to throw into bold relief the devices for distinguishing one set of facts from another. It is, however, necessary when data are classified into unequal-sized groups to use lines of different widths. In such cases it is the surfaces and not the linear dimensions which are important. The widths of lines will vary with the widths of groups but this need cause no confusion if the ordinate scales are properly written, and the surfaces are interpreted in terms of both scales. To depend on abscissa scales alone is inadequate. It is this error which often explains the misinterpretation of data so grouped. An illustration of the erroneous conclusions into which people are led in the use of both diagrams and tabulations by the failure to take into account the changing sizes of groups is given in a recent study of the national income tax.1 This failure is common and the reader should be constantly on the lookout for it when he is interpreting statistical diagrams.2 Frequently, confusion results from including too much in a single diagram, the complexity of detail in whole or in part defeating the functions which it otherwise would have. It is well to keep in mind the general rule that ease of comprehension is a vital consideration and that complex relations can generally more adequately be shown by tabulation. Frequently, however, even for relatively complex relationships, diagrams are of distinct service for the very reason that a number of comparisons can be made simultaneously. For those who are not accustomed to making and interpreting diagrams it is wise to be conservative on the amount of detail crowded into a single figure. There is no general and 1 See Falkner, Roland P., "Income Tax Statistics," Publications of the American Economic Association, June, 1915, pp. 523, 537. 2 See illustration in Report No. 4, Industrial Commission of Ohio on "Industrial Accidents in Ohio, January 1 to June 30, 1914," Columbus, Ohio, 1915, pp. 36-37. infallible rule respecting this matter, however, since much depends upon the size of illustrations, the skill with which they are drawn, etc. Plate 6 shows how successfully several facts may be shown on a well-drawn figure. The interesting thing about this figure is that absolute amounts are shown by widths of bars, lengths in all instances being identical and constituting 100 per cent. By cross-hatched surfaces not only are geographical divisions, but color, race, nativity, and parentage shown for the whole population of the United States. The figure admits of being read in two dimensions the same as a table, yet no confusion results. Instead, complex relations are admirably brought out. When it is necessary to use surfaces and volumes it is best to avoid the placing of areas within areas or contents within contents. If there is a real difficulty in using more than one dimension, it is increased by resorting to this device. It is not clear that such figures should be used except in cases where it is desired to show more than one relation. Even then, by using several illustrations employing lines or bars, the same results may generally be accomplished and with very much less likelihood of misinterpretation and confusion on the part of the reader. In the best statistical publications such figures are seldom used. Plate 7, showing the adult population in the United States and the number of insane in hospitals, is drawn first in the form of surfaces and second in the form of bars. The first defies comparison. Of course, it is evident that the adult population was greater in 1910 than in 1904, but how much greater is by no means revealed. According to the first method the absolute difference in the number of insane in hospitals at the two periods is barely capable of detection. The illustrations add nothing to the bare facts. So far as Proportion of Insane Enumerated January 1, to Adult Population, 1904 and 1910. (Surfaces within Surfaces and Lines) relations are concerned they are obscured by the manner in which they are shown. Graphically, little aid is given in establishing in either period the relation of the number of insane in hospitals to the total population. An alternative and not very satisfactory method in this case is to use bars. In summarizing the case for the use of lines and bars in illustrating statistical facts, attention should be called to the appeal which such figures make to the eye and to the ability which they have to make concrete relations and sequences which in tabular form remain abstract. For instance, a hundred per cent becomes significant in a line of a definite length. Likewise, any proportion of this amount is concretely represented by a line somewhat shorter than the one which represents the whole. Undoubtedly, when both the abstract quantity and the pictorial illustrations are employed there results something additional to that which comes from using either alone. It is this something which has its basis in the psychological truth that the intensity with which a thing is perceived varies directly with the number of channels through which it makes its appeal to the intellect. III. DIAGRAMS FOR ILLUSTRATING FREQUENCY OR MAGNITUDE IN RELATION TO SPATIAL DISTRIBUTION 1. The Psychological Bases for the Use of Statistical Maps In order to show the relations between magnitude or frequency and geographical distribution various types of statistical maps are employed. They are known as cartograms and are in current use in private and public statistical studies. It is our purpose briefly to discuss their psychological bases and to relate them to the principles of statistical methods. |