Holm Step-Down Procedure
Compare sorted p-values with rank-dependent family-wise thresholds and map decisions back to their original labels.
Free theory articleCompare sorted p-values with rank-dependent family-wise thresholds and map decisions back to their original labels.
Concept & interpretation
For valid individual p-values, the Holm step-down procedure strongly controls the family-wise error rate (FWER), the probability of making at least one false rejection, at level α. This means it offers protection against false rejections across an entire family of hypotheses, regardless of which hypotheses are truly null or their dependence structure.
Interactive Demonstration
Open the interactive experiment to visualize how the thresholds change for different p-value families and targets.
- Select the A family and α = 0.10. Observe the first failure stops the procedure.
- Select the C family and α = 0.05. Notice how all hypotheses can pass if they are sufficiently small, reflecting a sequential Bonferroni-style correction that gets less stringent.
- Select Threshold equality. Equality rejects only while the step-down procedure remains active: with Family alpha = 0.05, ID1 rejects, rank 2 fails, and ID4 remains retained even though it equals its own later threshold.