Consider a study that finds p < 0.05 but the observed effect size is small. What does this illustrate?

• A. Statistical significance does not necessarily imply a large or meaningful public health impact.
• B. It proves a large public health impact.
• C. It demonstrates causation.
• D. It invalidates the study.

Answer: (C)

Statistical significance shows whether an observed association is unlikely to be due to random variation, but it doesn't tell you how big or important the effect is in real-world terms. A small effect can still produce a p-value below 0.05 if the study has a large sample, so the result is statistically significant even though the actual difference would have little public health impact. This is why significance alone doesn’t imply a large or meaningful impact. It also doesn’t prove causation, since a low p-value only speaks to probability under the null hypothesis, not cause-and-effect. In short, you can have a statistically significant result with a tiny, potentially trivial effect size, so practical significance must be considered separately from statistical significance.