A data scientist obtains a statistically significant result with a p-value of 0.001 when comparing mean session durations between two product variants on a dataset of five million users. The observed difference in means is 0.4 seconds. A stakeholder asks whether this finding is practically important. What is the most accurate statistical reasoning?
- AThe result is automatically practically important, because a p-value as low as 0.001 indicates a large and meaningful effect on session duration.
- BThe result cannot be trusted at all, because a dataset of five million users will produce a p-value below 0.05 regardless of the true effect.
- CStatistical significance with a very large sample can reflect a tiny effect, so the practical importance depends on the effect size and context, not on the p-value alone. Correct
- DPractical importance is confirmed by recomputing the p-value at a stricter significance level of 0.01, which the result already satisfies.
Why A is wrong: Tempting because a small p-value feels decisive, but the p-value measures evidence against the null, not the magnitude of the effect, so it cannot establish practical importance.
Why B is wrong: Tempting because large samples often yield small p-values, but it overstates the case: large samples increase power, they do not force significance when no effect exists.
Why C is correct: Correct: very large samples make even negligible differences statistically significant, so a low p-value does not establish practical relevance, and the 0.4 second effect must be judged against the use case.
Why D is wrong: Tempting because tightening alpha sounds rigorous, but changing the threshold still only addresses significance and says nothing about whether a 0.4 second difference matters in practice.