When the direction of the allelic effect on gene expression is hard to predict, we can still employ the computationally more complex weighted sum of χ statistics within such categories (Davies, 1980).
In Zhou et al. [ 34], parametric approximations are only detailed for two self-contained gene set test statistics (sum of the score statistics and sum of the squares of the score statistics) and one non-directional competitive test statistic (a weighted sum of the squares of local score statistics).
Each gene set was assigned a score of differential expression between two conditions (essentially, the sum of t-statistics for each gene within the set), and the false discovery rate (Q) associated with this score was calculated via two separate permutation tests (permuting gene labels (Q1) and sample labels (Q2)).
Once the SNP-level measure is decided, the gene-level summary statistics are then derived as the highest SNP-level statistics [ 10], the sum of SNP-level statistics [ 9], or the combined p-value [ 1].
The case of sum statistics of k best alignments is included.
Cluster-level statistics were then computed as the sum of suprathreshold voxel statistics for all clusters in all maps.
Instead of only storing the top N genes in each of the resamplings, we sum the statistics (sum of ranks or sum of signal-to-noise ratios (SNRs)) of the genes across all the resamplings, and base the final ranking on this cumulative statistic.
Briefly, eLC directly combined correlated test statistics obtained from univariate GWAS meta-analyses with a weighted sum of univariate test statistics to empirically maximize the overall association signals and also to account for the phenotypic correlation between menarche and menopause.
With set association analysis (SAA), contributions from multiple SNPs are combined by forming a sum of single-marker statistics, which results in a single genome-wide test statistic with high power [ 14].
Similarly, mismatch distribution in the CR sequences (τ = 0.931, time since expansion ≈ 1.8 kyrbp, 1.3 – 2.7 kyrbp according to 95% CR) did not agree with a sudden expansion model, being the sum-of-squared-differences (SSD) statistics equal to 0.01, with p = 0.04 (Fig. 4).
