Practice question · Multiple choice
A study with 50,000 participants reports a statistically significant difference with Cohen's d = 0.02. Why is that result significant and unimportant at the same time?
Hints
- Ask what a p-value is actually testing, and whether that question is about size.
- What does sample size do to the standard error, and therefore to detectability?
Show the answer
B. Because a large enough sample distinguishes almost anything from zero.
Why
Detectability improves without limit as the sample grows, so with 50,000 people an effect of no consequence clears the threshold comfortably. Effect size asks how large, in units independent of n, and d = 0.02 means the distributions are almost entirely superimposed. The p-value is not meaningless; it is telling the truth about a question of limited interest.
Practise Power and Effect Size
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