, it’s not a hypothesis – simple as that.

For example, consider the hypothesis we mentioned earlier:

We could test this statement by undertaking a quantitative study involving two groups of students, one that gets 8 or more hours of sleep per night for a fixed period, and one that gets less. We could then compare the standardised test results for both groups to see if there’s a statistically significant difference.

Again, if you compare this to the original hypothesis we looked at – “Sleep impacts academic performance” – you can see that it would be quite difficult to test that statement, primarily because it isn’t specific enough. How much sleep? By who? What type of academic performance?

So, remember the mantra – if you can’t test it, it’s not a hypothesis 🙂

Defining A Research Hypothesis

You’re still with us? Great! Let’s recap and pin down a clear definition of a hypothesis.

A research hypothesis (or scientific hypothesis) is a statement about an expected relationship between variables, or explanation of an occurrence, that is clear, specific and testable.

So, when you write up hypotheses for your dissertation or thesis, make sure that they meet all these criteria. If you do, you’ll not only have rock-solid hypotheses but you’ll also ensure a clear focus for your entire research project.

What about the null hypothesis?

You may have also heard the terms null hypothesis , alternative hypothesis, or H-zero thrown around. At a simple level, the null hypothesis is the counter-proposal to the original hypothesis.

For example, if the hypothesis predicts that there is a relationship between two variables (for example, sleep and academic performance), the null hypothesis would predict that there is no relationship between those variables.

At a more technical level, the null hypothesis proposes that no statistical significance exists in a set of given observations and that any differences are due to chance alone.

And there you have it – hypotheses in a nutshell. 

If you have any questions, be sure to leave a comment below and we’ll do our best to help you. If you need hands-on help developing and testing your hypotheses, consider our private coaching service , where we hold your hand through the research journey.

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Triangulation: The Ultimate Credibility Enhancer

Triangulation is one of the best ways to enhance the credibility of your research. Learn about the different options here.

Research Limitations 101: What You Need To Know

Learn everything you need to know about research limitations (AKA limitations of the study). Includes practical examples from real studies.

In Vivo Coding 101: Full Explainer With Examples

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17 Comments

Very useful information. I benefit more from getting more information in this regard.

Very great insight,educative and informative. Please give meet deep critics on many research data of public international Law like human rights, environment, natural resources, law of the sea etc

In a book I read a distinction is made between null, research, and alternative hypothesis. As far as I understand, alternative and research hypotheses are the same. Can you please elaborate? Best Afshin

This is a self explanatory, easy going site. I will recommend this to my friends and colleagues.

Very good definition. How can I cite your definition in my thesis? Thank you. Is nul hypothesis compulsory in a research?

It’s a counter-proposal to be proven as a rejection

Please what is the difference between alternate hypothesis and research hypothesis?

It is a very good explanation. However, it limits hypotheses to statistically tasteable ideas. What about for qualitative researches or other researches that involve quantitative data that don’t need statistical tests?

In qualitative research, one typically uses propositions, not hypotheses.

could you please elaborate it more

I’ve benefited greatly from these notes, thank you.

This is very helpful

well articulated ideas are presented here, thank you for being reliable sources of information

Excellent. Thanks for being clear and sound about the research methodology and hypothesis (quantitative research)

I have only a simple question regarding the null hypothesis. – Is the null hypothesis (Ho) known as the reversible hypothesis of the alternative hypothesis (H1? – How to test it in academic research?

this is very important note help me much more

Hi” best wishes to you and your very nice blog” 

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13 Different Types of Hypothesis

Chris Drew (PhD)

Dr. Chris Drew is the founder of the Helpful Professor. He holds a PhD in education and has published over 20 articles in scholarly journals. He is the former editor of the Journal of Learning Development in Higher Education. [Image Descriptor: Photo of Chris]

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There are 13 different types of hypothesis. These include simple, complex, null, alternative, composite, directional, non-directional, logical, empirical, statistical, associative, exact, and inexact.

A hypothesis can be categorized into one or more of these types. However, some are mutually exclusive and opposites. Simple and complex hypotheses are mutually exclusive, as are direction and non-direction, and null and alternative hypotheses.

Below I explain each hypothesis in simple terms for absolute beginners. These definitions may be too simple for some, but they’re designed to be clear introductions to the terms to help people wrap their heads around the concepts early on in their education about research methods .

Types of Hypothesis

Before you Proceed: Dependent vs Independent Variables

A research study and its hypotheses generally examine the relationships between independent and dependent variables – so you need to know these two concepts:

• The independent variable is the variable that is causing a change.
• The dependent variable is the variable the is affected by the change. This is the variable being tested.

Read my full article on dependent vs independent variables for more examples.

Example: Eating carrots (independent variable) improves eyesight (dependent variable).

1. Simple Hypothesis

A simple hypothesis is a hypothesis that predicts a correlation between two test variables: an independent and a dependent variable.

This is the easiest and most straightforward type of hypothesis. You simply need to state an expected correlation between the dependant variable and the independent variable.

You do not need to predict causation (see: directional hypothesis). All you would need to do is prove that the two variables are linked.

Simple Hypothesis Examples

2. Complex Hypothesis

A complex hypothesis is a hypothesis that contains multiple variables, making the hypothesis more specific but also harder to prove.

You can have multiple independent and dependant variables in this hypothesis.

Complex Hypothesis Example

In the above example, we have multiple independent and dependent variables:

• Independent variables: Age and weight.
• Dependent variables: diabetes and heart disease.

Because there are multiple variables, this study is a lot more complex than a simple hypothesis. It quickly gets much more difficult to prove these hypotheses. This is why undergraduate and first-time researchers are usually encouraged to use simple hypotheses.

3. Null Hypothesis

A null hypothesis will predict that there will be no significant relationship between the two test variables.

For example, you can say that “The study will show that there is no correlation between marriage and happiness.”

A good way to think about a null hypothesis is to think of it in the same way as “innocent until proven guilty”[1]. Unless you can come up with evidence otherwise, your null hypothesis will stand.

A null hypothesis may also highlight that a correlation will be inconclusive . This means that you can predict that the study will not be able to confirm your results one way or the other. For example, you can say “It is predicted that the study will be unable to confirm a correlation between the two variables due to foreseeable interference by a third variable .”

Beware that an inconclusive null hypothesis may be questioned by your teacher. Why would you conduct a test that you predict will not provide a clear result? Perhaps you should take a closer look at your methodology and re-examine it. Nevertheless, inconclusive null hypotheses can sometimes have merit.

Null Hypothesis Examples

4. Alternative Hypothesis

An alternative hypothesis is a hypothesis that is anything other than the null hypothesis. It will disprove the null hypothesis.

We use the symbol H A or H 1 to denote an alternative hypothesis.

The null and alternative hypotheses are usually used together. We will say the null hypothesis is the case where a relationship between two variables is non-existent. The alternative hypothesis is the case where there is a relationship between those two variables.

The following statement is always true: H 0 ≠ H A .

Let’s take the example of the hypothesis: “Does eating oatmeal before an exam impact test scores?”

We can have two hypotheses here:

• Null hypothesis (H 0 ): “Eating oatmeal before an exam does not impact test scores.”
• Alternative hypothesis (H A ): “Eating oatmeal before an exam does impact test scores.”

For the alternative hypothesis to be true, all we have to do is disprove the null hypothesis for the alternative hypothesis to be true. We do not need an exact prediction of how much oatmeal will impact the test scores or even if the impact is positive or negative. So long as the null hypothesis is proven to be false, then the alternative hypothesis is proven to be true.

5. Composite Hypothesis

A composite hypothesis is a hypothesis that does not predict the exact parameters, distribution, or range of the dependent variable.

Often, we would predict an exact outcome. For example: “23 year old men are on average 189cm tall.” Here, we are giving an exact parameter. So, the hypothesis is not composite.

But, often, we cannot exactly hypothesize something. We assume that something will happen, but we’re not exactly sure what. In these cases, we might say: “23 year old men are not on average 189cm tall.”

We haven’t set a distribution range or exact parameters of the average height of 23 year old men. So, we’ve introduced a composite hypothesis as opposed to an exact hypothesis.

Generally, an alternative hypothesis (discussed above) is composite because it is defined as anything except the null hypothesis. This ‘anything except’ does not define parameters or distribution, and therefore it’s an example of a composite hypothesis.

6. Directional Hypothesis

A directional hypothesis makes a prediction about the positivity or negativity of the effect of an intervention prior to the test being conducted.

Instead of being agnostic about whether the effect will be positive or negative, it nominates the effect’s directionality.

We often call this a one-tailed hypothesis (in contrast to a two-tailed or non-directional hypothesis) because, looking at a distribution graph, we’re hypothesizing that the results will lean toward one particular tail on the graph – either the positive or negative.

Directional Hypothesis Examples

7. Non-Directional Hypothesis

A non-directional hypothesis does not specify the predicted direction (e.g. positivity or negativity) of the effect of the independent variable on the dependent variable.

These hypotheses predict an effect, but stop short of saying what that effect will be.

A non-directional hypothesis is similar to composite and alternative hypotheses. All three types of hypothesis tend to make predictions without defining a direction. In a composite hypothesis, a specific prediction is not made (although a general direction may be indicated, so the overlap is not complete). For an alternative hypothesis, you often predict that the even will be anything but the null hypothesis, which means it could be more or less than H 0 (or in other words, non-directional).

Let’s turn the above directional hypotheses into non-directional hypotheses.

Non-Directional Hypothesis Examples

8. Logical Hypothesis

A logical hypothesis is a hypothesis that cannot be tested, but has some logical basis underpinning our assumptions.

These are most commonly used in philosophy because philosophical questions are often untestable and therefore we must rely on our logic to formulate logical theories.

Usually, we would want to turn a logical hypothesis into an empirical one through testing if we got the chance. Unfortunately, we don’t always have this opportunity because the test is too complex, expensive, or simply unrealistic.

Here are some examples:

• Before the 1980s, it was hypothesized that the Titanic came to its resting place at 41° N and 49° W, based on the time the ship sank and the ship’s presumed path across the Atlantic Ocean. However, due to the depth of the ocean, it was impossible to test. Thus, the hypothesis was simply a logical hypothesis.
• Dinosaurs closely related to Aligators probably had green scales because Aligators have green scales. However, as they are all extinct, we can only rely on logic and not empirical data.

9. Empirical Hypothesis

An empirical hypothesis is the opposite of a logical hypothesis. It is a hypothesis that is currently being tested using scientific analysis. We can also call this a ‘working hypothesis’.

We can to separate research into two types: theoretical and empirical. Theoretical research relies on logic and thought experiments. Empirical research relies on tests that can be verified by observation and measurement.

So, an empirical hypothesis is a hypothesis that can and will be tested.

• Raising the wage of restaurant servers increases staff retention.
• Adding 1 lb of corn per day to cows’ diets decreases their lifespan.
• Mushrooms grow faster at 22 degrees Celsius than 27 degrees Celsius.

Each of the above hypotheses can be tested, making them empirical rather than just logical (aka theoretical).

10. Statistical Hypothesis

A statistical hypothesis utilizes representative statistical models to draw conclusions about broader populations.

It requires the use of datasets or carefully selected representative samples so that statistical inference can be drawn across a larger dataset.

This type of research is necessary when it is impossible to assess every single possible case. Imagine, for example, if you wanted to determine if men are taller than women. You would be unable to measure the height of every man and woman on the planet. But, by conducting sufficient random samples, you would be able to predict with high probability that the results of your study would remain stable across the whole population.

You would be right in guessing that almost all quantitative research studies conducted in academic settings today involve statistical hypotheses.

Statistical Hypothesis Examples

• Human Sex Ratio. The most famous statistical hypothesis example is that of John Arbuthnot’s sex at birth case study in 1710. Arbuthnot used birth data to determine with high statistical probability that there are more male births than female births. He called this divine providence, and to this day, his findings remain true: more men are born than women.
• Lady Testing Tea. A 1935 study by Ronald Fisher involved testing a woman who believed she could tell whether milk was added before or after water to a cup of tea. Fisher gave her 4 cups in which one randomly had milk placed before the tea. He repeated the test 8 times. The lady was correct each time. Fisher found that she had a 1 in 70 chance of getting all 8 test correct, which is a statistically significant result.

11. Associative Hypothesis

An associative hypothesis predicts that two variables are linked but does not explore whether one variable directly impacts upon the other variable.

We commonly refer to this as “ correlation does not mean causation ”. Just because there are a lot of sick people in a hospital, it doesn’t mean that the hospital made the people sick. There is something going on there that’s causing the issue (sick people are flocking to the hospital).

So, in an associative hypothesis, you note correlation between an independent and dependent variable but do not make a prediction about how the two interact. You stop short of saying one thing causes another thing.

Associative Hypothesis Examples

• Sick people in hospital. You could conduct a study hypothesizing that hospitals have more sick people in them than other institutions in society. However, you don’t hypothesize that the hospitals caused the sickness.
• Lice make you healthy. In the Middle Ages, it was observed that sick people didn’t tend to have lice in their hair. The inaccurate conclusion was that lice was not only a sign of health, but that they made people healthy. In reality, there was an association here, but not causation. The fact was that lice were sensitive to body temperature and fled bodies that had fevers.

12. Causal Hypothesis

A causal hypothesis predicts that two variables are not only associated, but that changes in one variable will cause changes in another.

A causal hypothesis is harder to prove than an associative hypothesis because the cause needs to be definitively proven. This will often require repeating tests in controlled environments with the researchers making manipulations to the independent variable, or the use of control groups and placebo effects .

If we were to take the above example of lice in the hair of sick people, researchers would have to put lice in sick people’s hair and see if it made those people healthier. Researchers would likely observe that the lice would flee the hair, but the sickness would remain, leading to a finding of association but not causation.

Causal Hypothesis Examples

13. Exact vs. Inexact Hypothesis

For brevity’s sake, I have paired these two hypotheses into the one point. The reality is that we’ve already seen both of these types of hypotheses at play already.

An exact hypothesis (also known as a point hypothesis) specifies a specific prediction whereas an inexact hypothesis assumes a range of possible values without giving an exact outcome. As Helwig [2] argues:

“An “exact” hypothesis specifies the exact value(s) of the parameter(s) of interest, whereas an “inexact” hypothesis specifies a range of possible values for the parameter(s) of interest.”

Generally, a null hypothesis is an exact hypothesis whereas alternative, composite, directional, and non-directional hypotheses are all inexact.

See Next: 15 Hypothesis Examples

This is introductory information that is basic and indeed quite simplified for absolute beginners. It’s worth doing further independent research to get deeper knowledge of research methods and how to conduct an effective research study. And if you’re in education studies, don’t miss out on my list of the best education studies dissertation ideas .

[1] https://jnnp.bmj.com/content/91/6/571.abstract

[2] http://users.stat.umn.edu/~helwig/notes/SignificanceTesting.pdf

• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd-2/ 10 Reasons you’re Perpetually Single
• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd-2/ 20 Montessori Toddler Bedrooms (Design Inspiration)
• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd-2/ 21 Montessori Homeschool Setups
• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd-2/ 101 Hidden Talents Examples

2 thoughts on “13 Different Types of Hypothesis”

Wow! This introductionary materials are very helpful. I teach the begginers in research for the first time in my career. The given tips and materials are very helpful. Chris, thank you so much! Excellent materials!

You’re more than welcome! If you want a pdf version of this article to provide for your students to use as a weekly reading on in-class discussion prompt for seminars, just drop me an email in the Contact form and I’ll get one sent out to you.

When I’ve taught this seminar, I’ve put my students into groups, cut these definitions into strips, and handed them out to the groups. Then I get them to try to come up with hypotheses that fit into each ‘type’. You can either just rotate hypothesis types so they get a chance at creating a hypothesis of each type, or get them to “teach” their hypothesis type and examples to the class at the end of the seminar.

Cheers, Chris

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Home » Research Hypothesis Vs Null Hypothesis

Research Hypothesis Vs Null Hypothesis

Table of Contents

The difference between Research Hypothesis Vs Null Hypothesis is as follows:

Research Hypothesis

A Research Hypothesis is a tentative statement that proposes a relationship between two or more variables. It is based on a theoretical or conceptual framework and is typically tested through empirical research.

Null Hypothesis

A Null Hypothesis is a statement that proposes that there is no relationship between two or more variables. It is the opposite of the research hypothesis and is used as a comparison in statistical analysis.

Comparison Table:

In summary, a research hypothesis proposes a relationship between variables, while a null hypothesis proposes no relationship between variables. The research hypothesis guides empirical research, while the null hypothesis is used as a comparison in statistical analysis. The research hypothesis is supported if statistical analysis provides evidence to reject the null hypothesis, while the null hypothesis is rejected if statistical analysis provides evidence to support the research hypothesis.

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What Is a Null Hypothesis?

The alternative hypothesis.

• Additional Examples
• Null Hypothesis and Investments

The Bottom Line

• Corporate Finance
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Null Hypothesis: What Is It, and How Is It Used in Investing?

Adam Hayes, Ph.D., CFA, is a financial writer with 15+ years Wall Street experience as a derivatives trader. Besides his extensive derivative trading expertise, Adam is an expert in economics and behavioral finance. Adam received his master's in economics from The New School for Social Research and his Ph.D. from the University of Wisconsin-Madison in sociology. He is a CFA charterholder as well as holding FINRA Series 7, 55 & 63 licenses. He currently researches and teaches economic sociology and the social studies of finance at the Hebrew University in Jerusalem.

Yarilet Perez is an experienced multimedia journalist and fact-checker with a Master of Science in Journalism. She has worked in multiple cities covering breaking news, politics, education, and more. Her expertise is in personal finance and investing, and real estate.

A null hypothesis is a type of statistical hypothesis that proposes that no statistical significance exists in a set of given observations. Hypothesis testing is used to assess the credibility of a hypothesis by using sample data. Sometimes referred to simply as the “null,” it is represented as H 0 .

The null hypothesis, also known as “the conjecture,” is used in quantitative analysis to test theories about markets, investing strategies, and economies to decide if an idea is true or false.

Key Takeaways

• A null hypothesis is a type of conjecture in statistics that proposes that there is no difference between certain characteristics of a population or data-generating process.
• The alternative hypothesis proposes that there is a difference.
• Hypothesis testing provides a method to reject a null hypothesis within a certain confidence level.
• If you can reject the null hypothesis, it provides support for the alternative hypothesis.
• Null hypothesis testing is the basis of the principle of falsification in science.

Alex Dos Diaz / Investopedia

Understanding a Null Hypothesis

A gambler may be interested in whether a game of chance is fair. If it is, then the expected earnings per play come to zero for both players. If it is not, then the expected earnings are positive for one player and negative for the other.

To test whether the game is fair, the gambler collects earnings data from many repetitions of the game, calculates the average earnings from these data, then tests the null hypothesis that the expected earnings are not different from zero.

If the average earnings from the sample data are sufficiently far from zero, then the gambler will reject the null hypothesis and conclude the alternative hypothesis—namely, that the expected earnings per play are different from zero. If the average earnings from the sample data are near zero, then the gambler will not reject the null hypothesis, concluding instead that the difference between the average from the data and zero is explainable by chance alone.

A null hypothesis can only be rejected, not proven.

The null hypothesis assumes that any kind of difference between the chosen characteristics that you see in a set of data is due to chance. For example, if the expected earnings for the gambling game are truly equal to zero, then any difference between the average earnings in the data and zero is due to chance.

Analysts look to reject   the null hypothesis because doing so is a strong conclusion. This requires evidence in the form of an observed difference that is too large to be explained solely by chance. Failing to reject the null hypothesis—that the results are explainable by chance alone—is a weak conclusion because it allows that while factors other than chance may be at work, they may not be strong enough for the statistical test to detect them.

An important point to note is that we are testing the null hypothesis because there is an element of doubt about its validity. Whatever information that is against the stated null hypothesis is captured in the alternative (alternate) hypothesis (H 1 ).

For the examples below, the alternative hypothesis would be:

• Students score an average that is not equal to seven.
• The mean annual return of a mutual fund is not equal to 8% per year.

In other words, the alternative hypothesis is a direct contradiction of the null hypothesis.

Null Hypothesis Examples

Here is a simple example: A school principal claims that students in their school score an average of seven out of 10 in exams. The null hypothesis is that the population mean is not 7.0. To test this null hypothesis, we record marks of, say, 30 students ( sample ) from the entire student population of the school (say, 300) and calculate the mean of that sample.

We can then compare the (calculated) sample mean to the (hypothesized) population mean of 7.0 and attempt to reject the null hypothesis. (The null hypothesis here—that the population mean is not 7.0—cannot be proved using the sample data. It can only be rejected.)

Take another example: The annual return of a particular  mutual fund  is claimed to be 8%. Assume that the mutual fund has been in existence for 20 years. The null hypothesis is that the mean return is not 8% for the mutual fund. We take a random sample of annual returns of the mutual fund for, say, five years (sample) and calculate the sample mean. We then compare the (calculated) sample mean to the (claimed) population mean (8%) to test the null hypothesis.

For the above examples, null hypotheses are:

• Example A: Students in the school don’t score an average of seven out of 10 in exams.
• Example B: The mean annual return of the mutual fund is not 8% per year.

For the purposes of determining whether to reject the null hypothesis (abbreviated H0), said hypothesis is assumed, for the sake of argument, to be true. Then the likely range of possible values of the calculated statistic (e.g., the average score on 30 students’ tests) is determined under this presumption (e.g., the range of plausible averages might range from 6.2 to 7.8 if the population mean is 7.0).

If the sample average is outside of this range, the null hypothesis is rejected. Otherwise, the difference is said to be “explainable by chance alone,” being within the range that is determined by chance alone.

Traditional null hypothesis testing, consisting of a comparative statistical test for two competing theories, was suggested by Ronald Fisher in 1925.

How Null Hypothesis Testing Is Used in Investments

As an example related to financial markets, assume Alice sees that her investment strategy produces higher average returns than simply buying and holding a stock . The null hypothesis states that there is no difference between the two average returns, and Alice is inclined to believe this until she can conclude contradictory results.

Refuting the null hypothesis would require showing statistical significance, which can be found by a variety of tests. The alternative hypothesis would state that the investment strategy has a higher average return than a traditional buy-and-hold strategy.

One tool that can determine the statistical significance of the results is the p-value. A p-value represents the probability that a difference as large or larger than the observed difference between the two average returns could occur solely by chance.

A p-value that is less than or equal to 0.05 often indicates whether there is evidence against the null hypothesis. If Alice conducts one of these tests, such as a test using the normal model, resulting in a significant difference between her returns and the buy-and-hold returns (the p-value is less than or equal to 0.05), she can then reject the null hypothesis and conclude the alternative hypothesis.

How Is the Null Hypothesis Identified?

The analyst or researcher establishes a null hypothesis based on the research question or problem they are trying to answer. Depending on the question, the null may be identified differently. For example, if the question is simply whether an effect exists (e.g., does X influence Y?), the null hypothesis could be H 0 : X = 0. If the question is instead, is X the same as Y, the H 0 would be X = Y. If it is that the effect of X on Y is positive, H 0 would be X > 0. If the resulting analysis shows an effect that is statistically significantly different from zero, the null can be rejected.

How Is Null Hypothesis Used in Finance?

In finance , a null hypothesis is used in quantitative analysis. It tests the premise of an investing strategy, the markets, or an economy to determine if it is true or false.

For instance, an analyst may want to see if two stocks, ABC and XYZ, are closely correlated. The null hypothesis would be ABC ≠ XYZ.

How Are Statistical Hypotheses Tested?

Statistical hypotheses are tested in a four-step process . The first is for the analyst to state the two hypotheses so that only one can be right. The second is to formulate an analysis plan, which outlines how the data will be evaluated. The third is to carry out the plan and physically analyze the sample data. The fourth and final step is to analyze the results and either reject the null hypothesis or claim that the observed differences are explainable by chance alone.

What Is an Alternative Hypothesis?

An alternative hypothesis is a direct contradiction of a null hypothesis. This means that if one of the two hypotheses is true, the other is false.

A null hypothesis states there is no difference between groups or relationship between variables. It is a type of statistical hypothesis and proposes that no statistical significance exists in a set of given observations. “Null” means nothing.

The null hypothesis is used in quantitative analysis to test theories about economies, investing strategies, and markets to decide if an idea is true or false. Hypothesis testing assesses the credibility of a hypothesis by using sample data. It is represented as H 0 and is sometimes simply known as “the null.”

Correction—July 23, 2024:  This article was corrected to state accurate examples of null hypothesis in the Null Hypothesis Examples section.

National Library of Medicine. " Current Controversies: Null Hypotheses in Statistical Testing ."

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Question: 4. The alternative hypothesis is also known as the _____ hypothesis. a. optional b. elective

4. The alternative hypothesis is also known as the _____ hypothesis.

a. optional b. elective c. null d. research 5. One-tailed alternative hypotheses use the _____ symbol. a. ≤ or ≥ b. = c. < or > d. ≠ 6. A type II error occurs when the a. null hypothesis is incorrectly rejected when it is true. b. null hypothesis is incorrectly accepted when it is false. c. test procedure itself is fundamentally biased. 4)The alternative hypothesis is also called research hypothesis, so option (D) is the answer. Not the question you’re looking for? Post any question and get expert help quickly. The Environmental Kuznets Curve (EKC) Hypothesis on GHG emissions: analyses for transportation industry of South Africa Open access Published: 27 September 2024 Volume 5 , article number  302 , ( 2024 ) Cite this article You have full access to this open access article Oluwole Joseph Oladunni   ORCID: orcid.org/0000-0002-2718-7974 1 , 2 , Oludolapo A. Olanrewaju 1 & Carman K. M. Lee 2   A series of energy-econometrics techniques were employed for a 5-year time span between 2016 and 2020. The tests of Environmental Kuznets Curve (EKC) hypothesis were conducted essentially to examine the significance of economic growth (GDP), energy consumption (EC), with energy intensity (EI), and on-road passenger vehicles (PV) as related to economic development on the mitigation of carbon emissions (CO 2 - eq ) in the transportation industry of South Africa. The findings from the prevailing research imply that, with respect to South Africa’s transportation industry, CO 2 - eq emissions increased in the course of early phases of economic growth while it tends to decline at certain levels of economic threshold. Though the nation maintains the edge of turning points in both the industrial and circular economy. The results further indicate a nexus between GDP and EC, which consequently affect the CO 2 - eq emissions. The findings proffer the needs to monitor the EC from the long-run impacts alongside the short run impacts of the forecast. The per capita GDP from the short-run impacts of t-stat—(4.928) to the long run effects of t-stat—(5.033) rises, indicating its improper influence in the industry. To limit the use of fossil-based fuels, as demonstrated in the negative signal of EI for long-run impacts of a p-value (0.2835), then to the short run effects which possess a significant p-value. It also highlights the directional correlation surfacing between EC, EI and South Africa’s on-road PV. In the computation context, the series was determined to be stationary at its first differences, as evident by the R 2 combined with the R 2 (Adjusted) values of 0.9837 and 0.9827, respectively, for both long-run and short-run assessments. The indication of the research among others further reveals that public transportation systems of road and rail options, which have the potentials to incorporate alternative energy sources, can be the required efforts to mitigate climate change and global warming effects in the transportation industry. Avoid common mistakes on your manuscript. 1 Introduction The World Health Organization links air pollution to airborne particles that are harmful to living beings when they exceed a certain concentration threshold [ 1 ]. Greenhouse gases (GHG) are the gaseous compounds present in the atmosphere. They absorb infrared radiation and retain heat in the atmosphere, this is responsible for the greenhouse effect, eventually leading to global warming. On the necessity of economic development, owing to the expansion of economic growth, there has been a significant rise in transportation activities, industrial production, energy use and other human activities. These increased activities typically rely on the utilization of polluting energies and natural resources to the extent that economic development is frequently considered as a possible contributor to environmental degradation. In 2018, the International Energy Agency ranked the transportation industry second by virtue of its extensive reliance on fossil fuels (FFs) globally in terms of energy-related GHG and carbon dioxide (CO 2 ) emissions [ 2 ]. In the near future, road transportation, including passenger and freight vehicles, is expected to use more energy, with increase in emissions of over 50% [ 3 , 4 , 5 ]. Global concerns include the need for immediate action to mitigate GHG emissions given the increasing impact of the transportation industry on the environment [ 6 ]. The emission of GHG particularly carbon compounds, has far-reaching effects that extend beyond the surface consequence of global warming alone. In addition to the increase in respiratory and cardiovascular diseases, the number of all types of such associated diseases are also on the rise for the concerns of public health. These diseases ultimately result in a reduced lifespan for humans [ 7 ]. The transportation sector is among the principal sectors that trigger a country’s economic growth, in full measure, it impacts daily activities. However, it is strained as one of the main sources of energy consumption, resulting in environmental degradation. The discourse among researchers and experts in twenty-first century has focused on the collateral damage to our world due to the unbearable increase in carbon emissions that led to global warming from the outcome of economic developments that resulted to environmental degradation [ 8 ]. Over the course of decades, the transportation industry has relied heavily on nonrenewable energy sources, mostly fossil fuels, this has led to severe environmental effects, significant and increasing contribution to global GHG emissions [ 9 ]. The transportation industry continues to play a significant role in all the economic sectors that are main contributors to carbon emissions. It was found that the reason for the increasing energy consumption in the transport sector is the escalating increase in passenger vehicles and the increase in income earned by vehicle users. The sector as indicated in the literature, has its primary direct causes of carbon emissions from multiple dimensions of privately acquired passenger vehicles, accounting for over 700 million on-road passenger vehicles globally [ 4 , 10 ]. It is now a well-known fact, that achieving emissions’ mitigation in transportation industry is more sophisticated than realizing reductions from stationary sources [ 11 ]. This ever-increasing debate in the turn of the twenty-first century has to focus on the economic development and environmental degradation associated to carbon emissions, and consequently the global warming [ 12 , 13 ]. This necessitates global exclamation for several quarters. The global CO 2 atmospheric emissions based on the analysis conducted from NOAA’s Global Monitoring Laboratory is 414.72 parts per million [ 14 ]. Although China and the United States remain the leading emitters, Africa as accounted by records of formal inspections is found to generate fewer emissions than the rest of the world. However, worldwide carbon emissions in global temperature have now exceeded 1.26 0 C, evident by Hansen et al. [ 15 ]. Moreover, it is not only in the interests of South Africa and Africa, or any nation and, or continent; our world at large are all to take responsibility and be accountable on the bearable reduction of GHG emissions for the required lively air quality with serenity. In OECD nations the effects of transport infrastructure, economic growth, energy consumption, energy sources and carbon emissions were investigated on both short run and long run to determine the level of negative impacts of air quality and the measures to be taken to have an eco-friendly sustainable environment [ 13 , 16 , 17 ]. Countries worldwide, particularly those of developed economies, have acknowledged the importance of proper energy use with by-product emissions for optimal and strategic reductions. It is imperative to address the concerns regarding carbon emissions because emanating emissions negatively impact all forms of mortality via their influence on environmental air quality [ 18 ]. Africa carries the upset notoriety of having the highest mortality rate globally, many due to improper air quality as evidenced by available data (World Health Organization, 2018). The primary source of energy used in the transportation sector is non-renewable energy of fossil fuel types, such as oil and gas, which discharge large amounts of GHG emissions [ 19 ]. This negatively impacts the environment and is responsible for a growing proportion of global emissions. The United Nations Conference on Trade and Development, which was established to further advance the role of the organization, stated that the transportation industry globally consumed approximately 67% of petroleum products in 2012. Based on the analysis, it has been forecasted that by the year 2035, if no drastic measures are taken, the energy consumption of fossil fuels will increase to 82%, and due to the persistent increase in passenger vehicles, its demand is deemed to rise to 78% by 2040 [ 20 ]. The outcomes surrounding these circumstances are the emissions of pollutants, particularly those of greenhouse gases present in the atmosphere, and of capable CO 2 equivalence. As it is estimated that there will be a 25% increase in CO 2 emissions only due to the combustion of fossil fuels in the transportation industry, it remains imperative to conduct research studies focusing on its mitigation. Furthermore, it is expected that CO 2 emissions will increase to 1.7% annually in industrialized emerging economies by 2030 [ 21 ], this is a better fit for concrete and genuine research engagements. The transportation industry is one of the largest energy consumers, with increasing access of connectivity for point-to-point transfer of peoples, goods and services over the years. This has contributed to the increasing economic development. Although there is a growing demand for transportation services, it will result in increased energy consumption as the case applies, and thus the burning of fossil fuels. Consequently, this degrades air quality and the environment. The mitigation of CO 2 emissions, air pollution control due to road transport activities, energy management, and required freight management have been the prioritized objectives of sustainable ecosystems that are eco-friendly. In Africa, the highest energy consumption is still in the order of fossil fuels > coal > natural gas. Fossil fuels are frequently used in the transportation sector, whereas renewable energy usage is very minute in comparison. Although Africa is rich in clean energy sources that could better enhance air quality, however due to concerns in technological advancements and innovations, drive and will, it still relies heavily on non-renewable sources that degrade the environment [ 6 , 22 ]. By virtue of the excesses in the utilization of fossils that are consequently factored in sectorial degradation, calls have been made to curb its menace by shifting to clean renewable energy sources, thereby enhancing environmental sustainability. Previous research has demonstrated a nexus between transport energy consumption, economic growth, and carbon emissions in the transportation sector. Transportation is crucial in South Africa and has a significant impact on how daily tasks are carried out. Over the past 20 years, South Africa's population has increased to 60 million, with an economic growth rate of 2.39% from 1994 to 2022. Human population and economic growth are the main influencing factors that enhance the transportation industry, and subsequently, passenger vehicles. Saidi et al. [ 23 ] found that an increase in freight transport and per capita income played a significant role in deteriorating the quality of the environment. Nevertheless, the transportation industry is one of the main sectors in which energy consumption is at high ratio. The transportation industry of South Africa has undergone significant growth over the years, however, this expansion has resulted in a number of environmental degradations, particularly those caused by CO 2 - eq emissions from excessive energy consumption. Estimates based on data provided by Statistics South Africa and South Africa Department of Transportation show that passenger turnover increased from 50.2 billion person-kilometres in 2010 to 152.6 billion person-kilometres in 2020, while it increased from 231.48 billion ton-km to 597 billion ton-km, for freight transportation [ 4 ]. According to the research conducted by Oladunni and Olanrewaju [ 6 ] of South Africa’s transportation industry, the energy (oil) consumption—EC of fossil fuels for the year 2020, which was estimated to be 74,498,076,377 L of kilometers covered, possesses a qualitative nexus to economic growth—in GDP of 101,659 Rand per capita. This, in turn led to the potency for energy intensity—EI of 523.359 tce/ Rand 10,000. Consequently, it produced degrading environmental impacts of around 426.3 million tons in equivalent of CO 2 emissions. This research is pertinent as it proposes actions to enhance air and environmental quality in reducing GHGs, particularly CO 2 emissions in the transportation industry. The ultimate objective of this study is to analyze the contributions of selected environmental driving forces to carbon emissions in the transportation industry of South Africa and how they impact economic development. Furthermore, it adds to the body of literature, for which few already available on the nexus among energy consumption, its intensity, economic growth, and the required decline in carbon emissions. Consequently, the examined model's study of South Africa presents vital engineering management techniques in addressing the prevailing concerns of GHGs, and more in particular that of the CO 2 emissions for the transportation industry by adopting energy econometrics approaches. The subsequent sections of the research are as follows: section two presents the literature of relevant studies to the present objective. The section three gives a comprehensive description of the parametric materials and variables, using the procedures that guided the study. The empirical results of the investigation are reported in the fourth section. The discussion of the findings is addressed in the fifth section, and concludes by outlining the practical implications, policy recommendations, study limitations and research gaps for further studies. 2 Literature review With the application of diverse econometric techniques, a sizable body of literature examines the viability of the EKC hypothesis in respect to GHG emissions of different countries and regions. This resulted in variations in the estimated results [ 24 , 25 ]. Based on this hypothesis, the links between environmental pollution and economic growth per capita are in many cases (on a few exception) indicated to be inverted U-shape. This implies that working population earnings increase in tandem with economic growth. Therefore, environmental concerns will not require immediate intervention in the early stages, when environmental quality improves while the per capita income reaches the threshold known as the turning point. This hypothesis is as well demonstrated by Kang et al. 2016 [ 24 ]. Findings in the year 2016 from the studies of Kais and Sami [ 26 ] and Bilgili et al. [ 27 ] on EKC for GHG emissions show that the results depend on the type of analysis used (panel or time series) as well as the time period and geographical location that were studied. The pattern of the EKC hypothesis additionally supported by Danesh et al. [ 28 ] found that the majority of principal pollutants, including carbon monoxide (CO), nitrogen oxides (NOx), and sulfur oxides (SOx), sensed an inverted U-trajectory and supported the EKC hypothetical concept. According to Galeotti et al. [ 29 ], this link indicates multiple and mixed notions. While certain investigators observed a typical inverted U-shaped pattern, others expressed the notion that the turning point could not have been perfectly ideal [ 30 , 31 ]. Other researchers supported the findings for the existence of N-shaped correlations, as can be seen in the works of [ 32 ] and [ 33 ]. Nevertheless, the overwhelming nature of this research niche shows that economic growth does not directly translate into a long-term decrease in GHG emissions, as emissions are linked to economic expansion through energy consumption [ 34 , 35 ]. There is general agreement that rising energy consumption, which depends on the amount of energy the transportation sector uses, is the main cause of rising CO 2 emissions. However, the empirical results have shown that the evidence lacks stability because of variations in methodological approaches and for local, provincial, national, and global considerations, more specifically, the studied time period. Using statistical data from the United States, the empirical tests outcomes of [ 36 ] indicate that there is an unavoidable nexus between transportation energy consumption, income and fuels prices, one of which is a long-run relationship. The panel cointegration analysis conducted on OECD member states indicates that there is no connection between the price of gasoline, the amount of gasoline used (energy consumption), income, and car ownership in the short term. However, the results of the parametric variables demonstrate that they are connected. In a case study of the Malaysian economy, [ 37 ] analyzed some dynamic relationships between income, transportation energy consumption, and CO 2 emissions. The results demonstrate that income and transportation energy consumption are linked through the Granger causality. In their study of 107 economies, Liddle and Lung [ 38 ] evaluated the connection between per capita GDP and transport energy consumption and arrived at empirical findings that indicate that there is a long-term, positive unidirectional nexus between the two driving variables. The Johansen cointegration results indicate that GDP impacts transportation energy consumption in the work of Achour and Belloumi [ 39 ]. However, the converse scenario is not applied in their analyses of the correlation between energy consumption and economic growth with respect to the economy of Tunisia. A generalized method of moments (GMM) was employed in the works [ 23 ] for the purpose of having a feedback confirmation on causality between transportation energy consumption and GDP of 75 nations of the world. Hence, determination was concluded. With the same methodology [ 40 ] empirically assessed the growth impact of public infrastructure under a panel of 18 OECD countries, revealing that infrastructure growth has a positive influence on labour productivity and total factor productivity. In recent years, a number of empirical studies have been conducted to better comprehend the variables of impacts on environmental quality, particularly energy consumption. Notwithstanding, there have been some attempts to shift from examining the environmental impacts of overall energy consumption to assessing the environmental effects of various energy sources, mostly non-renewable sources. To further examine the correlation pattern for a country with a large human population, Maparu and Mazumder [ 41 ] assess the long-run causal relationship between transportation and economic growth in India. Vector Auto-regression and Vector Error Correction models were used to carry out short- and long-run causality checks, and the outcomes showed no long-run relationship. ARDL testing approach to cointegration and vector error correction model representation have been adopted to evaluate both the long-run and short-run links between economic growth, energy consumption, and carbon emissions to determine their consequential differences in impacts [ 42 , 43 ]. Rehermann et al. [ 44 ] examined the non-linear relationship between GDP per capita and transport energy consumption for countries in Latin America and the Caribbean. The findings support the N-shaped curve, while the elasticity values of transportation energy consumption with respect to GDP per capita do not demonstrate a tendency to decline over time. Sharif et al. [ 45 ] of ARDL using quantitative-on-quantitative (QQ) empirical research on the transportation-growth nexus, demonstrates that the United States’ transportation services benefit from economic growth. In addition, also with some considerations of ARDL as applied to Iran to include renewable and nonrenewable energies [ 46 ]. The fact that they serve as the driving forces for industrial development and economic growth, conversely, they lead to increase in the demand for mobility, increasing energy consumption, and intensity, investments in transportation infrastructure such as roads, highways, and bridges, and rising income levels. All of these play critical roles in the unbearable CO 2 emissions. For the purpose of achieving sustainable economic growth, [ 47 ] with [ 48 ] examined the EKC hypothesis in relation to substitution effect, growing contribution of transportation energy consumption to the resulting energy intensity and consequently the resulting GHG emissions. Energy intensity, which is a measure of a country’s energy efficiency, can be calculated either as total-factor energy efficiency or single-factor energy efficiency, as proposed by Pan et al. [ 49 ]. Being aware of how energy functions are essential, as increased energy consumption not only draws economies on track for industrialization, but also has the potential to worsen sustainability concerns [ 49 ]. Moreover, researchers continue to find it pertinent to investigate the response pattern of per capita GDP on the economy as it impacts transportation industry. The forecasts increase in GDP per capita in square or cubic functional forms can be measurable with considerable efforts. Taking into account the precepts of per capita GDP, the empirical test of [ 50 ] established long-standing assertions that adhering to environmental degradation in the short run would lead to positive environmental effects in the long run. The per capita GDP can be in its short-span increase or squared, and possibly with allowance, and then more. In EU countries, Sterpu et al. [ 51 ] investigate the validity of the EKC hypothesis by extending the per capita GDP to its quadratic [ 27 , 48 , 52 ] and cubic functional forms [ 53 , 54 , 55 ], examining the correlation between GHG emissions and per capita with the impact of energy consumption on GHGs. This is especially significant in urban areas where demand for automobile is highest [ 56 , 57 ]. In the modeled works of Gjorgievski et al. [ 58 ] as in the case of India argued that promoting nuclear energy production is the remedy to the nation’s GHG/CO 2 problems. The findings revealed that in the long term, increased nuclear energy use mitigates India’s carbon emissions. These have shown to be far-reaching evidence that one of the most important sectors for reducing carbon emissions is the transportation industry. With respect to transportation, Alimujiang and Jiang [ 59 ] argue that energy is an essential component to maintaining economic growth, adding that an excessive reliance on fossil fuels could have two main adverse effects: (1) climate change and (2) air pollution, both of which pose threats to the planetary existence. Thus, the task of controlling air quality and climate change is critical. Nevertheless, new research endeavour are confirming the link between air pollution and global warming Zandalinas et al. [ 60 ]. Although relevant research on GHGs and CO 2 emissions from the transportation industry has made real strides, more actions are still required. Lu et al. [ 61 ] forecast future development trends for energy (oil) consumption and CO 2 emissions in the road transport industry and made recommendations to reduce intolerable oil usage. To forecast future development trends of energy consumption and GHG emissions for China and India’s road transport industry, Mittal et al. [ 62 ] created a good-fit model and assessed potential emission reduction programs. It is found that the study of China CO 2 emissions attracted lots of scrutiny. Wang et al. [ 63 ] assessed the EKC hypothesis through panel techniques by adopting provincial data of China and found the presence of a U-shaped theorem between economic growth and CO 2 emissions. On some occasions, energy intensity is assessed with convincing results to be a driving force for increasing and (primarily depending on its adaptability) mitigating CO 2 emissions and to ease the transition to low-carbon economy [ 64 ]. There is now large-scale evidence that economic development has a positive impact on the environment, while the same economic growth under loose regulatory conditions leads to increased energy consumption. As proposed by researchers, there are causal correlations between the driving forces of GHG emissions Hasan et al. [ 15 ]. The correlation between economic growth, energy consumption and intensity, passenger vehicles, and CO 2 reduction having studied by Roinioti and Koroneos, [ 65 ] demonstrates that they have both positive and negative impacts on human lives and air quality as further indicated by Khan et al. [ 66 ]. Based on these considerations, to efficiently reduce carbon emissions and enhance clean energy use, it is imperative to determine the correlation among energy consumption, its intensity, and economic growth on carbon emissions Zhao et al. [ 67 ]. Ensuing the well-known EKC framework Alataş [ 68 ], salient literary discussions have been held over the past two decades regarding the nexus between energy consumption, its intensity, and economic growth that led to deteriorating effects on air quality, which account for the increase in GHG emissions. Researchers, especially energy economics experts in the niche, have proffered that, buttressing the significance test of this hypothesis [ 69 , 70 , 71 ]. A growing body of research has looked at economic growth and energy consumption, but not simultaneously with their energy intensity to the yielding impacts of carbon emissions on the environment [ 71 , 72 ]. These studies examined developed, developing, and regional economies. South Africa is investigated among the five developing countries examined by Sarkodie and Strezov [ 73 ] to determine the relationship between energy consumption and CO 2 emissions. Khan et al. [ 66 ] used the GMM technique to investigate the effects of energy consumption in transportation and logistics operations on environmental quality in 43 countries. Energy use and its intensities were demonstrated to determine the intensities of energy and how economic expansion affects environmental activities and the ensuing degradation in Malaysia and the OPEC countries, respectively [ 74 , 75 ]. Paramati et al. [ 76 ] applied FMOLS, CCEMG, and DOLS for their analysis to explore how energy can positively impact trade openness and economic growth in OECD countries. Further research activities reliably revealed that the ecological footprint (EF) for carbon emissions in the United States can be mitigated with controlled measures for natural resources, human capital, energy consumption, and economic growth impacts on EF of the United States. This is related to the determination of energy efficiency and its maximization for sectorial use, with respect to the transportation industry. Consequently, the outcomes of the ARDL further confirm that human capital can reduce EF, as energy consumption affects environmental deterioration [ 39 ]. In conclusion, no universally consistent nexus exist among variables, as already supported by the evidence of the EKC presented on the graph of the inverted U-shaped function, which is inconclusive. The findings have been subject to regional and national specifics, namely development path, population size and quality, economic structure, natural endowments, trade policy, and capacity of functioning institutions, as further envisaged in the empirical studies of Onafowora and Owoye [ 77 ] and Dijkgraaf and Vollebergh [ 78 ]. It can be seen that only few studies consider the presence of energy intensity in their investigative analyses, and far less considered the mixed relationship of transport energy consumption with energy intensity, that has been demonstrated in this research. As the South African transportation sector’s rising GHG or CO 2 - eq emissions becomes the focus of the present study, there exists a correlation between energy consumption, energy intensity, and economic growth. Based on previous research using similar approaches [ 4 , 6 , 20 ] the present research studies make efforts to literature by further widening the analysis of the correlations among the economic variables of impacts (–EC–EI–PV–GDP—CO 2 - eq emissions) taken from the transportation industry of South Africa as a reference case with the employment of datasets from 2016 to 2020. 3 Data and method The 5-year dataset utilized as the parametric variables in this investigation was obtained from [ 6 ] for the nine provinces of South Africa between 2016 and 2020. The variables include the following: Carbon emissions as per capita greenhouse gas (GHG) emissions, taken in tones of CO 2 equivalent. Per capita gross domestic product (GDP), taken in South Africa Rand. Per capita gross energy (oil) consumption (EC) taken in tons of oil equivalent. Per capita energy intensity (EI), taken in Tce per 10,000 Rand. Number of on-road passenger vehicles (PV) contributing to carbon emissions. Taking into account the fact that the data for each province is different by characteristics in terms of population, energy use, and economic growth, it is observed that using variable per capita values will lead to significant results. To conduct these precepts, as in the case of South Africa, the nominal indices are operated over the population numbers. The employed datasets are presented in panel: The panel dataset provides the values for the driving forces under investigation, namely EC, EI, GDP, and CO 2 - eq emissions, for the nine provinces of South Africa. Time series data provide parametric values for each of the variables from the time period of 2016 to 2020 for each of the nine provinces of South Africa. The data series were set up using a panel design. Data for the 2021–2023 timeframe are yet to be drawn to fit the investigation for public purposes. In the current research analysis of EKC, three different types of empirical specifications are generally considered: (i) linear specifications, (ii) quadratic (inverted-U) specifications, and (iii) cubic (N-shaped) or sideways-mirrored (S-shaped) specifications [ 77 ]. The graph in Fig.  1 as shown illustrates the Environmental Kuznet Curve concepts and perspectives as demonstrated by the authors. This posits a correlation between the indicators of environmental degradation and economic development. It also suggests that during the early stages of industrialization and the absence of knowledge and circular economy, GHG emissions increase as environmental quality decreases. However, beyond a certain level of economic development, which varies based on different indicators, the trend reverses, with high economic growth and the inclusion of circular economy resulting in environmental improvement. Enviromental energy-econometrics analysis of EKC hypothesis [Author’s design] There are broad functional forms that possess additional pertinent factors, namely, external variables of time, provincial characteristics, and technical factors. The general form of the equation is as follows: In accordance with the EKC specifications provided above, this study examines CO 2 - eq emissions (Q) as the dependent variable, per capita yearly GDP (Y) as the independent variable, time period (t) as a factor, and the explanatory variables (X). Furthermore, ɛ represents the random error component, and a i denotes the coefficients of the model, which can also be referred to as the marginal propensity for emissions. Upon conducting the EKC analyses for the three specifications, several technical details can be discerned: IF ( →) a 1  >  0— linearity of correlation around GDP with CO 2 - eq emissions. [a 1 must be significant] IF ( ↔)  a 1  <  0— monotonic decrease linkage around GDP and CO 2 eq  emissions. [a 1  must be significant] IF a 1  >  0 , a 2  <  0 & a 3  =  0— quadratic linkage around GDP and CO 2 - eq  emissions. [Equilibria to be reached] This is to evaluate the existence of an EKC-type nexus between CO 2 - eq emissions, economic growth, and the impact of energy consumption on CO 2 - eq emissions in the transportation industry, employing two energy-econometrics’ models as the basis for further analyses. To measure the environmental impacts, we use CO 2 - eq emissions as a dependent variable, while GDP, and EC, EI and PV are taken as the independent, controlling independent variables, respectively as the case applies. 3.2.1 Model 1 Taken as the first model, we employ quadratic to perform test on the EKC hypothesis as follow: where Q corresponds to CO 2 - eq emissions, Y is the GDP per capita, X 1 … X n are the covariate explanatory variables. The ɛ it represents the error term, i denotes the provinces of South Africa while t is the time period. Other studies have employed similar approach, however, with different explanatory driving factors [ 78 ]. 3.2.2 Model 2 Using the cubic equation, we applied the second model to conduct tests on the N-Shape hypothesis for the Kuznets curve as demonstrated: The order of representations are as specified in Eq. ( 1 ). There are other researchers who employed a cubic model similar to the one utilized in this study due to their close proximity [ 48 ]. The parametric variables are taken in their logarithmic transform. The sign for coefficients of Y , Y 2 , Y 3  applied to economic growth and the specific correlations among them regulate the shape of the approximating surface. We employed the ARDL bounds testing approach to reconfirm the presence of EKC and cointegration of variables as proposed by [ 79 ]. Eq. ( 5 ) fully remodeled in Eq. ( 6 ) from [ 48 ] background as: where Δ denotes variable’s first difference operator, P stands for lag lengths. To use ARDL we first demonstrate cointegration among the variables. To proceed, the null hypothesis test of no cointegration is conducted against the alternative hypothesis in this other of format: F-statistic is inculcated with respect to the series being integrated either at I(0) or I(1). As the case applies, if the F-statistic value is greater than the upper bound value, there exists cointegration among the variables. If the F-statistic value is below the crucial lower bound value, the acceptance of null hypothesis that there is no cointegration is observed, as no precision will be made following that F-statistic lies between upper and the lower bound values [ 52 ]. For the study’s validation, the critical and F-statistic values are selected by applying cointegration technique as put forward by [ 52 ]. The estimates of the short run coefficients are obtained by ( P ) whilst the long run dynamics are estimated with the coefficients \(\vartheta_{1} ,\vartheta_{2} ,\vartheta_{3} ,\vartheta_{4} ,\vartheta_{5} ,\vartheta_{6}\) as expressed in Eq. ( 6 ). The ARDL bound testing approach is an effective method for simultaneously determining better estimates of both short-run and long-run dynamics. It achieves this through a modest linear transformation, which provides a superior approach for obtaining more accurate estimates. To assess the robustness entirety of the empirical models, diagnostic tests on heteroskedasticity, normality and autocorrelation tests are conducted, thereby running the validity and consistency of the long run dynamics. This is carried using canonical cointegration regression, dynamic ordinary least square (DOLS), and modified least square (FMOLS). Modeling the data to be analyzed [ 6 ], and the time span of 5 years in real terms along with their provincial locations are illustrated in Fig.  2 a, and b respectively as shown: a South Africa’s driving forces impacts on GHG/CO 2 - eq emissions in transportation industry, 2016–2020. b. South Africa’s driving forces impacts on GHG / CO 2 - eq emissions in transportation industry, 2016–2020 4 Empirical results and analysis The study investigates how economic growth in GDP per capita and its extensions, CO 2 - eq emissions, energy consumption, its yielding energy intensity and the on-road passenger vehicles cointegrate to bring forth the observable environmental impacts in the transportation industry of South Africa. We applied ARDL bound testing method in achieving this and to also prevent spurious regression. It is essential to examine the order of integration prior to ARDL bound testing method. Augmented Dickey-Fuller (ADF) and Philips Pearson (PP) tests are employed in attaining the consequential values in order to proceed. The findings of both ADF and PP indicate that none of the series is stationary at Level, as illustrated in Table  1 . Hence, the hypothesis of no stationary is rejected, as it implies that all the variables are integrated at first difference. The results further show that none of the variables is integrated at I(2). By the revealing response, the ARDL bounding technique is found appropriate. When it has been demonstrated that none of the variables are integrated in the order I(2), the cointegration between them is further evaluated. The decision is prerequisite prior assessments of parametric variables for cointegration. To begin with, unrestricted VAR models are utilized and to subsequently identify the optimal lag length of 2 using SIC criterion. The optimal lag length of 2 adjustments is imperative at the selection of the optimal length. Thereafter, proceeding to find adjustments from the parametric variables. In confirming the cointegration, Wald test is applied to determine the value of F-statistic. The findings of Table  2 reveal the rejection of null hypothesis on the condition that no cointegration on the modeled equations. Johansen cointegration test is employed to verify the validity of the F-statistic as generated by Wald test performance. In conducting Johansen cointegration, Trace statistics with Eigen-values were obtained. The relevance of Trace statistics and that of Eigen-values demonstrates the cointegration correlation among the investigated parametric variables. These are as presented in Table  3 in which the analyses made it evident that at the very least, cointegration correlations exist. Hence, Johansen cointegration results validate Wald statistics. Both long run and short run estimates for Eq. ( 6 ) were conducted to determine the level of significance of the exogenous variable of CO 2 - eq emissions and the underlying independent variables. In Table  4 , it can be observed that all the coefficients possess the responsive signs. More so, all the series are made significant at 0.05% level. In other words, the indication of GDP positive-path coefficient buttress that CO 2 - eq emissions in the transportation industry surfaces with increasing economic growth in both forecasts for long run and the short run. In contrast as revealed in Table  4 , there are strong indications of long run and short run correlations among economic growth in square and cubic forecast with CO 2 - eq emissions found possessing negative sign coefficients. The implication as derived, implies that CO 2 - eq emissions in South Africa’s transportation industry increases at the early industrial phase of economic growth and fall after reaching certain level of economic expansion. The investigation validates the U-shaped EKC hypothesis in South Africa relating to transportation sector. The findings are related to [ 42 ] who conducted such line of analyses to confirm the existence of EKC in Italy, and in Turkey by [ 80 ], more so, in OECD countries [ 13 , 16 , 17 ]. With the peculiar case of South Africa transportation industry in the staggering amount of energy (oil) consumed, the on-road passenger vehicles, energy in oil consumption with its intensity are integrated in the model. This offers new directions to mitigate carbon emissions on the level at which South Africa’s economic development has reached from the general interpretation for the U-shaped EKC hypothesis, a level being depicted in Fig.  3 . It is observed that from the level at which energy are used in the transportation sector of South Africa, Energy consumption as inspected with its intensity contributes to the emissions of GHGs/CO 2 - eq  in South Africa. On the other hand, although in the long run passenger vehicles do not reveal a negative impact, however, in the scale of short run it possesses a sensitive negative impact. The demonstrated energy-econometrics analysis implies that increasing passenger vehicles (IC Engines) concurrently lead to increase in energy (oil) consumption vis-à-vis energy intensity. Plot-trends correlations between economic growth and CO 2 - eq emissions in SA transport The findings of the study relate to that of Zhao et al. [ 67 ] with a similar outcomes for China. Based on the research conducted, it was discovered that in numerous instances, public transportation alternatives are more eco-friendly for South Africa's transportation systems than the high volume of passenger vehicle traffic, which was found to be one of the primary contributors to CO 2 - eq emissions in the transportation industry. This is proved viable as South Africa heavily relies on conventional (fossil) energy sources such as oil and coal, particularly oil (in fossil) for its transportation activities. Already, well over 90% of the energy use in the transportation industry is fossil-based fuels. To check the capacity of the analyses, the resulting model of Eq. ( 6 ) is assessed by employing three different techniques, namely, fully modified least squares (FMOLS), dynamic least squares (DOLS), and canonical cointegration regression (CCR), purposed to examine the validity and reliability of the obtained outcomes through the ARDL bound test approaches [ 80 ]. The findings of Table  5 indicate that whilst economic growth possess a positive and significant impact on CO 2 - eq emissions, the square and cubic of economic growth ( GDP 2 and GDP 3 ) have negative significant impacts. This is the implied case applied to the transportation industry of South Africa. In addition, from the analytical interpretations being sensitive of the GDP flow-line, it can be rewarding to improve eco-friendly environment. Ultimately, the results of the ARDL bound test approach applied under three distinct techniques support the findings of the research which are further presented in Table  5 . The CUSUM and CUSUMsq are performed with high sensitivity to verify the lack of structural invariance, endogeneity tests, and the reliability and stability of the models for both long and short run estimations. The results are graphically presented in Fig.  4 a and Fig.  4 b. The assessed stability diagnostics for both tests largely reside between the critical (red) lines; this implies that the model can be put forward for policy recommendations with respect to the availability of the data employed. They are found fit. It is noteworthy that, based on the most current literature, this research is considered to be forthcoming in South Africa and the continent of Africa. In Fig.  4 b, it can be observed that the data as they were not readily available from a single source of a database. a Trend-plot for cummulative sum of recursive residual at critical bound of 5% significance. b  Trend-plot for cummulative square of recursive residual at critical bound of 5% significance The readings may not be efficient and robust enough, however optimum determination has been exercised. Figure  4 b can only further implies that at the readings of 5% level of significance CUSUMsq for high sensitivity can be determined (as it also travels between red-lines indicator) with respect the prevailing empirical analysis. As presented in Fig.  5 a, both the short-run and long-run impacts are identified. The parametric variables taken into consideration are contingent on the interpretations of EKC hypothesis in the derived models of energy econometrics technique for the South Africa's transportation sector. This serves as the underlying approach of the research studies. The interpretation of the readings depicts that for both long and short runs, indications exist for the correlation between economic growth in GDP per capita ( A region) and GHG emissions ( E ) of the transportation industry. As Energy Intensity (in the C” region) has to bridge the gap, there also exists a causal relationship between Energy Consumption—EC in the B’ region and Passenger Vehicles—PV in the D region. Along the axis of A-D-E in the composition of GDP, PV and GHGs there exist an indication of causal interconnection between the variables as evidently provided in empirical analyses of the 5-year employed dataset of transportation industry of South Africa. a Acyclic model indicator of parametric variables-flow on EKC hypothetical analysis. b Directional linkages of resource-controls among selected driving forces over GHG/CO- eq emissions Figure  5 b, as indicated, conveys the relational linkages of variables’ controls that exist among the selected driving forces impacting on GHG emissions in the transportation sector of South Africa. In line with the analyses performed on the hypothetical EKC, it can be deduced that the outcomes of GHG emissions are well dependent on variable’s computational inputs both quantitatively and qualitatively. As investigated for all the nine provinces of South Africa with time period of five years spanning from 2016 to 2020. The alterations and the adjustments of one or two or more of the endogenous variables can significantly lead to the required environmental outcomes. 5 Conclusion and policy implication 5.1 policy implications for reducing ghg emissions in transportation. The study delves into the concept of energy econometrics complexity and applies the Environmental Kuznets Curve hypothesis, commonly utilized to analyze the nexus between economic development and environmental quality. South Africa is still a developing nation, despite being more developed of Africa's member states. In line with its Paris Agreement obligations, South Africa has been determined to further reduce its transportation sector GHG emissions from the 10-year of 60MtCO 2 - eq . This value serves as the share of the tranportation industry from the South Africa’s overall contribution of 1.2% of the world’s GHG emissions, totaling 8.08 billion metric tons in CO 2 equivalent, globally. Identifying the pattern of the Environmental Kuznets Curve (EKC) hypothesis as it pertains to economic development and environmental degradation for the requisite air quality is essential for assessing the impacts of the driving forces in the industry that contribute to carbon emissions. Provinces in South Africa should be cognizant of their respective stages of economic development, energy use, and GHG emissions, particularly that of transportation sector. They should make targeted advances in economic development while effectively mitigating GHG emissions. At present, all the provinces are in the rising stage and have not yielded to the turning point of the interpreted EKC. The rising economic development due to carbon intensive energy is the primary reason for the accounted carbon emissions in the industry. Although, significant environmental degradation has been recorded, the nation still requires a lot of transportation systems to move people, goods, and services, nevertheless, those with sustainable air quality. According to the analysis of the development trend of transportation in various cities and provinces of South Africa at this stage, there are still problems of energy sources for both renewable and nonrenewable, and that of transportation means and modes. This, obviously lack transportation’s economic development objevtives. By updating the economic structure and controlling the development of transportation systems reasonably, a high developed economy with low carbon emissions can be achieved. With a measure of controlling unbearable population and decreasing mortality rates while improving technological innovations, the effect of passenger vehicles on traffic emissions can be restrained. More to this effect, passengers can be guided on individual and personal benefits of choosing clean and green travel options. The transportation pricing index has the potential to be a significant factor in reducing carbon emissions. Altering consumption approach can be a viable strategy for achieving balance between the economy and the environment that will lead to sustainable development.Furthermore, the government should promote and incentivize the use of environmentally-friendly modes of transportation and the use of clean products among local residents. Modifying the cost of transportation services is an essential measure that can influence people's travel choices and subsequently impact the energy demand and carbon emissions in the transportation industry. Efforts should be made to enhance the affordability and convenience of public transportation in order to change people's preconceived notions about travel. Highway transportation is among the passenger travel that should be considered, particularly intercity and city buses, which mostly relies on fossil fuels for passenger transit. By so doing, the use of energy for automobile will predominantly shift towards natural gas and electricity. The government has the ability to diminish individuals' reliance on gasoline-powered vehicles by implementing tax policies, fuel surtaxes, and vehicle purchase taxes that are tailored to particular vehicle types. Furthermore, providing policy assistance for environmentally friendly automobile manufacturers to foster the growth of automobile industry that is clean. Offering of incentives and benefits to consumers who purchase such automobiles, can encourage individuals who use private cars to transition to a more environmentally friendly mode of transportation with reduced carbon emissions. To encourage long-distance of on-road travel that is environmentally friendly, it is important to build gas stations and charging infrastructures along the highway. This will gradually shift people's transportation practices and promote the development of low-carbon traffic in South Africa transportation sector and elsewhere. It is important to note that there are limitations and gaps in the research. This study investigates the nexus between economic development and environmental degradation, specifically focusing on the income-emissions aspect of the EKC hypothesis in the transportation industry of South Africa. Due to limitations in data and geographic scope, our analysis is restricted to the nine provinces of South Africa over a five-year period from 2016 to 2020. Additional research investigations have the potential to broaden the temporal scope and increase the number of countries examined. Moreover, it has the capability to examine many sectors or industries both independently, and as integrated concerns, resulting in changes to the methods, and scale of the tests and diagnostics, which will ultimately lead to more outcomes. 5.2 Conclusion Using energy econometrics techniques, this study investigates the effects of economic growth (GDP per capita), with it being squared and cubic, followed by energy consumption (EC), energy intensity (EI), and on-road passenger vehicles (PV) on the mitigation of GHG emissions in CO 2 equivalence for the transportation industry of South Africa. A five-year dataset spanning from 2016 to 2020, as it appears in Fig.  2 a, and b are adopted. The year can further be extended, only to portray an extension for subsequent forecasts. The study examined South Africa's nine provinces, considering their varying rates of economic development and dependence on fossil fuels for energy in the sector across all the provinces. From the study period of 2016 to 2020 as 2021 only being the model’s extension forecast, South Africa’s per capita GDP ranges from R71, 920.00 to 101,659.00. The country’s energy (in oil) consumption (EC) from 2016 to 2020 is estimated ranging from 6,925,070,093 to 7,799,172,128 L and in conversion it tallies between 39.850 to 41.039 metric tons of oil consumption in energy content. The energy intensity (EI) for the study periods is within the range of 513 Tce per R10, 000.00 to 537 Tce per R10, 000.00 from 2016 to 2020 as estimated. South Africa’s on-road passenger vehicles for the research period of 2016 to 2020 are taken in units of vehicle population within the range of 11,964,234 and 12,701,630 of vehicle units. Considering the energy-econometrics debates around the EKC hypothesis sectioned into four main categories, namely; cointegration of the parametric variables, endogeneity concerns, simultaneity and omission bias for variables, the prevailing econometrics instruments are employed in the peculiar case of South Africa’s transportation industry. In the context of South Africa, economic growth in GDP (inculcating GDP 2 and GDP 3 ), energy consumption with its intensity, and on-road passenger vehicles are modeled on CO 2 - eq emissions. In the investigation, the EKC test is employed to South Africa’s industry using the aforementioned variables as explanatory while taking CO 2 - eq emissions as the dependent variables. With the outcome of the prevailing research, CO 2 - eq emissions in South Africa’s transportation industry grew through the early phases of its economic expansion at specific level of economic threshold. To clarify the research main contribution, the study further demonstrates the directional nexus among South Africa’s on-road PV, EC, EI and per capita GDP with its excesses which is negatively probable, especially the economic expansion by a cubic scenario. The ARDL bound test approach was employed to analyze the cointegration correlation among the parametric variables. For the high performance of the model, three high-powered techniques were employed to examine the accuracy and reliability of the results from the ARDL bound test approach: FMOLS, DOLS and CCR, respectively. Quantitatively, the series were determined to be stationary at their first differences, as indicated by R 2 and R 2 ( Adjusted ) values of 0.9837 and 0.9827 , respectively, for both long-run and short-run estimations. From the deductions of the findings, it is imperative to monitor the reactions of EC on the long effects of the t-stat —( 0.393 ) and p-value —( 0.6947 ) alongside the short run forecast impact of the t-stat —( 0.383 ) and p-value —( 0.7019 ). From the short run effects shown in the t-stat—( 4.928 ) with p-value ( 0.0000 ) to the long run effects demonstrated with p-value ( 0.0000 ), the per capita GDP increases, indicating its improper influence in the sector. Limiting the burning of fossil fuels is essential as shown by the negative signal of EI for the short run impacts of t-stat ( -1.100 ) with p-value ( 0.0000 ) and the long- run impacts shown of t-stat ( -1.076 ) with p-value ( 0.2835 ). From these analyses, the following conclusions have been drawn: There are implications of Environmental Kuznets curve (EKC) hypothesis in the significance of economic growth, energy consumption with its intensity, and on-road passenger vehicles in the transportation industry of South Africa. Economic growth has a significant positive impact over GHG/CO 2 - eq emissions provided that it is checked without spanning out of control. In both the long and short run paths, energy intensity can have significant positive impacts in South Africa. Under proper investigation, the neutrality hypothesis is confirmed, as a correlation exist between CO 2 - eq emissions and economic growth which at large contribute to economic development. There is also evidence of proportional nexus between the energy consumption and passenger vehicles with CO 2 - eq emissions in the transportation industry of South Africa. In line with the outcomes of the research studies, it can be put forward for decision making, that there are convincing revelations between per capita economic growth and energy (oil) consumption that led to CO 2 - eq emissions. Automobiles that are IC-Engines running on fossil fuels should be minimized in order to contribute to the efforts of mitigating the impacts of climate change. By doing so, the mass transit can be cushioned. In addition, South Africa’s GHGs intensity can be mitigated by further enhancing renewables in the energy mix. To further support an eco-friendly environment, decision and policy makers should support alternative energy transport vehicles to limit the consumption of fossils. Based on the accounts of this study, the following implied  knowledge among others are derived: First, South Africa can further restructure the transportation industry to develop in a more sustainable ways, as its impacts on the environment are significantly dominant. Similarly, developing countries as a case with South Africa can focus on how their transportation systems and economic development affect environmental degradation to fully achieve intergovernmental sustainability goals, such as the ones outlined by the United Nations. For instance, that of the sustainable development goals. Consequently, this can further align South Africa's policies framing with those that are highly developed. Furthermore, in the era of information age, the structure of the economy can be enhanced to move from carbon intensive energy to knowledge and circular economies. Notwithstanding their complexities, they are reliable path to post-industrial economy. Passenger vehicles contribute significantly to South Africa's total vehicle fleet GHG emissions. However, with rigorous fuel economy standards and increasing use of hybrid and electric vehicles, this share can be expected to decline over time as indicated by the EKC. To achieve sustainable development, it is imperative that governmental bodies prioritize policies targeting commercial vehicles, with particular emphasis on passenger on-road vehicles, in domains such as fuel economy regulations and electric vehicle (EV) deployment. 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Author information Authors and affiliations. Department of Industrial Engineering, Durban University of Technology, Durban, South Africa Oluwole Joseph Oladunni & Oludolapo A. Olanrewaju Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hung Hom, Hong Kong SAR, China Oluwole Joseph Oladunni & Carman K. M. Lee You can also search for this author in PubMed   Google Scholar Contributions OJO: Conceptualization, methodology, software application, validation, formal analysis, investigation, data resources, data curation, writing—original draft preparation, writing—review and editing, OJO, OAO and CKM Lee: visualization, project administration. OAO and CKM Lee: supervision. OAO and CKM Lee: internal funding acquisition. Corresponding author Correspondence to Oluwole Joseph Oladunni . Ethics declarations Ethics approval and consent to participate. We declare that we have no human participants, physical contacts and human data. 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Provided by the Springer Nature SharedIt content-sharing initiative CO 2 -e q  emissions Economic growth Energy consumption Passenger vehicles Transportation Climate mitigation Find a journal Publish with us Track your research 444 IMAGES Null hypothesis 15 Null Hypothesis Examples (2024) Null Hypothesis Examples Research Hypothesis Vs Null Hypothesis How to Write a Null Hypothesis (with Examples and Templates) Research hypothesis VIDEO Hypothesis Testing: the null and alternative hypotheses Testing of Hypothesis|Null & Alternative hypothesis|Level Of Significance|Critical Region|Lecture 22 Writing the Null and Alternate Hypothesis in Statistics Hypothesis lesson 10 research hypothesis and null hypothesis Understanding the Null Hypothesis COMMENTS Null & Alternative Hypotheses The null and alternative hypotheses offer competing answers to your research question. When the research question asks "Does the independent variable affect the dependent variable?": The null hypothesis (H0) answers "No, there's no effect in the population." The alternative hypothesis (Ha) answers "Yes, there is an effect in the population." The null and alternative are always ... Null hypothesis In scientific research, the null hypothesis (often denoted H0) [ 1 ] is the claim that the effect being studied does not exist. [ note 1 ] The null hypothesis can also be described as the hypothesis in which no relationship exists between two sets of data or variables being analyzed. If the null hypothesis is true, any experimentally observed effect is due to chance alone, hence the term "null ... Null Hypothesis: Definition, Rejecting & Examples The null hypothesis in statistics states that there is no difference between groups or no relationship between variables. It is one of two mutually exclusive hypotheses about a population in a hypothesis test. When your sample contains sufficient evidence, you can reject the null and conclude that the effect is statistically significant. Null and Alternative Hypotheses The null and alternative hypotheses offer competing answers to your research question. When the research question asks "Does the independent variable affect the dependent variable?", the null hypothesis (H 0) answers "No, there's no effect in the population.". On the other hand, the alternative hypothesis (H A) answers "Yes, there ... 7.3: The Research Hypothesis and the Null Hypothesis The Research Hypothesis. A research hypothesis is a mathematical way of stating a research question. A research hypothesis names the groups (we'll start with a sample and a population), what was measured, and which we think will have a higher mean. The last one gives the research hypothesis a direction. In other words, a research hypothesis ... 8.1: The null and alternative hypotheses The Null hypothesis \(\left(H_{O}\right)\) is a statement about the comparisons, e.g., between a sample statistic and the population, or between two treatment groups. The former is referred to as a one-tailed test whereas the latter is called a two-tailed test. The null hypothesis is typically "no statistical difference" between the ... An Introduction to Statistics: Understanding Hypothesis Testing and In statistical terms, this belief or assumption is known as a hypothesis. Counterintuitively, what the researcher believes in (or is trying to prove) is called the "alternate" hypothesis, and the opposite is called the "null" hypothesis; every study has a null hypothesis and an alternate hypothesis. Null Hypothesis Definition and Examples The null hypothesis is useful because it can be tested and found to be false, which then implies that there is a relationship between the observed data. It may be easier to think of it as a nullifiable hypothesis or one that the researcher seeks to nullify. The null hypothesis is also known as the H 0, or no-difference hypothesis. 9.1 Null and Alternative Hypotheses The actual test begins by considering two hypotheses. They are called the null hypothesis and the alternative hypothesis. These hypotheses contain oppos... 9.1: Null and Alternative Hypotheses The actual test begins by considering two hypotheses. They are called the null hypothesis and the alternative hypothesis. These hypotheses contain opposing viewpoints. Since the null and alternative … What Is The Null Hypothesis & When To Reject It A null hypothesis is a statistical concept suggesting that there's no significant difference or relationship between measured variables. It's the default assumption unless empirical evidence proves otherwise. Null & Alternative Hypotheses Alternative Hypothesis (Ha) - This is also known as the claim. This hypothesis should state what you expect the data to show, based on your research on the topic. Null Hypothesis vs. Hypothesis: What's the Difference? A hypothesis, also known as an alternative hypothesis, is an educated theory or "guess" based on limited evidence that requires further testing to be proven true or false. What Is A Research Hypothesis? A research hypothesis (also called a scientific hypothesis) is a statement about the expected outcome of a study (for example, a dissertation or thesis). To constitute a quality hypothesis, the statement needs to have three attributes - specificity, clarity and testability. Let's take a look at these more closely. 13 Different Types of Hypothesis A good way to think about a null hypothesis is to think of it in the same way as "innocent until proven guilty" [1]. Unless you can come up with evidence otherwise, your null hypothesis will stand. A null hypothesis may also highlight that a correlation will be inconclusive. Research Hypothesis Vs Null Hypothesis The difference between Research Hypothesis Vs Null Hypothesis is as follows: A Research Hypothesis is a tentative statement that proposes a relationship between two or more variables. It is based on a theoretical or conceptual framework and is typically tested through empirical research. Wiseman Chapter 8-9,12-13 The null hypothesis is also known as the research hypothesis because it represents the position the researcher wants to establish. TRUE FALSE False Null Hypothesis: What Is It, and How Is It Used in Investing? The null hypothesis, also known as "the conjecture," is used in quantitative analysis to test theories about markets, investing strategies, and economies to decide if an idea is true or false. CH 7 Flashcards 11. A null hypothesis is also referred to as a (n): 1. statistical hypothesis. 2. research hypothesis. 3. alternative hypothesis. 4. scientific hypothesis. Alternative hypothesis The alternative hypothesis and null hypothesis are types of conjectures used in statistical tests, which are formal methods of reaching conclusions or making judgments on the basis of data. In statistical hypothesis testing, the null hypothesis and alternative hypothesis are two mutually exclusive statements. What is the difference between the null hypothesis and the Null Hypothesis vs Research Hypothesis In the context of statistical analysis and research, the null hypothesis and the research hypothesis (also known as the alternative Question: 4. The alternative hypothesis is also known as the ... 4)The alternative hypothesis is also called research hypothesis, so option (D) is the answer. The alternative hypothesis is also known as the: Find step-by-step Statistics solutions and the answer to the textbook question The alternative hypothesis is also known as the: a. null hypothesis b. optional hypothesis c. elective hypothesis d. research hypothesis. The alternative hypothesis is also known as the: a. null hypothesis b Hypothesis testing The hypothesis test is the statistical test and it is generally divided in two part which include the null and alternative hypothesis. P-value and critical value approach is used to find the conclusion of the hypothesis test. The Environmental Kuznets Curve (EKC) Hypothesis on GHG ... A series of energy-econometrics techniques were employed for a 5-year time span between 2016 and 2020. The tests of Environmental Kuznets Curve (EKC) hypothesis were conducted essentially to examine the significance of economic growth (GDP), energy consumption (EC), with energy intensity (EI), and on-road passenger vehicles (PV) as related to economic development on the mitigation of carbon ... assignment essay homework paper phd report resume review thesis