In statistics, what does a p-value represent?

A p-value represents the probability of obtaining results at least as extreme as those observed, given that the null hypothesis is true. This concept is fundamental in hypothesis testing because it helps assess the strength of evidence against the null hypothesis. When researchers conduct a statistical test, they start with a null hypothesis, which typically reflects a state of no effect or no difference. The p-value quantifies how compatible the observed data is with this assumption. A small p-value indicates that the observed data would be very unlikely under the null hypothesis, providing evidence to reject the null hypothesis in favor of the alternative hypothesis. This measure is crucial for determining statistical significance in a study.

In contrast, the other options address different statistical concepts that do not define a p-value. The average of all test outcomes pertains to measures of central tendency, the proportion of variance explained by a model relates to the goodness-of-fit in regression analysis, and the total number of observations refers to the size of the data sample, which does not directly connect to the concept of a p-value.