p-value

Last revised by Stefan Tigges on 6 Jan 2024

A p-value is the probability of observing a difference between groups at least as extreme as what was observed. Since a p-value is calculated assuming that the null hypothesis (H0) is true, the expectation is that there is no difference between the groups being evaluated. The process of evaluating the plausibility of H0 using a p-value is called hypothesis testing.

By convention, p-value ≤0.05 is considered statistically significant. It should be noted that statistically significant is not the same as clinically significant as this implies the p-value is a measure of treatment effectiveness which it is not.

The p-value is used in deciding if the null hypothesis made before the start of the study should be rejected (i.e. it is an indication of the likelihood of making an alpha or type I error1. Because the p-value is calculated assuming that the null hypothesis is true, the null is not "accepted": a p-value >0.05 means that there is insufficient evidence to reject H0. The p-value gives no information regarding beta or type II error (a false negative trial result). For radiologists, it may be easier to remember that an alpha error is a false positive result and that beta error is a false negative result.

Practical points

  • if a p-value is equal to or below the p-value cutoff, this does not mean that the results of the study are valid or that a study is meaningful; it only tells you that the difference between the mean values of the test group and control group would occur by chance only ≤5% of the time

  • p=0.001 is not necessarily a 50x better study than p=0.05, the difference between the means must be taken into account

    • e.g. a study that shows 1% increased enhancement with a new MRI imaging agent at p=0.001 is not nearly as interesting as a new imaging agent that shows 20% increased enhancement at p=0.05; however, in the former study there is a considerably reduced probability that the observed difference occurred by chance

  • because a p-value is calculated assuming that H0 is true, it is a conditional probability: P(data observed|H0 true)

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