Which statement best describes the relationship between statistical significance and practical significance?

Which statement best describes the relationship between statistical significance and practical significance?

• A. Statistical significance implies practical importance in real-world settings.
• B. Statistical significance and practical significance are the same concept.
• C. Statistical significance assesses the probability that the observed result occurred by chance.
• D. Power has no relation to sample size.

Answer: (C)

The main idea here is that statistical significance and practical significance convey different things. Statistical significance is about probability: it asks whether the observed result would be unlikely if there were no true effect, usually assessed with a p-value. If that probability is low, we say the result is statistically significant. But this doesn’t tell you how large or important the effect is in real-world terms. A study with a very large sample can find a statistically significant result for a tiny, barely noticeable difference, while a study with a small sample might miss a meaningfully large effect. Practical significance, on the other hand, concerns the real-world impact of the finding. To judge it, you look at the size of the effect (the effect size), how precise that estimate is (confidence intervals), and whether the difference would matter in real life, costs, or policy decisions. So the best description is that statistical significance assesses the probability that the observed result occurred by chance, while practical significance is about the real-world importance of that result. Why the other ideas don’t fit: significance does not guarantee practical importance, so it’s not the same thing; they’re related but distinct concepts; and power is indeed related to sample size because larger samples increase the ability to detect effects, which contradicts the notion that there is no relation.

The main idea here is that statistical significance and practical significance convey different things. Statistical significance is about probability: it asks whether the observed result would be unlikely if there were no true effect, usually assessed with a p-value. If that probability is low, we say the result is statistically significant. But this doesn’t tell you how large or important the effect is in real-world terms. A study with a very large sample can find a statistically significant result for a tiny, barely noticeable difference, while a study with a small sample might miss a meaningfully large effect.

Practical significance, on the other hand, concerns the real-world impact of the finding. To judge it, you look at the size of the effect (the effect size), how precise that estimate is (confidence intervals), and whether the difference would matter in real life, costs, or policy decisions. So the best description is that statistical significance assesses the probability that the observed result occurred by chance, while practical significance is about the real-world importance of that result.

Why the other ideas don’t fit: significance does not guarantee practical importance, so it’s not the same thing; they’re related but distinct concepts; and power is indeed related to sample size because larger samples increase the ability to detect effects, which contradicts the notion that there is no relation.