38 EMPIRICAL STUDIES OF MEASUREMENT 



Special precautions were taken to have the errors artificially in- 

 duced in the 200 measures such as would come in reality from 

 variable errors of apparatus, observation and record. The errors 

 were in fact a random sampling of the errors actually made by a 

 psychologist in estimating areas. A series of 121 rectangles of 

 approximately the same shape, 40, 41, 42 ... 160 sq. cm. with 

 also many duplicates were used. The area of each was estimated, 

 the slips being drawn in a random order, and the error -\- or 

 from the true area was recorded. The errors used by me were 

 those made after from 3 to 5 trials with the series and were little in- 

 fluenced by practice (the sums of the errors regardless of signs were 

 for successive repetitions of the series 605, 614, 563, 613, 587, 637, 

 531, 542, 578, 581). I used the deviation from the standard if the 

 constant error for the given area was less than 1 sq. cm. and the 

 approximate deviation from the subject's own average judgment 

 if the constant error was over 1 sq. cm. The errors taken were 

 those (10 in each case) made with areas 43 sq. cm. up through 122 

 sq. cm., four errors being taken for each of the 200 accurate meas- 

 ures. These errors were assigned to the accurate measures so that 

 the magnitude of the area with which the error of estimation was 

 made corresponded roughly to the magnitude of the measure to 

 which the error was assigned. Thus errors from areas 43-53 would 

 be put with measures 27, 25, 23 and the like, and errors from 

 areas 110-122 would be put with measures +17, -f- 19, -(-27 and 

 the like. The true measures and the errors assigned to each are 

 given in Table XV. 



If now to each true measure is added (regarding signs) its as- 

 signed error, we have (four errors having been assigned to each) 

 four series of inaccurate measures of two series whose true values 

 and true correlation are known. These facts give the data for test- 

 ing the Spearman formulas. 1 



1 These errors can of course be used with any series of 400 or less measures 

 to test Spearman's formulae, as I have done for this series (r = .281 of Series B) . 



