Bonferroni and Šidák Corrections
Compare two family-wise error thresholds and see when independence matters.
Free theory articleCompare two family-wise error thresholds and see when independence matters.
Concept & interpretation
When performing multiple statistical tests, the chance of making at least one Type I error (a false positive) increases. To control the Family-Wise Error Rate (FWER)—the probability of one or more false discoveries—we must require a stricter threshold for each individual test. The Bonferroni and Šidák methods provide two classical ways to calculate this per-test threshold.
Experiment
In the interactive module, you can investigate how changing parameters affects these error rates.
- Adjust the Test count (m) control to 20 and the target Family alpha (α) to 0.05.
- Observe the calculated threshold spans. The Šidák threshold exactly hits the expected line on the visual plot, and the Bonferroni threshold falls slightly lower.
Notice that for m=1, the two thresholds are mathematically identical.