MEASUREMENTS OF RELATIONSHIPS 37 



of testing it (and in a measure the first formula also) inductively. 

 This I have done to some extent for values of r where the r's from 

 accurate measures are from .70 to .80 in connection with my 'Meas- 

 urements of Twins' (Archives of Philosophy, Psychology and Scien- 

 tific Methods, No. 1, September, 1905). 



I had records from 50 pairs of twins in 5 tests of efficiency of 

 perception; (1) in marking A's on a sheet of printed capitals, (2) 

 in marking A's on a second sheet of printed capitals, (3) in mark- 

 ing words containing e and r on a page of Spanish, (4) in marking 

 words containing a and t on a page of Spanish and (5) in marking 

 misspelled words on a page of narrative, 100 of whose words were 

 misspelled. I had also 6 tests in efficiency of controlled association, 

 tests 6 and 7 being addition, 8 and 9 being multiplication and 10 

 and 11 being writing the opposites of two lists of words. 



If we combine all 5 of the tests of efficiency of perception allow- 

 ing approximately equal weight to each, we have a measure which 

 is presumably close to the true measure of a child's capacity at a 

 certain day and hour to pick out small details efficiently. The cor- 

 relation between twin and twin is for this combined score .697. 

 Similarly the combined measure for addition, multiplication and 

 opposites gives a measure presumably close to the true measure of a 

 child's ability at a certain day and hour to make proper mental 

 connections. The correlation between twin and twin is .815. The 

 .697 and .815 are presumably only slightly below the true r's. 



Now the correlations for twin and twin in tests 1-11 were in 

 order .607, .633, .595, .428, .754, .645, .644, .653, .579, .734 and .560. 

 Subjecting these values to correction by Spearman's formulas, 

 taking, as he does, the mean of both corrected r's I obtained 

 for the perception tests: Marking A's, true r=.69; marking 

 letters in words, true r = .71 ; misspelled words, not corrected 

 because only one test was given. The Spearman correction 

 thus produced results in accord with the expectation derived from 

 the value r .697 for the combined mark. For the association tests 

 J obtained after correction: Addition, true r=.75; multiplication, 

 true r = .84 ; opposites, true r = .90. The average of these, .83, is 

 again closely in accord with the .815 from the combined measure. 

 In both cases the result by correction is slightly higher than the 

 result empirically obtained from the more accurate data, as of 

 course it should be. 



I have made a test ad hoc in the case of a series of 100 pairs 

 drawn at random from Series B which give a true r of .281. These 

 100 pairs of accurate measures I made inaccurate artificially. I 

 then calculated the r's obtained from such inaccurate measures, 

 applied the Spearman formulas and in so far tested their validity. 



