What is a null hypothesis?

All statistical tests have a null hypothesis. For most tests, the null hypothesis is that there is no relationship between your variables of interest or that there is no difference among groups.

For example, in a two-tailed t test, the null hypothesis is that the difference between two groups is zero.

Example: Null and alternative hypothesis

You want to know whether there is a difference in longevity between two groups of mice fed on different diets, diet A and diet B. You can statistically test the difference between these two diets using a two-tailed t test.

Null hypothesis (H₀): there is no difference in longevity between the two groups.
Alternative hypothesis (H_A or H₁): there is a difference in longevity between the two groups.

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What exactly is a p value?

The p value, or probability value, tells you how likely it is that your data could have occurred under the null hypothesis. It does this by calculating the likelihood of your test statistic, which is the number calculated by a statistical test using your data.

The p value tells you how often you would expect to see a test statistic as extreme or more extreme than the one calculated by your statistical test if the null hypothesis of that test was true. The p value gets smaller as the test statistic calculated from your data gets further away from the range of test statistics predicted by the null hypothesis.

The p value is a proportion: if your p value is 0.05, that means that 5% of the time you would see a test statistic at least as extreme as the one you found if the null hypothesis was true.

Example: Test statistic and p value

If the mice live equally long on either diet, then the test statistic from your t test will closely match the test statistic from the null hypothesis (that there is no difference between groups), and the resulting p value will be close to 1. It likely won’t reach exactly 1, because in real life the groups will probably not be perfectly equal.

If, however, there is an average difference in longevity between the two groups, then your test statistic will move further away from the values predicted by the null hypothesis, and the p value will get smaller. The p value will never reach zero, because there’s always a possibility, even if extremely unlikely, that the patterns in your data occurred by chance.