Application of Equal Local Levels to Improve QQ Plot Testing Bands with R Package qqconf
Abstract
QuantileQuantile (QQ) plots are often difficult to interpret because it is unclear how large the deviation from the theoretical distribution must be to indicate a lack of fit. Most QQ plots could benefit from the addition of meaningful global testing bands, but the use of such bands unfortunately remains rare because of the drawbacks of current approaches and packages. These drawbacks include incorrect global Type I error rate, lack of power to detect deviations in the tails of the distribution, relatively slow computation for large data sets, and limited applicability. To solve these problems, we apply the equal local levels global testing method, which we have implemented in the R Package qqconf, a versatile tool to create QQ plots and probabilityprobability (PP) plots in a wide variety of settings, with simultaneous testing bands rapidly created using recentlydeveloped algorithms. qqconf can easily be used to add global testing bands to QQ plots made by other packages. In addition to being quick to compute, these bands have a variety of desirable properties, including accurate global levels, equal sensitivity to deviations in all parts of the null distribution (including the tails), and applicability to a range of null distributions. We illustrate the use of qqconf in several applications: assessing normality of residuals from regression, assessing accuracy of p values, and use of QQ plots in genomewide association studies.
 Publication:

arXiv eprints
 Pub Date:
 November 2021
 arXiv:
 arXiv:2111.15082
 Bibcode:
 2021arXiv211115082W
 Keywords:

 Statistics  Computation;
 Quantitative Biology  Quantitative Methods;
 Statistics  Applications