Applied Statistics: Analysis of Variance and Regression

Abstract

This is book 78 in the publisher’s statistics series. It is subtitled “A Collection of Quantile-Quantile Plots.” Although I certainly had seen references to quantile-quantile (Q-Q) plots in various \ourceb, I did not think that I really knew what a Q-Q plot was. I quickly found out. however, that one of everybody’s favorite graphical tools. the probability plot. was a Q-Q plot. Q-Q plots have percen@z points, the quantiles, on one axis for one distribution and on the other axis for another distribution. For a normal probability plot. one of the axes is an observed distribution and the other axis is the theoretical normal distribution. The first three sections of this book. a mere 26 pages, comprise the te\t. Section 4. all of the rest except for two appendixes. provideh 452 pages of Q-Q plots, usually two per page. Now that is a lot of plots. and I will admit to being very curious concerning why one ever would need all of these Q-Q plots. In Section 3, “Uses of the Folio.” the author suggests three situations-the illustration of limiting properties. the determination of the shape of comparison distributions with respect to reference distributions and each other, and the suggestion of distribution for observed data. The first two are in the domain of the theoretician. The third, however. is most appropriate for a practitioner of normal probability plotting. In this situation. one collects some data. makes a normal probability plot. and looks at its shape Ifit is not a straight line, then one goes to the Q-Q plot folio, looks at Q-Q plots of other distributions versus the normal as a reference. and tinds some Q-Q plot that has the same shape as the probability plot for the data. A similar shape wjill indicate that the theoretical distribution that was plotted versus the normal distribution in the Q-Q plot would be the one to check next wjith a probability plot. ifthat is possible. The utility of the book for anyone certainly depends on the menu of distributions. There are three reference distributions: (a) normal, (b) exponential. and (c) uniform. Perhaps more references could have been used, particularly the lognormal according to my experiences. The I5 comparison distributions are beta, Cauchy. F. gamma, Inverse Gaussian, Johnson SB, Johnson SU. logistic. lognormal. Pareto. power law. slash. stable. t. and Weibull. I had never heard of the slash or stable distributions. I also have a number of dilrerent chi-squared probability papers and certainly am curious about a possible explanation for the exclusion of chi-squared distributions. Various shape and scale parameters result in many forms for many of these comparison distributions. which explains why there can be nearly 900 comparative plots in the folio. The History of Statistics, by Stephen Stigler. Cambridge. MA: Harvard University Press. 1986, xvi + 416 pp., 95.