Page:Graphic methods for presenting facts (1914).djvu/57

 for example, one and a half, the average reader would be completely nonplussed, as he would not trouble to go through the mental arithmetic of multiplying one and a half by one and a half. In general, the comparison of two circles of different size should be strictly avoided.

Fig. 37. Total Yearly Value for the United States of Combined Imports and Exports by Land and by Sea

In this illustration the data have been represented by circles drawn on a diameter basis. The right-hand circle appears more prominent than the data would justify. Circles compared on a diameter basis mislead the reader by causing him to over-estimate the ratios. Compare Fig. 38

Many excellent works on statistics approve the comparison of circles of different size, and state that the circles should always be drawn to represent the facts on an area basis rather than on a diameter basis. The rule, however, is not always followed and the reader has no way of telling whether the circles compared have been drawn on a diameter basis or on an area basis, unless the actual figures for the data are given so that the dimensions may be verified.

Fig. 38. Total Yearly Value for the United States of Combined Imports and Exports by Land and by Sea

Here the data of Fig. 37 have been shown by means of circles drawn on an area basis, as recommended by many authorities on statistical work. The right-hand circle, however, shows up less prominently than the figures would justify. Circles compared on an area basis mislead the reader by causing him to underestimate the ratios. Circles of different size should never be compared. Horizontal bars have all the advantages of circles with none of the disadvantages

In Fig. 37 the figures are given, and the circles have been drawn on a diameter basis. It will be noted that the figures for 1910 are roughly twice those for 1890. The circle, however, has roughly four times the area of the circle for 1890 and, accordingly, seems to have much more than twice the importance. In Fig. 38, the same data have been shown on an area basis as most of the authorities on statistical work recommend. If the figures were not given, the reader would be forced to fit the left-hand circle into the right-hand circle on an area basis, or else make a ratio between the diameters and then square the ratio. Either process is almost impossible to accomplish and there is