Theoretical Quantile-Quantile Plots:

the stereogram dataset

The dataset is taken from Graphical Methods for Data Analysis (GMDA), by Chambers, Cleveland, Kleiner, and Tukey, Wadsworth and Brooks, 1983, Dataset 26.

"Length of time in seconds taken by subjects to see a three dimensional object, (a spiral ramp coming out of the page), in a random dot stereogram. The subjects were given varying prior information about the object; 42 receiving either no information or verbal information only (nv), and 35 receiving both verbal and visual information (vv). ... Data were digitalized from the article and rounded. Source: Frisby and Clatworthy (1975), [Chapter 6]."

Original dataset: diagnostic views (incl. histogram, boxplot and standard normal plot) and the empirical quantile-quantile plot

Diagnostic view for nv

Datasets after the power normal transformation: diagnostic views (incl. histogram, boxplot and standard normal plot) and empirical quantile-quantile plot

Diagnostic view for powernormal(nv,0.1)

Note: here powernormal(x,theta) is defined as -(xtheta) if theta is negative (cf. GMDA, by Chambers et al, p214).

(A rightward shift is to be used if x assumes negative values. )

For another definition of powernormal(x,theta) see Visualizing Data, by Cleveland, p56, where

powernormal2(x,theta) is defined simply as xtheta for a negative theta.

[for negative theta both transformations reverse the upper and lower tails of the distribution]

Quantile-quantile plot: powernormal2(vv,-0.1) vs. powernormal2(nv,0.1)

04/22/2005 F by TL