Which statement correctly distinguishes p-value from effect size?

• A. P-value tests whether the observed effect could occur by chance under the null hypothesis; effect size measures the practical importance of the effect.
• B. P-value measures the magnitude of the effect, and effect size measures significance.
• C. P-value tests whether the observed effect could occur by chance under the null hypothesis; effect size quantifies the magnitude of the effect regardless of sample size.
• D. P-value is the probability that the alternative hypothesis is true; effect size is the probability that the null is true.

Answer: (C)

The key idea here is separating what each quantity tells you about the data. A p-value is about significance under the null: it asks how likely the observed result (or something more extreme) would be if there were no true effect. It doesn’t tell you how big the effect is. An effect size, on the other hand, communicates how large the actual difference or association is—the magnitude of the effect—independent of how many data points you collected.

That makes the best statement the one that says the p-value measures how likely the observed effect could occur by chance under the null, while the effect size quantifies the magnitude of the effect regardless of sample size. It captures the distinction between significance (are we confident there’s an effect?) and magnitude (how big is the effect?).

Notes: you can have a tiny p-value with a very small or very large effect depending on sample size, and you can have a sizable effect with a non-significant p-value if the sample is small. But the central, correct distinction is that p-value concerns chance under the null, whereas effect size concerns the actual size of the effect.