If a study fails to reject the null hypothesis, what can be concluded?

• A. There is definitely no association between exposure and outcome.
• B. There is an association, but the study lacked power.
• C. The alternative hypothesis is true.
• D. The data show no evidence of an association at the chosen significance level.

Answer: (D)

Interpreting a non-significant result in hypothesis testing: failing to reject the null means the data did not provide enough evidence, at the pre-specified significance level, to conclude there is an association between exposure and outcome. It does not prove there is no association; it only indicates that the observed data are not compelling enough to reject the null under the chosen alpha. Because of this, the correct conclusion is that there is no evidence of an association at the chosen significance level. The other statements overstate what can be concluded from a non-significant result: you can’t claim there is definitely no association, nor that the alternative hypothesis is true, and while a lack of power could explain a non-significant result, that cannot be asserted as the conclusion without separate power analysis and context.