On certain independent factors in mental measurements

Abstract

In a paper Published in the ‘American Journal of Psychology’ for 1904, Prof. Spearman Argued that “all branches of intellectual activity have in common one fundamental function (or group of functions),” and even that this fundamental function enters into sensory discrimination no less truly than into more complicated intellectual activities. In 1909 Mr. Cyril Burt described experiments on two groups of Oxford schoolboys undertaken “with a view a testing in practice the mathematical methods of Prof. Spearman.” Mr. Burt calculated the correlations between the performances of his subjects in 12 different tests, which one (the twelfth) test of voluntary attention. Mr. Burt’s results were consistent with the view that all the correlations were due to the operation of one and only one general factor. Two years later Prof. Spearman and Dr. Hart proposed an new test for a (single) general factor; namely that, in such a correlation table as those published by Mr. Burt, in the form (27) below, the correlation between every pair of columns should, with proper allowance for sampling errors, be +1, or, as Dr. Webb pointed out afterwards, -1. Their formula for column correlation, correct for errors of sampling, is R ab ’=S( ρ xa ρ xb )-( n -1) r ab σ xa σ xb /√[s( ρ xa 2 )-( n -1)σ xa 2 ]√[s( ρ ab 2 )-( n -1)σ xb 2 ] in which the ρ’s are the correlation coefficients r measured from from the mean of the column, and the σ’s are the probable errors of the r’s divided by 0·6745. The bar indicated mean values. The authors decided that, for the purpose of calculating a “correlation between columns,” only those pairs of columns could be used in which S( ρ 2 ) is at least twice the correction ( n -1)σ 2 . With this limitation, they applied their formula to the five largest pairs and the five smallest pairs (or as many as were up to the correctional standards) of columns in 14 published tables of correlation coefficients dating from various periods up to 30 years back. They found that “from beginning to end, the correlation between columns is positive and very high; the mean is almost complete +1. This is just the value demanded by the theory of a [single] General Factor. Dr. Webb, in his essay on “Character and intelligence,” to which reference has just been made, prepared a further correlation table of five columns (and five rows) the results of five examination tests set 96 training college students. Nine out of the ten pairs of columns were up to the correctional standards of Prof. Spearman and Dr. Hart, and the application of their formula to those nine pairs yielded 1·02 ± 0·08 as the average correlation between columns. This result, says Dr. Webb, “is an additional item of evidence in support of the theory of a general factor.....It takes its place in the huge array of evidence collected by Prof. Spearman from experimental tests by many investigators-the steadiness of results being such as to rival the niceties which physical measurements reveal. It should be remembered that the raw material for our own (comparatively small) contribution to this result consisted of test-papers numbering nearly 10,000.”