metic reasoning, vocabulary, general information and comparison. The rest are closely clustered about twenty. A large proportion of the maximum ability appears to be attained early (that is, the curve is relatively further skewed to the left) in arithmetic reasoning, form combination, substitution and comparison—indicating perhaps an early acquisition of what might be called the simpler "natural" abilities, and a certain forcing due to the school. The reverse is the case in vocabulary, analogies, and possibly symbol-series completion, these involving apparently relatively mature forms of ideation-a conclusion which derives some support from introspective observation. The standard deviation curves are extremely difficult to interpret; it is not easy to see why the variability should rise and decline with the mean. Nevertheless there seems to be distinguishable a type with initial peak, like the means, and another more nearly symmetrical. Number series completion and history-literature information come definitely under the first category, with intermediates in form combination, analogies and general information. Conforming more nearly to the second type are opposites, symbol-series completion and vocabulary, along with the extremely pronounced comparison, substitution, where the condition is slightly reversed, and arithmetic reasoning, where there is almost no "swell" at all. The study of the growth and decline of these constants deserves more attention. There is apparently a general growth law running through them, not only in the psychological but also in the physiological field, but so far as the writer knows. it has never been clearly and comprehensively enunciated. The similarity with certain physiological findings may be noted in passing. Mr. William Arthur, in Biometrika, Vol. 16, investigating the relationship between strength of grip and certain reaction-times and sensory functions, presents curves showing means of arrays vs. age for right and left hand grip (p. 302) and vital capacity (p. 327); and corresponding ones for standard deviations in the grip function (p. 306). All these closely resemble the curves here presented. The curves for brain weight are said to do the same. Here, then, we have an instance of the important case in which, while the actual connection is as perplexing as ever, distribution of mental and bodily characteristics exhibit the same properties. The analogy is, of course, so far as it goes, immensely strengthened. Some light is also shed hereby on the occasionally recurring discussion concerning the "age of mental maturity." William James, for example, is said to have considered the individual to attain the peak of his powers at about 25—an estimate not widely variant from the evidence here presented. Another such conjecture is that of Ostwald in his "Grosse Männer” (reported to the writer, but not checked). His theory, one of energetics, takes strictly mental growth to be continuous, though with negative acceleration; while physical well-being and energy are highest at the beginning of life and decline rather steadily; the result is a combined maximum in the neighborhood of 25-30 years. There is also the famous jest of Sir William Osler to the effect that in the interests of progress everybody should be chloroformed on reaching 40 (or 60); here there seems to be in the background some sort of clinical observation of a peak of efficiency about 10-20 years earlier. This matter also assumes some importance in the assignment of 16 as the age beyond which growth is negligible for the purpose of estimating intelligence by the Stanford-Binet test. If the curves here shown have any general application, it would appear that a more accurate method would be to equate chronological ages beyond the peak to corresponding ages on the rising limb of the curve; e.g., instead of referring the performance of a 50-year-old to age 16, it might prove a desirable refinement to refer it to the abscissa of the point of the rising curve having the same level as at 50-1412 perhaps. By the use of these curves, however, the approximately 6600 individual z-scores were secured for use in the correlations. Test correlations of these with age (four tests) through both the rising and falling limbs of the mean-curve demonstrated that the procedure was successful in removing age-influence, since these test results were all well within their probable errors. The Correction for Attenuation. The conversion made, and its efficacy so tested, the main familial correlations were a matter of straightforward calculation. It was deemed a useful, if slight, refinement to correct them for attenuation. Since the correlations were computed from the z-scores, it was greatly preferable to estimate the reliability coefficients to be used in the correction for attenuation from these rather than from the raw scores. It was necessary to compute the z-score corresponding to the raw score on half the test only, since the sum of the z-scores for the halves must equal the z-score for the whole; the tests were divided in the usual fashion into oddnumbered and even-numbered halves, and the odd half was converted. The procedure here was a repetition of that used for the undivided score. Z-scores for odd and even halves were correlated, and the reliability computed by means of the special case of "Brown's formula." The groups entering into the correlations differing to an unknown degree, it was deemed safest to compute the reliability of each group so entering. This involves, in the case of marital coefficients, for instance, the calculation of a reliability coefficient for husbands and another for wives; in the case of female maternals, of mothers of sons, and again of sons of mothers (tested). The investigator allowed himself some latitude in throwing out individuals who affected the coefficients out of proportion to their significance and whose tests were known for any reason to be questionable. Notation of these is made (p. 260). The reliability coefficients (p. 260), the uncorrected (p. 260), and the corrected (p. 261) coefficients of familial resemblance are presented herewith. In making the correction, the procedure used was to divide the raw coefficient by the product of the square roots of the reliability coefficients involved." "Kelley [13], p. 206, formula 158. FAMILY MENTAL-TEST ABILITIES 259 Glancing over this table for general tendencies, we find that, comformably with the conditions governing the selection of the tests, the reliabilities are very good; only a few are below .70, while several are above .90. In general, the older age groups yield the more reliable results; this is probably chiefly a function of sustained attention, and at any rate indicates that the tests are a more adequate measure for individuals in whom the habits, mental and motor, involved are more automatic. The size of the groups, as mentioned before, ranges from 40 to about 110-large enough, on the whole, to give fairly reliable results. The exclusion of single individuals whose performance seemed particularly erratic, and whose inclusion lowered the coefficients to a disproportionate extent, is of necessity too subjective a process for entire comfort; but it was done as carefully as possible, and notations of the reason therefor are appended. As between tests, the "verbals" (1, 3, 5, 7, 9, 10) are in general somewhat higher; this may be partly due to the fact that fewer of the younger children took them. It may be remembered, too, that not a great deal of importance need be attached to minor differences in the reliability coefficients unless these coefficients themselves be an object of interest; the entire correction for attenuation might have been dispensed with without much error, from the point of view of family similarities. A raw coefficient of .4, for example (which is representative), would be raised only to .5 by two reliability coefficients of .8, whereas the standard error of such a coefficient in the first place would be in the TABLE I THE UNCORRECTED FAMILIAL COEFFICIENTS AND THE RELIABILITY COEFFICIENTS USED IN THEIR CORRECTION (MS indicates the uncorrected (mother-son) coefficient; M will here indicate the reliability of the mother group entering into this particular correlation; and S, similarly.) Test 1 2 3 4 5 6 7 8 9 10 11 Mother-Son 29 .19 .25 .43 .48 .17 MS 24 33 23 41 41 MD 23 .37 34 23 .28 .18 .43 20 43 .40 .20 Exclusions D 77 78 79 75 82 .63 .69 .77 .91 .781 85 14, young; from .52 Father-Son FS .36 .32 .16 .31 .33 .14 .38 .32 .40 .49 .13 F .93 85 .78 .92 79 77 .91 88 .92 .97 .91 S .74 .74 49 86 .81 .68 .73 .77 .92 .87 .81 OB .881 .88 .67 79 78 80 .90 85 .96 .92 .89 11, young, Chinese; Sister-Sister SS .29 .46 .26 .31 .21 .28 .30 .48 .38 .44 .42 BS .30 .31 37 31 .28 .16 .28 .36 23 Husband-Wife from .76 731 .70 14, young; from --.03 83 .70 31 27 .84 .88 792 .83 11, young; from .56 23, young; from 48 HW.34 .17 .34 .50 .41 .25 .26 .56 43 .55 .41 Test 8 not being susceptible of division into equivalent halves, the reliabilities used therein are averages of those for the remaining ten tests; the essential soundness of this procedure would seem to be indicated by the fact that the average of the reliabilities of the child-groups above differs by less than .005 from that (.788) determined for a large population, in three school grades, on a closely related symbol-digit test of the same number of elements. Figures are individuals excluded; "young" is below about 7, where the curves are first well-defined; coefficients are those resulting from failure to exclude. |