An Improved Graphical Analysis and Comparison of Series of Samples

OVER the past few decades graphical methods have been developed and increasingly used for the comprehensive analysis and for the rapid and economical comparison of series of samples. These methods are applicable to any type of data involving random variation, but are of particular concern to systematists, who are constantly confronted with data derived from series of varying samples. In his pioneering study of variation and speciation in the garter snakes (Thamnophis), Ruthven (1908) showed by graphs the range, the mean, and the number of specimens for the scale counts of each of several geographically arranged groupings. He indicated the ranges by vertical lines on which the means were located by symbol according to sex. The means were connected so as to portray the variational trends (now called clines). This presentation was useful and promising, but failed to indicate the of the observed differences or to give more than the crudest idea of the degree of overlap or separation between samples. A valuable and clever addition to Ruthven's format was proposed by Dice and Leraas (1936). In each vertical line showing the range and the mean for a sample they inserted a rectangular bar, like those in Figure 1, outlining two standard errors of the mean (2aM) on either side of the mean. This method was designed to indicate and to test the of the difference between the means of each pair of samples portrayed. 'It was shown that the level of significance arbitrarily adopted by biologists was just about satisfied when two rectangles met, end to end, on the same horizontal. Following the same lead, Hubbs and Perlmutter (1942) pointed out that this is a special case; we need some indication too of the of the differences (t values), corresponding to the varying relative lengths, and to the varying overlap or separation, of the rectangles. Though many biologists and some statisticians still accept such an arbitrary distinction, there is no magic line (as P= .05 or .01), where totally unreliable evidence suddenly gives way to completely trustworthy indications of significant difference (see Figure 4). With the aid of biometrician Charles W. Cotterman, Hubbs and Perlmutter indicated in tabular form just what degree of reliability can be attributed to data showing, when graphed as in Figure 1, varying degrees of overlap or of separation between the bars outlining 2aM on either side of the mean. They concluded