# MultiplicityAdjustment

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## MultiplicityAdjustment

Multiplicity Adjustments used in Array Studio for multiple comparisons

 FDR_BH False Discovery Rate Benjamini & Hochberg This correction is one of the least stringent of all the options, and therefore tolerates more false positives. There will be also less false negative genes. Here is how it works: 1) The p-values of each gene are ranked from the smallest to the largest. 2) The largest p-value remains as it is. 3) The second largest p-value is multiplied by the total number of genes in gene list divided by its rank. If less than 0.05, it is significant. Corrected p-value = p-value*(n/n-1) < 0.05, if so, gene is significant. 4) The third p-value is multiplied as in step 3: Corrected p-value = p-value*(n/n-2) < 0.05, if so, gene is significant. And so on. FDR_BY False Discovery Rate Benjamini & Yekutieli Benjamini, Y., and Yekutieli, D. (2001). The control of the false discovery rate in multiple testing under dependency. Annals of Statistics 29, 1165-1188. ||Benjamini & Yekutieli (2001) added upon the FDR_BH method above for the case of negative or positive correlation among tests. Bonferroni http://en.wikipedia.org/wiki/Bonferroni_correction Uses t tests to perform pairwise comparisons between group means, but controls overall error rate by setting the error rate for each test to the experiment wise error rate divided by the total number of tests. Hence, the observed significance level is adjusted for the fact that multiple comparisons are being made. Sidak http://www.uky.edu/ComputingCenter/SSTARS/www/documentation/MultipleComparisons_3.htm#b4 Pairwise multiple comparison test based on a t statistic. Sidak adjusts the significance level for multiple comparisons and provides tighter bounds than Bonferroni The Sidak test gives slightly smaller adjusted p-values than Bonferroni, but it guarantees the strict control of familywise error rate (FWE) only when the comparisons are independent as, for example, orthogonal contrasts. StepDown Bonferroni This correction is very similar to the Bonferroni, but a little less stringent: 1) The p-value of each gene is ranked from the smallest to the largest. 2) The first p-value is multiplied by the number of genes present in the gene list: if the end value is less than 0.05, the gene is significant: Corrected P-value= p-value * n < 0.05 3) The second p-value is multiplied by the number of genes less 1: Corrected P-value= p-value * n-1 < 0.05 4) The third p-value is multiplied by the number of genes less 2: Corrected P-value= p-value * n-2 < 0.05 It follows that sequence until no gene is found to be significant. StepDownSidak The benefit of using stepdown methods is that the tests are made more powerful (smaller adjusted p-values) while, in most cases, maintaining strong control of the familywise error rate. The stepdown method was pioneered by Holm (1979) and further developed by Shaffer (1986), Holland and Copenhaver (1987), and Hochberg and Tamhane (1987). StepUp Step-up multiple test procedure tests the t statistics for the k hypotheses in order starting with the least significant one and continues as long as an acceptance occurs. (By contrast, the step-down approach, which is usually used, starts with the most significant and continues as long as a rejection occurs.) QValue The q-value is similar to the well known p-value. It gives each hypothesis test a measure of significance in terms of a certain error rate. The p-value of a test measures the minimum false positive rate that is incurred when calling that test significant. Likewise, the q-value of a test measures the minimum false discovery rate that is incurred when calling that test significant.

Note: The Multiplicity adjustment takes into account the total number of tests performed within a given analysis. There is the ability to set the default option to adjust p-values on a per-test basis.