Sample size effect on statistical testing

• A. The larger the sample, the less likely to reject the null
• B. The larger the sample, the greater the probability that the statistical test will reject the null hypothesis
• C. Sample size has no impact on power
• D. Larger samples always guarantee clinical significance

Answer: (B)

Increasing sample size improves the precision of our estimate and the power of the statistical test. When you have more data, the variability of your estimate shrinks (the standard error gets smaller), so for a given true difference between groups, the test statistic becomes larger in magnitude. That makes it more likely to exceed the cutoff for rejecting the null hypothesis, so the probability of detecting a real effect rises. In other words, larger samples give you a higher chance of finding statistical significance when there is a true effect, provided the effect size is not zero.

Power depends on the effect size, the chosen significance level, and the sample size. As n grows, power increases; with too small a sample, you might miss real differences because of imprecision. This is why bigger studies are more able to detect modest but real differences.

The other statements don’t fit this relationship. Increasing sample size does not make you less likely to reject the null; it makes it more likely to reject when there is a true effect. Sample size does influence power, so saying it has no impact is incorrect. And larger samples do not guarantee clinical significance—statistical significance can occur with very small, possibly clinically irrelevant differences, so significance in a study doesn’t automatically mean the finding is clinically meaningful.