The primary trade-off when using Bonferroni correction is between

• A. Bias and precision
• B. Power and false positive rate
• C. Sample size and effect size
• D. Confidence interval width and p-values

Answer: (B)

The key idea is that Bonferroni correction protects against false positives when you run many tests, but it makes it harder to detect real effects. By dividing the overall significance level by the number of tests, each individual test becomes harder to reach significance, which lowers the chance of any false positive across all tests (the family-wise error rate). That tightened threshold, however, reduces statistical power—the probability of finding true effects—especially when effects are small or the number of tests is large. So the primary trade-off is between power and the false positive rate.

Other options don’t capture this balance as directly: bias and precision refer to systematic error and estimate variability, not the decision threshold across multiple tests; sample size and effect size influence power but aren’t the correction’s fundamental trade-off; and confidence interval width versus p-values describe related but different inference aspects rather than the core adjustment Bonferroni makes.