In hypothesis testing, what does a p-value represent?

The p-value is a fundamental concept in hypothesis testing that quantifies the strength of the evidence against the null hypothesis. Specifically, it represents the probability of observing the data or something more extreme, assuming that the null hypothesis is true. This means that a lower p-value indicates stronger evidence against the null hypothesis, suggesting that the observed results are less likely to occur under its assumption.

In practical terms, if the p-value is less than the chosen significance level (commonly set at 0.05), it suggests that the observed results could be statistically significant, leading to the potential rejection of the null hypothesis in favor of the alternative hypothesis. This is why understanding the p-value is crucial for making informed decisions based on statistical analysis.

The other options refer to different concepts in hypothesis testing:

• The maximum error rate allowed in experiments relates to the concept of the significance level, which is predetermined and not the same as the p-value itself.
• The significance level is denoted by alpha and is set before conducting the test; it establishes the threshold for determining whether to reject the null hypothesis.
• The average difference between groups is a measure of effect size, which describes the extent of differences in outcomes rather than the probability of observing data given the null hypothesis is