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 Navigation: PRINCIPLES OF STATISTICS > P Values Advice: How to interpret a small P value

## Before you interpret the P value

Before thinking about P values, you should:

Review the science. If the study was not designed well, then the results probably won't be informative. It doesn't matter what the P value is.

Review the assumptions of the analysis you chose to make sure you haven't violated any assumptions. We provide an analysis checklist for every analysis that Prism does. If you've violated the assumptions, the P value may not be meaningful.

## Interpreting a small P value

A small P value means that the difference (correlation, association,...) you observed would happen rarely due to random sampling. There are three possibilities:

The null hypothesis of no difference is true, and a rare coincidence has occurred. You may have just happened to get large values in one group and small values in the other, and the difference is entirely due to chance. How likely is this? The answer to that question, surprisingly, is not the P value. Rather, the answer depends on the scientific background of the experiment.

The null hypothesis is false. There truly is a difference (or correlation, or association...) that is large enough to be scientifically interesting.

The null hypothesis is false. There truly is a difference (or correlation, or association...), but that difference is so small that it is scientifically boring. The difference is real, but trivial.

Deciding between the last two possibilities is a matter of scientific judgment, and no statistical calculations will help you decide.

## Using the confidence interval to interpret a small P value

If the P value is less than 0.05, then the 95% confidence interval will not contain zero (when comparing two means). To interpret the confidence interval in a scientific context, look at both ends of the confidence interval and ask whether they represent a difference between means that you consider to be scientifically important or scientifically trivial. This section assumes you are comparing two means with a t test, but it is straightforward to use these same ideas in other contexts.

There are three cases to consider:

The confidence interval only contains differences that are trivial. Although you can be 95% sure that the true difference is not zero, you can also be 95% sure that the true difference between means is tiny and uninteresting. The treatment had an effect, but a small one.

The confidence interval only includes differences you would consider to be important. Since even the low end of the confidence interval represents a difference large enough that you consider it to be scientifically important, you can conclude that there is a difference between treatment means and that the difference is large enough to be scientifically relevant.

The confidence interval ranges from a trivial to an important difference. Since the confidence interval ranges from a difference that you think would be scientifically trivial to one you think would be important, you can't reach a strong conclusion. You can be 95% sure that the true difference is not zero, but you cannot conclude whether the size of that difference is scientifically trivial or important.