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

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

: Q-Q plots, equal local levels, Kolmogorov-Smirnov, GWAS, multiple testing, global
testing, simultaneous region.

Quantile-quantile (Q-Q) 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 Q-Q 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 Q-Q plots and probability-probability (P-P) 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 Q-Q 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 Q-Q plots in
genome-wide association studies.

Eric Weine

https://www.jstatsoft.org/article/view/v106i10

University of Chicago

March 2023

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