87 | 95 | 96 | 94 | 102 84 | 85 | 87 | 93 | 87 83 | 106 | 91 | 87 | 104 80 | 77 | 91 | 80 | 84 80 | 84 | 75 | 79 | 84 | | | | 80 | 89 | 107 | 88 | 86 78 | 87 | 90 | 93 | 85 60 | 69 | 56 | 71 | 77 -------------+------------+----------+----------+----------- The intercorrelations of the quotients of these 48 cases for all periods may be seen in Table 3 (page 21). The correlations with IQ and the intercorrelations of the SQ’s have increased toward positive unity or rather toward the limits of a correlation with tools of measurement such as we have used. This limit is a function of the reliability of the tests employed. It is customary to use a formula to correct for attenuation in order to find the percentage which the correlation is of the geometric mean of the two reliability coefficients. This is tantamount to saying that any correlation can go no higher than the geometric mean of the reliability coefficients of the tests used. It is better to assume that an _r_ can go as high as the ∜(_r_₁₁⋅_r_₂₂) since an _r_ can go as high as the square root of its reliability coefficient. Dr. Truman L. Kelley has shown that the correlation of a test with an infinite number of forms of the same test would be as the square root of its correlation with any one other form. The reliabilities and limits defining a limit as the fourth root of the multiplied reliability coefficients are in Table 4. Correction for attenuation is often ridiculously high because the reliability coefficient of one of the measures used is so low. If an element is included in the two tests which are correlated, but not in the other forms of each test used to get reliability, the “corrected coefficient” is corrected for an element which is not chance. Whenever the geometric mean of the reliabilities is less than the obtained _r_, the corrected _r_ is over 1.00 and hence absurd.[12] Therefore we use here instead, a comparison to the maximum possibility in a true sense. Since a test correlates with the “true ability” √(_r_₁₁), ∜(_r_₁₁⋅_r_₂₂) is the limit of an _r_, its optimum with those tools. Although these limits apply, strictly speaking, only to the total correlations, since the reliability correlations are with all the data; we may assume that the same facts hold with regard to the correlations of each of the grades, that is, the reliability is a function of the test not of the data selected. TABLE 3 INTERCORRELATION OF ALL QUOTIENTS FOR ALL PERIODS OF THE 48 CHILDREN WHO TOOK ALL TESTS NOVEMBER, 1918 IQ VQ RQ S.D. M IQ 19.12 105.15 ±1.32 ±1.86