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THE AMEBIC AN NATURALIST [Vol. XL HI 



figure was .51 or greater. When the decimal part of the record 

 was .49 or less the integral part stood unchanged. In the 450 

 measurements there were six cases in which the decimal portion 

 of the record was exactly .50. In one half of these cases the 

 record was raised 1 mm. and in the other half was left un- 

 changed, when the decimals were discarded. This is obviously 

 the only fair way of dealing with such cases since, for example, 

 51.50 is exactly as near to 51 as it is to 52. 



The original measurements and the "millimeter" data after 

 discarding the decimals were then each added and re-added with 

 a calculating machine. The resulting sums were: 

 When the measurements were kept When the measurements were 

 to the nearest hundredth of a mm. kept to the nearest whole mm. 

 25,341.95 25,346 



Dividing each of these figures by the total number of cases, 

 450, we get for the means the following : 



Mean from " hundredth mm. data " Mean from " millimeter data " 

 56.315 56.324 



The difference between these two figures is .009. That is, there 

 is no difference between the two averages until the third decimal 

 place is reached. To two places of figures both means are 56.32. 

 But this can only mean that the mean or average obtained when 

 the records are made only to the nearest millimeter is more 

 accurate, by two places of decimals, than the data on which it 



In interpreting this statement of fact it must not be held to 

 signify that biometric measurements' should not be made with 

 the greatest attainable degree of accuracy. Because statistical 

 constants, when the number of cases dealt with is large, are 

 more accurate than the data on which they are based gives no 

 excuse for rough measuring. The reason for this, of course, 

 lies in the principle, which actual experience shows to be cor- 

 rect, that the finer and more accurate the measuring the less 

 chance of the data being unconsciously biased. Statistical con- 

 stants can only be more accurate than the original data when 

 the data are strictly unbiased. The "applied psychology" of 

 practical measuring teaches that unconscious bias goes out of the 

 records just in proportion as the measurements are made finer. 



Raymond Pearl. 



