neighborhood of .08 or .09. The coefficients, as finally corrected, are given in Table II. TABLE II SUMMARY OF THE CORRECTED COEFFICIENTS Non Test Verbal Verbal Total 1 2 3 4 5 6 7 8 9 10 11 Ave. Ave. Ave. Parentals Maternals Male, r .28 .42 .32 .47 .48 .39 .23 .29 .46 .52 .19 F'male, r .27 .44 .41 29 31 27 52 24 47 47 .33 Paternals Male, r 41 .37 .25 .35 .40 .20 .47 .39 .43 .53 .15 Male, r .52 .56 .50 .39 .58 .35 .36 .36 .55 .51 .18 Fraternals 43 .50 .45 .38 .40 .32 .39 .48 .41 .48 .37 r .37 .20 .47 .55 .48 .33 .30 .65 .46 .58 45 Total Ave 38 42 42 .39 .37 .30 .39 41 41 49 .28 .44 .37 37 .36 .26 .31 .35 .37 .44 .52 .45 .35 .36 .42 .44 .44 .41 .36 .39 Several interesting trends are indicated in this, the central finding of the study. (In considering the matter from this common-sense standpoint, however, it must not be forgotten that these trends are only indicative, suggestive; it will be noted later-p. 269—that the establishment of any of them on a firm statistical foundation is, in view of the small size of the populations and several technical difficulties such as overlapping of population, etc., extremely difficult and perhaps impossible.) The total average of all these familial correlations is virtually .4; this is in line with the findings of a considerable number of such correlational studies in both mental and physical, not to mention human and sub-human, fields. Such a figure seems to arise from the fact that (Fisher, p. 403 ff.) the genetic correlation, i. e., the theoretical correlation between relatives tak-ing account only of genetic constitution and neglecting dominance, phenotypic and environmental variation from the geno 262 GENETIC PSYCHOLOGY MONOGRAPHS type, is in the case of both parental and fraternal relationships .5, deviations therefrom being therefore due to these causes (the marital coefficient, which affects these averages to the extent of one-eighth, depends of course entirely on the psychology rather than the biological results of mating). Dominance is said to have a lowering effect upon the genetic correlation, twice as much in degree in the case of parentals as in that of fraternals. Environment, on the other hand, would seem a priori to exercise a heightening effect, a supposition for which there is some evidence in the superiority of the "verbal" to the "non-verbal" average (the division being admittedly somewhat subjective, but probably having some correspondence with reality). Considering still the total averages, we find those for the separate tests very close to .4, with the exception of the history-literature information, a test obviously affected by training, which rises to .49, and the form-combination and comparison, sinking to about .30. Considering the differences by relationship, it is evident that Fisher's discovery of the double lowering, from .5, of the parentals as compared with the fraternals, due (among other things, in the present case) to dominance, is very closely approximated. The exact correspondence of the verbal and nonverbal averages in the maritals suggests that with mature individuals, in whom the word-techniques have become as automatic as others (or conversely) the tests become a truer measure of total mental ability rather than a discriminatory device as between specific abilities. The greater difference between verbal and non-verbal averages in the parentals than in the fraternals may perhaps indicate that the total environmental effect tends to assimilate children to the parental type of culture slightly more than to each other's. The close similarity between the properties of the same-sex coefficients should not escape attention; the girl is like her mother to the same degree in both verbal and non-verbal abilities as the boy is like his father. The effect of the mother's larger amount of assocation with the children of both sexes is discernible; it may De remarked particularly as between the father and daughter, where the sex difference and the comparative absence from home reinforce each other. The differences between individual tests must be evaluated with even greater caution, on account of the small numbers involved and the consequent possibility that a few typical individuals may indicate an unsound generalization. We may note, however, that both children tend to resemble the father in opposites ability; that the boys resemble their mothers more than do the girls in series completion and vocabulary, while this condition is strikingly reversed in analogies; that the boys also tend to resemble their fathers more than do the girls in vocabulary and information (both kinds), this being reversed in arithmetic reasoning. There is a general tendency for the same-sex fraternals to exceed the mixed, which may perhaps reflect environment simply; but there is a pronounced exception in the case of arithmetic reasoning. The boys are markedly more alike than the girls in all the verbals except analogies and history-literature information, while in the substitution and comparison the girls clearly have the lead. The averages somewhat reflect this, and suggest that (somewhat in contradiction to certain current opinions) girls tend to be more like each other in abilities not involving language, while their brothers are similar in language abilities; in all this, of course, no account is taken of the respective levels, except in so far as, perhaps, a high correlation might occasionally come about from a wide spread rather than a closer similarity with a narrower spread. That some of the marital non-verbals are as high as they are occasions some surprise; in so far as it is the verbals which are high, however, mate selection on a cultural basis seems to be indicated. A few words may be said concerning the fact that these coefficients are all positive and of considerable size. The average intercorrelations of the verbals are high (.5 to .9) and to some extent they may be regarded as different manifestations of the same or slightly different abilities; the non-verbals, how ever, are not so some of their inter-correlations run down to .2 or below. If, in consequence, we do not wish to think of eleven different tests in which the familial coefficients are all positive, we may at least consider that we have a composite measure of a rather wide ability, which we are sampling at various points; and although it would be somewhat difficult to evaluate the statistical measure thereof, probably no serious disagreement would be provoked by a statement that a constant and strong factor, most likely heredity, is assisting in the causation thereof. Additional light may be derived from the preliminary findings of the unpublished Burks-Terman study of foster-children and their adoptive parents, where (in Binet ability) the correlation between father and child is about equal to its standard error, that between mother and child is .18, and that between child and a fair measure of "general cultural environment" is .25. Here we have all (that we can measure by the best means now available) that environment can do alone; the result is still considerably short of the present parental average .4. Attention is also invited, though without assurance of the accuracy of the measure, to the Fisher "coefficient of environment" .54 derived from the present correlations (p. 269). These figures represent the attainment of the chief objective of the investigation-the determination of the strength of the familial relationships. It remains to estimate their unreliability. Unreliability of the Corrected Coefficients. This is not easy to compute rigorously, since all possible pairs were used in the calculations (e.g., a father appears twice in the father-son table if he has two sons; six sibling-pairs are comprised in a four-sibling family, etc. The indifference of this procedure to the coefficients themselves, in the case of fraternal tables at least, has been demonstrated empirically9); and also because of the indeterminateness of populations-i.e., the indefinite nature of a "family group" and the intricate consequences of Cf. Hildreth, Teachers' College Contr. No. 186, p. 38 ff.; Stone, C. P., unpublished study; and others. the varying intercorrelations of its members. We may first eliminate the maritals from the problem; they at least are clearcut. Their probable errors are as follows: 1 2 .07 8 9 3 4 5 6 7 10 11 .08 .08 .05 .07 .05 .08 .05 .05 .06 .06 The parentals are perhaps a little less complicated than the fraternals. If each mother, for example, had but a single son, the number of mother-son pairs, obviously, would be the number of either mothers or sons, and this would be the effective N of the formulas. But the number of sons is greater than that of mothers. If now this greater number of sons could have each, so to speak, a complete mother all to himself, the effective N would be the present number of sons. Hence the real effective N lies somewhere between the number of mothers and the number of sons. Let us analyze in this light the population involved in, say, Test 4: This test is probably rather well adapted for experimentation on this point, as being an easy and attractive non-verbal test some of the young sons would participate who would not be able to enter into the distributions of verbals. We know, as stated above, that the effective N lies between 88 and 131. The arithmetic mean is 110 (109.5); the geometric mean, 107 (107.3). The probable errors corresponding to these four values are: Let us add to these, as useful mile-posts, the values one-third and two-thirds the distance from 88 to 131, viz., 102.3 and 116.7 respectively. The corresponding probable errors are .058 and .054 respectively. |