What does a p-value represent in hypothesis testing?

The p-value is fundamentally a measure of the evidence against the null hypothesis in a hypothesis test. Specifically, it indicates the probability of obtaining a sample statistic as extreme as, or more extreme than, the one observed, given that the null hypothesis is true. This concept is crucial because it quantifies how compatible the observed data is with the assumption that the null hypothesis holds.

When you calculate a p-value, you are determining how likely it is to observe the data you did (or something more extreme) solely under the assumption that the null hypothesis is correct. A smaller p-value suggests stronger evidence against the null hypothesis, prompting researchers to consider rejecting it in favor of the alternative hypothesis.

Understanding this concept is key for interpreting the results of hypothesis tests, as it helps to assess whether the data provides sufficient evidence to support the alternative hypothesis.