False Discovery Rate Correction
This is a correction applied to p-Values to take into account the multiple comparisons problem. The correction is computed as:
Corrected p-Value = p × k
- p is the p-value.
- k is the correction and is determined by:
- Ranking all the comparisons according to the p-value, from smallest to largest.
- Computing p × m / i, where:
- m refers to the number of comparisons.
- i refers to the rank order of the p-values, where the smallest has a value of i of 1, the second smallest has a value of 2, etc.
- Identifying the largest value of i such that p × m / i < α, where α is the Overall significance level. If no values are significant, then we set i = 1, which reduces to the Bonferroni correction.
- Setting k as m / i where i is the largest rank as identified in the previous step.
Note that FDR is actually a method to adjust the cut-offs for significant p-values; there is no standard way of reporting p-values corrected by FDR. The p-values reported in Q differ from the values given in R using p.adjust because R does not set k to a single value. This does not affect the conclusions, but it means that corrected p-values cannot be compared to each other.
- A worked example of the FDR being applied here.
- Multiple Comparisons (Post Hoc Testing) for a description of how this correction is applied in Q.
- The Multiple Comparisons (Post Hoc Testing) page on SurveyAnalysis.org for more information about the theory and practice of correcting for multiple comparisons using the false discovery rate.