## Introduction

Many clinicians consider the *P* value as an almost magical number that determines whether treatment effects exist or not. Is that a correct understanding?

In order to grasp the conceptual meaning of the *P* value, consider comparing two treatments, A and B, and finding that A is twice as effective as B. Does it mean that treatment A is better in reality? We cannot be sure from that information alone. It may be that treatment A is truly better than treatment B (i.e., true positive). However, it may also be that by chance we have collected a sample in which more people respond to treatment A, making it appear as more effective, when in reality it is equally effective as treatment B (i.e., false positive).

*P*value can help us with that. Conceptually, the

*P*value can be thought of as the probability of observing these results (A is twice as effective as B) by chance if in reality there is no difference between A and B. It is therefore the probability of having a false-positive finding (also called type I or alpha error).

## An arbitrary definition

If the *P* value is less than 5% (*P* less than .05) that means that there is less than a 5% probability that we would observe the above results if in reality treatment A and treatment B were equally effective. Since this probability is very small, the convention is to reject the idea that both treatments are equally effective and declare that treatment A is indeed more effective.

The *P* value is thus a probability, and “statistical significance” depends simply on 5% being considered the cutoff for sufficiently low enough probability to make chance an unlikely explanation for the observed results. As you can see this is an arbitrary cutoff; it could have been 4% or 6%, and the concept would not have changed.^{1}

## Power

Thus, simply looking at the *P* value itself is insufficient. We need to interpret it in light of other information.^{2} Before doing that, we need to introduce a new related statistical concept, that of “power.” The power of a study can be conceptually understood as the ability to detect a difference if there truly is one. If there is a difference in reality between treatments A and B, then the power of a study is the ability to detect that difference.

Two factors influence power: the effect size (that is, the difference between A and B) and the sample size. If the effect size is large, then even with small samples we can detect it. For example, if treatment A was effective in 100% of the cases, and treatment B only in 10% of cases, then the difference will be clear even with a small number of patients. Conversely, if the effect size is small, then we would need a very large sample size to detect that difference. For example, if treatment A is effective in 20% of cases, and treatment B is effective in 22% of cases, the difference between them could be observed only if we enrolled a very large number of patients. A large sample size increases the power of a study. This has important implications for the interpretation of the *P* value.