In hypothesis testing, what does the p-value measure?

In hypothesis testing, the p-value measures the strength of evidence against the null hypothesis. It quantifies how compatible your observed data are with the assumption that the null hypothesis is true. Specifically, the p-value indicates the probability of observing data as extreme as, or more extreme than, what you have observed, assuming that the null hypothesis is accurate.

A small p-value suggests that the observed data are unlikely under the null hypothesis and provides stronger evidence against it, often leading researchers to consider rejecting the null hypothesis in favor of an alternative hypothesis. Conversely, a large p-value indicates that the data are consistent with the null hypothesis, providing weaker evidence against it.

Understanding the p-value is crucial for interpreting results in hypothesis testing because it informs decisions based on statistical significance, helping researchers to evaluate whether or not their findings are likely to have occurred by random chance.