# 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*

where:

*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.

- Ranking all the comparisons according to the

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.

## See also

- 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 Displayr for more information about the theory and practice of correcting for multiple comparisons using the false discovery rate.