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Table 3 Percentages of significant cases detected (Detected) and false discovery rate (FDR) after multitest adjustment when the p-values come from families of homogeneity tests where some (% effect) of the alternative hypotheses were true.

From: A new multitest correction (SGoF) that increases its statistical power when increasing the number of tests

  Weak    SB BH SGoF
N % effect S Significant Detected FDR Detected FDR Detected FDR
20 5% 100 5.7 0.10 73 0.10 72 0.10 77
20 5% 1000 5.7 0.01 53 0.01 57 0.07 78
20 5% 10000 5.7 0.00 65 0.00 61 0.25 55
20 10% 100 6.2 0.07 51 0.08 51 0.18 68
20 10% 1000 6.1 0.01 41 0.01 40 0.19 56
20 10% 10000 6.1 0.00 40 0.00 33 0.68 33
20 20% 100 6.8 0.14 39 0.16 38 0.30 52
20 20% 1000 7.0 0.01 24 0.01 25 0.70 35
20 20% 10000 7.0 0.00 16 0.00 16 1.58 19
    Mean 0.04 44.7 0.04 43.7 0.45 52.6
    SD 0.052 18.17 0.058 18.06 0.482 20.37
40 5% 100 6.0 0.14 45 0.15 46 0.13 69
40 5% 1000 6.0 0.02 31 0.02 33 0.15 57
40 5% 10000 6.0 0.00 22 0.01 23 0.61 37
40 10% 100 7.0 0.21 26 0.25 28 0.33 51
40 10% 1000 7.0 0.03 18 0.04 20 0.71 38
40 10% 10000 7.0 0.01 12 0.01 14 1.56 17
40 20% 100 8.9 0.34 20 0.45 21 1.02 32
40 20% 1000 8.9 0.05 8 0.10 9 2.50 21
40 20% 10000 8.9 0.01 5 0.04 7 3.44 6
    Mean 0.09 20.8 0.12 22.3 1.16 36.4
    SD 0.117 12.34 0.148 12.23 1.143 20.19
  1. Weak: The alternative hypothesis is weak. N: sample size. % effect: % of real true alternatives. S: number of tests. Significant: % of significants before adjustment. Detected: % of significant tests after adjustment. FDR: false discovery rate. SB: Sequential Bonferroni. BH: Benjamini and Hochberg. SGoF: Sequential Goodness of Fit.
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