The Power to See: A New Graphical Test of Normality

Many statistical procedures assume that the underlying data-generating process involves Gaussian errors. Among the popular tests for normality, only the Kolmogorov–Smirnov test has a graphical representation. Alternative tests, such as the Shapiro–Wilk test, offer little insight as to how the observed data deviate from normality. In this article, we discuss a simple new graphical procedure which provides simultaneous confidence bands for a normal quantile–quantile plot. These bands define a test of normality and are narrower in the tails than those related to the Kolmogorov–Smirnov test. Correspondingly, the new procedure has greater power to detect deviations from normality in the tails. Supplementary materials for this article are available online.

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