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.
Key Takeaways
- Null Hypothesis (H0): States there is no effect or relationship between variables; any observed difference is put down to chance.
- Never “Accepted”: Researchers only ever reject or fail to reject H0; a lack of evidence against it is not proof that it is true.
- What Gets Tested: A significance test evaluates the null hypothesis directly; the alternative hypothesis (H1) is never tested itself.
- The P-Value: A smaller p-value is stronger evidence against the null. When p is at or below your significance level (often .05), you reject it.
- Type I/II: Rejecting a true null is a Type I error (a false positive); failing to reject a false null is a Type II error (a false negative).
- Why It Matters: Testing the null gives research an objective, neutral starting point before crediting any result as a real effect.
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
| Research Question | Null Hypothesis |
|---|---|
| Do teenagers use cell phones more than adults? | Teenagers and adults use cell phones the same amount. |
| Do tomato plants exhibit a higher rate of growth when planted in compost rather than in soil? | Tomato plants show no difference in growth rates when planted in compost rather than soil. |
| Does daily meditation decrease the incidence of depression? | Daily meditation does not decrease the incidence of depression. |
| Does daily exercise increase test performance? | There is no relationship between daily exercise time and test performance. |
| Does the new vaccine prevent infections? | The vaccine does not affect the infection rate. |
| Does flossing your teeth affect the number of cavities? | Flossing your teeth has no effect on the number of cavities. |
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.
Using the P-Value to Decide
If the collected data does not fit the null hypothesis, this counts as evidence against it. The null hypothesis is then 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 are not statistically significant, the null hypothesis is retained rather than rejected. Researchers then conclude there is not enough evidence of a relationship between the variables.
A statistical test is required. It checks how consistent your data are with the null hypothesis, using a p-value as the measurement.
Calculating the p-value is central to null-hypothesis testing. It shows how strongly the sample data contradict the null hypothesis.
The result is a number between 0 and 1: the smaller the p-value, the stronger the evidence that the null hypothesis should be rejected. That is the whole rule.
Usually, a researcher uses a confidence level of 95% or 99% (p-value of 0.05 or 0.01) as a general guideline for whether to reject or keep the null.
The rule is simple. When your p-value is less than or equal to your significance level, you reject the null hypothesis.
Smaller p-values count as stronger evidence against the null hypothesis. When the p-value is greater than your significance level, you fail to reject it instead.
In this case, the sample provides insufficient evidence that the effect exists in the population. Because researchers can never know with complete certainty whether a population effect exists, their conclusions will sometimes be wrong.
Type I and Type II Errors
Getting this decision wrong is always possible. There are two ways it can happen.
A Type I error happens when a researcher rejects a null hypothesis that is actually true: a false positive, concluding an effect exists when it does not.
A Type II error happens when a researcher fails to reject a null hypothesis that is actually false: a false negative that misses a real effect. Its rate is called beta, and it depends on the true effect size, the sample size, and the significance level chosen.
Why Do We Never Accept The Null Hypothesis?
We do not say we “accept the null” because we start by assuming it is true. A study then looks for evidence against it, and even when none turns up, the null hypothesis is still 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 the null hypothesis is true just because no evidence was found against it. Other researchers, elsewhere, may already have disproved it.
For this reason, a null hypothesis is never accepted. It can only be rejected, or not rejected.
Why Do We Use The Null Hypothesis?
We can never prove with complete certainty that a hypothesis is true. We can only gather evidence that supports it.
Testing sets the stage for rejecting or retaining that hypothesis, within a stated confidence level.
The null hypothesis is useful because it shows whether a study’s results come from random chance or from a real effect. This works at a chosen level of confidence.
A null hypothesis is rejected when the data are significantly unlikely to have occurred by chance. It is retained when the observed outcome is consistent with what the null hypothesis predicts.
Rejecting the null hypothesis opens the door to further experimentation. Hypothesis testing is a systematic way of backing predictions with statistical evidence, deciding whether a study’s results support a given theory.
Purpose of a Null Hypothesis
- Disproving Assumptions: The primary purpose of the null hypothesis is to disprove an assumption about the population.
- Advancing Theory: Whether rejected or retained, testing the null hypothesis helps move a theory forward.
- Checking Consistency: It shows how consistent the results of multiple studies are, using the same neutral baseline each time.
Starting from the null hypothesis keeps research objective. Every study begins from the same neutral assumption, that there is no effect, rather than from what the researcher hopes to find. Most statistical tests are designed specifically to test this neutral claim.
This shared starting point gives psychology a common standard. Two researchers testing the same question can compare their results directly, because both begin from the same baseline and the same decision rule.
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 about the effect of the independent variable on the dependent variable. Only one of the two can be true.
The null hypothesis states there is no effect in the population. The alternative states there is a statistically significant effect between the two variables.
The goal of hypothesis testing is to draw inferences about a population from a sample. Both hypotheses are needed for this. State your research hypothesis as a null version and an alternative version, together covering every possible outcome of the study.
Critical Evaluation of Null Hypothesis Testing
Rejecting or retaining the null hypothesis is not as clean a verdict as it can look. Two issues are worth understanding before treating a p-value as the final word.
Common Misinterpretations of the P-Value
A p-value is one of the most misread numbers in psychology. It answers a narrow question. It is not the probability that the null hypothesis is true, and it is not the probability that a finding will replicate.
It only measures how surprising the data would be if the null hypothesis were correct. A smaller p-value does not mean a bigger or more important effect either. Size and importance are separate questions.
The two are easy to confuse.
The p-value depends on both effect size and sample size, so a very large sample can turn a tiny, unimportant difference into a significant result. Statistical significance is therefore not the same as practical significance. A result can matter statistically and mean very little in practice.
This is why researchers increasingly report effect size and a confidence interval alongside the p-value, rather than the p-value on its own. These figures show how large an effect is and how precisely it was measured.
Contemporary Research
A large-scale study has since tested how often a rejected null hypothesis actually holds up when the same research is repeated.
- Aim: The Open Science Collaboration (2015) set out to measure how often a properly powered replication of a published, statistically significant psychology finding would also reject the null hypothesis.
- Method: Two hundred and seventy researchers ran 100 replications of studies from three major psychology journals, using high-powered designs agreed with the original authors wherever possible.
- Results: 97% of the original studies had rejected the null hypothesis, but only 36% of the replications did, and the average replicated effect was about half the original size.
- Conclusion: A single significant result is a weaker guarantee of a real effect than researchers had assumed, and published effect sizes tend to be inflated.
The finding does not mean most psychological effects are false. It means that rejecting the null once is not the same as showing an effect is real and repeatable.
FAQs
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.
Sources
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.
Open Science Collaboration. (2015). Estimating the reproducibility of psychological science. Science, 349(6251), aac4716. https://doi.org/10.1126/science.aac4716
Rozeboom, W. W. (1960). The fallacy of the null-hypothesis significance test. Psychological bulletin, 57(5), 416.
