One-tail vs. two-tail P values

When comparing two groups, you must distinguish between one- and two-tail P values. Some books refer to one- and two-sided P values, which means the same thing.

Both one- and two-tail P values are based on the same null hypothesis, that two populations really are the same and that an observed discrepancy between sample means is due to chance.

Note: This example is for an unpaired t test that compares the means of two groups. The same ideas can be applied to other statistical tests.

Two-tail P value

The two-tail P value answers this question:

Assuming the null hypothesis is true, what is the chance that randomly selected samples would have means as far apart as (or further than) you observed in this experiment with either group having the larger mean?

One-tail P value

To interpret a one-tail P value, you must predict which group will have the larger mean before collecting any data. The one-tail P value answers this question:

Assuming the null hypothesis is true, what is the chance that randomly selected samples would have means as far apart as (or further than) observed in this experiment with the specified group having the larger mean?

A one-tail P value is appropriate only when previous data, physical limitations or common sense tell you that a difference, if any, can only go in one direction. The issue is not whether you expect a difference to exist – that is what you are trying to find out with the experiment. The issue is whether you should interpret increases and decreases in the same manner.

You should only choose a one-tail P value when both of the following are true.