  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 recently-developed 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.
