| Family-wise error rate |
αFW = 1- (1- αPC)C |
where C refers to the number of comparisons performed, and αPC refers to the per contrast error rate, usually 0.05 |
| Bonferroni correction |
p’i = npi ≤ α |
the p-value of each test (pi) is multiplied with the number of performed statistical tests (n). If the corrected p-value (p’i) is lower than the significance level, α (usually 0.05), the null hypothesis will be rejected and the result will be significant |
| Sidak-correction |
p’i = 1- (1—pi)n ≤ α. |
where pi refers to the p-value of each test, and n refers to the number of performed statistical tests (n) |
| False discovery rate |
FDR = E [V / R] |
where E refers to the expected proportion of null hypotheses that are falsely rejected (V), among all tests rejected (R), thus it calculates the probability of an incorrect discovery. |
| Storey’s positive FDR |
FDR (t) = (π0 x m x t) / S(t) |
where t represents a treshold between 0 and 1 under which p-values are considered significant, m is the number of p-values above the treshold (p1, p2, pm), π0 is the estimated proportion of true nulls (π0 = m0 / m) and S(t) is the number of all rejected hypotheses at t |
| Benjamini and Yekutieli |
FDRi ≤ (n x pi)/(nRi x c(n))’ |
where c(n) is a function of the number of tests depending on the correlation between the tests. If the tests are positively correlated, c(n) = 1 |
| Proportion of false positives (PFP) |
PFP = E (V) / E (R) |
where E refers to the expected proportion of null hypotheses that are falsely rejected (V), among all tests rejected (R). V and R are both individually estimated |
| q-value |
q(pi) = min FDR (t) |
the q-value is defined as the minimum FDR that can be achieved when calling that "feature" significant |
