# Probability plotting methods for the analysis of data

**M. B. Wilk****R. Gnanadesikan****Bell Telephone**

CiteWeb id: 20160000022

CiteWeb score: 1091

SUMMARY This paper describes and discusses graphical techniques, based on the primitive empirical cumulative distribution function and on quantile (Q-Q) plots, percent (P-P) plots and hybrids of these, which are useful in assessing a one-dimensional sample, either from original data or resulting from analysis. Areas of application include: the comparison of samples; the comparison of distributions; the presentation of results on sensitivities of statistical methods; the analysis of collections of contrasts and of collections of sample variances; the assessment of multivariate contrasts;_ and the structuring of analysis of variance mean squares. Many of the objectives and techniques are illustrated by examples. This paper reviews a variety of old and new statistical techniques based on the cumulative distribution function and its ramifications. Included in the coverage are applications, for various situations and purposes, of quantile probability plots (Q-Q plots), percentage probability plots (P-P plots) and extensions and hybrids of these. The general viewpoint is that of analysis of data by statistical methods that are suggestive and constructive rather than formal procedures to be applied in the light of a tightly specified mathematical model. The technological background is taken to be current capacities in data collection and highspeed computing systems, including graphical display facilities. It is very often useful in statistical data analysis to examine and to present a body of data as though it may have originated as a one-dimensional sample, i.e. data which one wishes to treat for purposes of analysis, as an unstructured array. Sometimes this is applicable to ' original' data; even more often such a viewpoint is useful with 'derived' data, e.g. residuals from a model fitted to the data. The empirical cumulative distribution function and probability plotting methods have a key role in the statistical treatment of one-dimensional samples, being of relevance for summarization and palatable description as well as for exposure and inference.

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