Which statement best describes the relationship between effect size and p-values?

• A. Effect size is the probability of observing the data under the null.
• B. P-value measures the magnitude of the effect.
• C. Effect size quantifies the magnitude of the effect; p-value assesses evidence against the null.
• D. P-value and effect size provide the same information.

Answer: (C)

The key idea is that effect size and p-values answer different questions about a study. Effect size tells you how big the observed effect is in practical terms—how large the difference or association actually is. Examples include Cohen’s d for group differences, a correlation coefficient for association strength, or an odds ratio for binary outcomes. These numbers help you judge whether the effect is small, medium, or large and how meaningful it might be in real-world terms.

A p-value, by contrast, measures the strength of the evidence against the null hypothesis. It asks: if there were really no effect, what is the probability of obtaining data as extreme as what was observed (or more)? A small p-value suggests the data are unlikely under the null, so you’d consider the result statistically significant. But the p-value does not indicate how big the effect is, and its value is influenced by sample size: you can get a very small p-value from a tiny effect if the study has a large sample, or a large p-value from a big, important effect if the study has little data.

So the statement that best captures the relationship is that effect size quantifies the magnitude of the effect, while the p-value assesses evidence against the null.