Variations of Q–Q Plots: The Power of Our Eyes!

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.

COVID-19 virus outbreak forecasting of registered and recovered cases after sixty day lockdown in Italy: A data driven model approach

“…Packages("forecast") library(forecast) library(readxl) worldcovid19 <-read_excel("Italycovid19.xlsx") View(worldcovid19) tsworldcovid19 <-ts (Italycovid19$'daily registered Cases', frequency Z 1,start Z c(15/02/2020,1)) tsworldcovid19 <-ts (Italycovid19$'daily recovered Cases', frequency Z 1,start Z c(15/02/2020,1)) plot(tsworldcovid19) A data driven predictive model approach for COVID-19 3 The 60-days COVID-19 forecasting graphs of register along recovery cases (Fig. 4), and normalized QQ plots 9 were computed ( Fig. 5).…”

Words That Move Us. The Effects of Sentences on Body Sway

“…The arithmetic mean SD in each language condition and body sway axis was estimated for each participant, and the normality of the SD distribution for each language condition in the ML and AP axes was examined graphically via Q-Q plots (see Loy, Follett, & Hofmann, 2016) and statistically via the Shapiro-Wilk normality test (see Marmolejo-Ramos & González-Burgos, 2013). The Shapiro-Wilk test indicated that some vectors of data did not distribute normally in both AP and ML data; specifically, for the AP axis: W HE = 0.95, p = .2805, W LE = 0.93, p = .051, and W NE = 0.85, p < .001; and for the ML axis: W HE = 0.89, p = .004, W LE = 0.88, p = .003, and W NE = 0.87, p = .001.…”

Sensitivity of binomial N‐mixture models to overdispersion: The importance of assessing model fit

“…In applications, we suggest using graphical checks via qq plots and plots of residuals against fitted values and covariates because such checks provide more information about the nature of the lack of fit than a p-value does. To get an understanding of the variability that would be expected in a qq plot if the model was correct it can also be useful to compare qq plots for the fitted model to a few qq plots for data generated from a standard normal distribution with the same sample size (Loy, Follett, & Hofmann, 2016).…”