The significance of the correlation coefficient when applied to Mendelian distributions / by John Brownlee.

  • Brownlee, John, 1868-1927.
Date:
1910
Catalogue details

Licence: In copyright

Credit: The significance of the correlation coefficient when applied to Mendelian distributions / by John Brownlee. Source: Wellcome Collection.

Provider: This material has been provided by The University of Glasgow Library. The original may be consulted at The University of Glasgow Library.

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    The correlations in these two cases are respectively (a) r = %578, and (b) r = -330.* This process may be continued indefinitely, and likewise results may be obtained on the second hypothesis. If the excess of recessive be maintained for four generations the corre- lations are as follows :— A. B. Parental .... •578 •638 Grandparental •330 •451 Great-grandparental . ■200 •309 Great-great-grand parental . •no •216 But the heredity has not been quite this. The proportion of dark and light horses in each generation when means of each parentage are taken has altered in the following manner:— Dark. Light. Total. Great-great-grandparents . 641 359 1000 Great-grandparents . 664 336 1000 Grandparents 712 288 1000 Parents .... 728 272 1000 So that for two generations the proportion of recessive is one-third and above, and for the last two approaching the ratio of one-quarter, though, as before remarked, this is not of a Mendelian origin. If we calculate, then, the correlations for the great-great-grandparents on the hypothesis that the recessive is equal to one-third of the total for two generations and to one-quarter of the total during the next two generations, and for the grand- parents that on the hypothesis that the recessive numbers one-third for * These and the subsequent correlations have been obtained by the fourfold method though not by the full process. They have been calculated by the formula, n 2 4a6cdN2 2 Vl+F Wh6n k = (ad- bc)-(a + d)(b + c) and where the fourfold division is This formula gives results very near the truth. When those coefficients, previously calcu- lated in this paper by the full method, were checked by the method here referred to, the result has been so close that in the present instance where many coefficients are required the extra labour of calculation has not seemed necessary.