Digit Bias in Measuring and a Device to Overcome It
O. E. Sette · Copeia · 1941
5W5 HENEVER measurements are made by comparing the position of the boundary of an object with a graduated scale, as in measuring fish, even with the aid of pointers or cross hairs, there is a tendency, differing with observers, to favor certain digits. With trained observers carefully using good instruments, this bias should be slight. In the vast majority of instances where the results of groups of measurements are reduced to averages, it is of no consequence. Where the measurements are assembled into frequency distributions it may introduce artificial irregularities which may be bothersome when significance is to be attached to the shape of the curve. The irregularities can be reduced and sometimes obliterated by appropriate grouping into class intervals, or by mathematical smoothing. But when the frequency distribution is to be compared to theoretical curves by critical statistical methods such as the chi square test, such bias-induced irregularities form a serious, if not insurmountable, obstacle. This became obvious in my work on a series of tens of thousands of measurements of the Pacific sardine, or pilchard, Sardinops caerulea, accumulated over a period of years by a number of observers of the California Division of Fish and Game, and kindly loaned to the United States Fish and Wildlife Service for a special analysis involving curve fitting. These measurements had been made carefully by trained observers with the aid of a measuring board equipped with a sliding rider which could be placed so that its cross hair or thread would be over the point to be measured on the fish, running from there to a point over a rule which was graduated in millimeters, and the readings were made to the nearest millimeter. The length of the fish ranged from 150 to 300 mm. When the measurements were grouped according to observer and classified according to the final digit of the reading, it was apparent that each person had a different bias pattern. Some of these are shown in fig. 1. An example of odd-even bias is given by A. The probabilty (P), computed by the chi square method, that purely random variations would exceed the observed variations from the mean, is 0.002. A case of bias in favor of five and zero and against four and seven is given by B (P = <0.001). The three curves were of measurements by the same observer and grouped by time periods. During the first two months, C, there was a marked bias favoring zero and five mainly at the expense of one, four, six, and nine (P = <0.001). At the end of this time the observer must have noted its existence, and attempted to avoid it, for the third month, C' (P = <0.001), exhibits the opposite of the former bias with respect to zero and five. Apparently noting this also, the observer again changed his habits during the succeeding three months, C (P = <0.001), practically eliminating bias as concerns zero and five, though retaining significant bias, now favoring three and eight mainly at the expense of four and seven. Such biases can be eliminated by incorporating in the measuring mechanism a mechanical selector. The one devised for the sardine measuring board