One thousand permutations with a sequential Bonferroni correction were used to derive significance levels for multiple comparisons.
As no exact distribution of EIPR is available yet, we make use of bootstrapping in order to numerically derive significance thresholds.
Permutation was used to derive significance thresholds for replication of each epistatic pair at the region level, where phenotypes were permuted and the highest −log10 Pint value of 121 (ie, 11 × 11) interaction tests was recorded in each of 1000 iterations.
After doing this, 5 of the 8 tests were still significant under the newly derived significance levels, judged by a test of P i ≤ α/(1 + k - i) where each P-value is ranked in ascending order (P1, P2... P i ) for k tests.
In truth, Miranda's national plan of 1801 derives significance from the fact that it was a unique proposal to superimpose a representative government of a monarchical type upon modified Spanish institutions.
The last column (ID.with.stars) shows the P adjusted derived significance (*** P adjusted < 0.001, ** P adjusted < 0.01 and * P adjusted < 0.05).
We fitted a generalized extreme value distribution to these scores and derived significance thresholds from the quantiles of this distribution (Knijnenburg et al. 2009).
For these analyses, we calculated genetic differentiation, analysis of molecular variance (AMOVA -based FST (Excoffier et al., 1992), for 5 kbp windows covering the entire genome and identified outliers using an empirically derived significance threshold.
Empirically derived significance thresholds for one-QTL vs. no-QTL test statistics were estimated using the permutation test (Churchill & Doerge, 1994 100000 permutations of the data were analyzed as for the unpermutated data.
We found evidence for seven new AITD risk loci (P < 1.12 × 10−6; a permutation test derived significance threshold), five at locations previously associated and two at locations awaiting confirmation, with other immune-mediated diseases.
We compared four algorithms: single-locus χ test with Bonferroni correction for multiple testing, the χ test using permutation tests derived significance thresholds, AdaBoost with 1000 trees and finally the BEAM algorithm.
