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Quantile-Quantile (Q-Q) plots are often difficult to interpret because it isunclear how large the deviation from the theoretical distribution must be toindicate a lack of fit. Most Q-Q plots could benefit from the addition ofmeaningful global testing bands, but the use of such bands unfortunatelyremains rare because of the drawbacks of current approaches and packages. Thesedrawbacks include incorrect global Type I error rate, lack of power to detectdeviations in the tails of the distribution, relatively slow computation forlarge data sets, and limited applicability. To solve these problems, we applythe equal local levels global testing method, which we have implemented in theR Package qqconf, a versatile tool to create Q-Q plots andprobability-probability (P-P) plots in a wide variety of settings, withsimultaneous testing bands rapidly created using recently-developed algorithms.qqconf can easily be used to add global testing bands to Q-Q plots made byother packages. In addition to being quick to compute, these bands have avariety of desirable properties, including accurate global levels, equalsensitivity to deviations in all parts of the null distribution (including thetails), and applicability to a range of null distributions. We illustrate theuse of qqconf in several applications: assessing normality of residuals fromregression, assessing accuracy of p values, and use of Q-Q plots in genome-wideassociation studies.

Application of Equal Local Levels to Improve Q-Q Plot Testing Bands with R Package qqconf