What does a p-value indicate in hypothesis testing?

A p-value is a statistical measure that helps to determine the significance of results obtained from a hypothesis test. Specifically, it indicates the probability of observing the data, or something more extreme, assuming that the null hypothesis is true. Essentially, a p-value assesses whether any observed differences or relationships in the data could have occurred by random chance.

When you obtain a low p-value (commonly below a threshold such as 0.05), it suggests that the likelihood of the results occurring due to chance alone is very low, reinforcing the idea that there may be a significant effect or difference present worth further consideration. Thus, a p-value serves as a critical tool in hypothesis testing to help researchers decide whether to reject the null hypothesis in favor of the alternative hypothesis based on statistical evidence.

In contrast, the other options focus on different aspects of statistical analysis. The strength of the relationship between variables is typically measured by correlation coefficients rather than p-values. The size of the effect measured refers to effect size metrics that quantify the magnitude of differences, while the proportion of variance explained generally pertains to measures like R-squared in regression analyses. Each of these concepts serves distinct purposes in statistical analysis, but they do not specifically pertain to what a p-value indicates.