Null distributions of the regression coefficients and tests statistics in the ridge regression model for data with binary outcomes. Left column - histogram of fitted coefficients in the permutation test, with the coefficient fitted to the original data indicated by a vertical line. Right column - Null distribution of the test statistic used in the approximate test (a standard normal distribution) with the test statistic of the fitted coefficient indicated by a vertical line. Top row, a SNP associated with phenotype; bottom row, a SNP not associated with phenotype. The causal and non-causal SNPs are from the same replicate in the simulation study where n = 500, m = 20, λ = 1. p-values are shown above each plot.