The pair chart

Summary Given two random samples X1X2XnX and Y1, Y2Yny a “pair chart” is constructed as follows. Draw a rectangle of width nX units and height ny units. Starting from its lower left comer, draw a line one unit to the right (upwards) if the smallest observation in the combined samples is an X(a Y). Then, starting from the end of this line, draw another to the right (upwards) if the second smallest observation is an X (a Y). Continue through the largest observation, thus producing a path to the upper right comer of the rectangle. The paper explains how such a chart can be interpreted as a descriptive tool in comparing the two samples. There are figures which illustrate the typical effects on pair charts of differences between the underlying populations in location, scale, and shape. It is also shown how the pair chart can be used as an aid in calculating and interpreting various nonparametric procedures for the two‐sample problem These include: the one‐ and two‐ sided Kolmogorov‐Smirnov tests; the Wald‐Wolfowitz runs test; the Wilcoxon‐Mann‐Whitney test; Sukhatme's test for scale differences given both medians known; the Ansari‐Bradley scale test; Mood's squared‐rank test, and the Crouse‐Steffens modification of it; and Lehmann's two‐sample test. All of these are illustrated for three Examples, one of which has extensive ties.