Variations of Q-Q Plots -- The Power of our Eyes!

TL;DR

This paper demonstrates that lineup protocols enhance the power of Q-Q plots for distributional assessment, outperforming traditional tests and de-trended plots, with broad applicability beyond normality.

Contribution

It introduces the use of lineup protocols to improve the interpretability and power of graphical distributional assessments, comparing them favorably to formal tests.

Findings

Lineup of standard Q-Q plots is more powerful than de-trended Q-Q plots.

Lineup tests outperform traditional normality tests.

Method is general and applicable to other distributions.

Abstract

In statistical modeling we strive to specify models that resemble data collected in studies or observed from processes. Consequently, distributional specification and parameter estimation are central to parametric models. Graphical procedures, such as the quantile-quantile (Q-Q) plot, are arguably the most widely used method of distributional assessment, though critics find their interpretation to be overly subjective. Formal goodness-of-fit tests are available and are quite powerful, but only indicate whether there is a lack of fit, not why there is lack of fit. In this paper we explore the use of the lineup protocol to inject rigor to graphical distributional assessment and compare its power to that of formal distributional tests. We find that lineups of standard Q-Q plots are more powerful than lineups of de-trended Q-Q plots and that lineup tests are more powerful than traditional tests of normality. While, we focus on diagnosing non-normality, our approach is general and can be directly extended to the assessment of other distributions.