Girls Boys case we first divided our statistics into two groups only, one or both parents drink and neither parent drinks and worked the correlations out by the new method discussed by Professor Pearson in Biometrika, Vol. VII. p. 96*. The first step in this method of finding a correlation coefficient is to find the means of the classes. We found that the mean height of the sons of non-drinking parents was 47.5 inches and of the sons of drinking parents was 47.9 inches and the correlation was '07, that is to say a very slight connection between drinking parents and taller sons and we found much the same for weight; the mean weight of the sons of non-drinking parents was 53.8 lbs. and of the sons of drinking parents was 550 lbs. and the correlation between drinking parents and heavier sons was found to be 06. We had to put all ages together so we had next to correct for the correlation between the drinking of the parents and age of the children †. We found that the mean age of the sons of non-drinking parents was 9.4 and of drinking parents was 9.8 and the correlation between drinking parents and older sons was 11. Using the formula for partial correlation we found that the coefficient between drinking parents and poorer physique in their sons for a constant age was 04 for height and 05 for weight. The results are given in Table I for girls and boys. The minus sign when it occurs means that a better condition in the child is correlated with drink in the parent. The results differ slightly for girls and boys as the table shows, and in the final results given in the last two columns we see that the correlation coefficient between drinking and less height is 04 for boys and 09 for girls and between drinking and less weight is 05 for boys and 08 for girls. This is a case where a probable error is a necessity in order to enable us to judge whether these results are significant. The probable error for the partial correlation coefficient has been shown by Mr Heron to be the same in form as for the absolute * "On a new method of determining correlation between a measured character A, and a character B, of which only the percentage of cases wherein B exceeds (or falls short of) a given intensity is recorded for each grade of A." + i.e. as the parents grow older, the children grow older, and some alcoholism develops with the parents' age. Biometrika, Vol. VII. Part III. Daughters Sons coefficient and it is equal to '03 in each of the above cases. With a probable error of 03 one can only say that values of '04 and 05 are insignificant and only slight significance attaches to values of '08 and 09. We next separated the father and mother and worked out the correlations between the father's drink and his child's height and weight and between the mother's drink and her child's height and weight; the results are given in Table II. The last two columns give the final results, i.e. the correlation between the drink of the father and mother and the height and weight of their children. The drinking of the mother is seen to have more effect on her child's physique than the drinking of the father. There is practically no correlation between the father's alcoholism and his child's physique for either boys or girls, but there is a connection between the mother's alcoholism and her child's physique, and this connection appears to be greater for girls than boys. The last fact makes it very difficult for us to assert that the slightly poorer physique is a result of a toxic influence. There is no reason to suppose that such would affect the male less than the female; it is far more probably due to the factor of undesirable home environment; the alcoholism of the mother throws more home duties on the girl-child; lessened care would affect boy and girl alike and probably does so. Some of the greater influence of the alcoholic mother as compared with the alcoholic father may be due to the fact that alcoholism in the mother is correlated with another environmental factor, which we have found associated with slightly lessened physique in the offspring, I refer to the employment of the mother. From the Edinburgh Report we find that 43.6°% of drinking mothers are employed and only 26-4° of sober mothers; the correlation between employment and drink is 28. We have thus distinct evidence that alcohol quite apart from any toxic effect is associated with a modified home environment*. If we allowed for this fact of greater employment of alcoholic mothers we should find some reduction in the intensity of the correlation of maternal alcoholism and physique of offspring, but it would not account for the whole value. It is chiefly of interest as showing that we cannot conclude from a correlation of the child's physique and parental alcoholism the * It is also conceivable that the alcoholic mothers are racially differentiated, and this would produce a physical differentiation in the offspring of alcoholic mothers. Son Son existence of a toxic effect until we have considered how far the parental alcoholism is associated with differentiation in the occupations or habits of the parents—shortly with environmental differences, which do not necessarily flow even from the alcoholism, but may like the mother's employment be possibly the source of the alcoholism itself. We may we think infer from the above results that the father's alcoholism has no sensible influence on the physique of the child. The mother's alcoholism has a small but quite sensible influence on the height and weight of the child, more sensible in the case of the girl than the boy. It is probably due, not to any toxic effect of the alcoholism, but to increased unfavourable home environment. Even where the relation is the highest, i.e. 14, it has only about the intensity of parental heredity. (5) Parental Alcoholism and General Health of Offspring. We will next consider the general health of the children of alcoholic parents. The tables are numbers XVII to XXIV inclusive in the Appendix. (i) Manchester. From Miss Dendy's manuscript account of the children in the special schools of Manchester* we have been able to divide the health of the brothers and sisters of the defective child into the following classes: (a) Normal, (b) Delicate, (c) Phthisical and Epileptic, (d) Died young of "fits," "wasting" etc. The parents in this case could be divided into two classes only, those who are temperate and those who are intemperate. The percentages of children of temperate and intemperate parents having the different grades of health are given below. It will be seen from these percentages that the differences between the health of the children of temperate and intemperate parents are very slight having regard to the numbers available and there is a certain amount of irregularity. The only fact that is constant throughout the four tables is the larger percentage of children suffering from epilepsy and phthisis among the children of temperate parents and an examina * The medical details of this account were prepared under the control of the late Dr Ashby. tion of the curves (p. 10) shows this very clearly. In three out of four cases we find a slightly larger number of healthy children among the children of intemperate parents and a slightly larger number of delicate; in the "died young" class we find in two cases the larger number among the children of intemperate and in two cases among the children of temperate parents. It is obvious from these tables that the correlations will be very small and that it will be difficult to decide whether, taken as a whole, they are to be considered positive or negative, i.e. whether the connection is between intemperance and bad health or between intemperance and good health. These correlations have been worked out in two ways: (i) by a method giving which will be discussed by Professor Pearson in the next number of Biometrika * and (ii) by the fourfold method giving r. In using the fourfold method we grouped "delicate," phthisical, epileptic and "died young" together. In using the first method we grouped phthisical and epileptic together. It may be objected that it is not legitimate to group in this manner, but the number of phthisical children is too small to keep them separate and for both diseases there is a distinctly greater percentage in the temperate group; it seemed therefore better to group the phthisical with the epileptic children than to group phthisis with delicate where this predominance does not occur. In the tables in the Appendix, the original numbers in the two classes are given. See Tables XVII to XX inclusive. An examination of the curves on p. 10 will indicate the source of the divergence in the results by the two different methods. These curves show the mean alcoholism of the parents for each grade of health (intelligence, etc.), in the children measured by the deviation from the dividing line between alcoholic and sober parents. The dividing line is drawn in each case; the further below this line any point is situated the more sober is the parent and the deviations will have a minus sign; the further above this line the more drunken is the parent and the deviations will be positive. The vertical scale is measured in terms of the Standard Deviation. The dotted line shows the average amount of alcoholism in all the parents of the children under consideration. Sobriety is thus on the diagrams a negative alcoholism. The average Manchester and Edinburgh mothers are sober, the average Manchester father is also sober, but not the average Edinburgh father. The standards of the recorders have, of course, to be allowed for, but there is good reason to believe that the Edinburgh * Vol. vii. p. 248: "On a New Method of determining Correlation, when one Variable is given by alternative and the other by multiple Categories." †The reader will bear in mind that the correlation ratio has no sign by its nature and is only equal numerically to the correlation coefficient when the regression is linear. G. M. X. 2 agree population is really as well as apparently more alcoholic than the Manchester. It will be seen that it is the dip into the sober class of parent of epileptic and phthisical children which is the source of the higher value found for 7, and in the only case where this dip is slight the two values found by n and the fourfold method η well numerically. The number of phthisical and epileptic children is comparatively few and we should probably be nearer the truth if we take the lower values given by the fourfold method for the influence of drink on general health. The value found is negative, FIG. 1. PARENTAL ALCOHOLISM AND HEALTH OF CHILDREN (MANCHESTER). |