# The Benjamini-Hochberg Correction

Scaffold, Q+, Q+S and Scaffold perSPECtives allows users to apply corrections for controlling the error rate in experiments with multiple statistical tests. The following document explains the steps for the calculation of one of these methods, the Benjamini-Hochberg Correction.

• The p-value is calculated for each comparison
• The p-values are ranked in order from smallest on the top to largest on the bottom
 Rank p-value Critical Value 1 0.0044 0.00047 2 0.023 0.00093 3 0.046 0.00140 4 0.046 0.00187 5 0.05 0.00234 6 0.059 0.00280 7 0.083 0.00327 8 0.099 0.00374 9 0.11 0.00421 10 0.11 0.00467 11 0.12 0.00514 12 0.12 0.00561 13 0.12 0.00607 14 0.12 0.00654 15 0.12 0.00701 16 0.13 0.00748 17 0.14 0.00794 18 0.15 0.00841 19 0.15 0.00888 20 0.15 0.00935

Figure 1. A portion of the values used in the calculation of the corrected significance level. The total number of tests was 107 with the top 20 reproduced above.

• The critical value is calculated for each calculated p-value. The formula is as follows:

Critical Value = (RankNumber of Tests) Significance Level

• The number of tests is equal to the number of p-values calculated. In an experiment where there are 100 proteins compared the number of tests is 100
• Scaffold allows users to set the Significance Level using the Quantitative Analysis Setup dialog. The default is p < 0.05
• Find the highest p-value that is less than its Critical Value. This Critical Value is the corrected significance level.
• For the example data above there are no p-values that are less than their associated critical value. Thus the corrected significance level is 0.0047 and no p-values are significant after correction.