On the handicapping of the first-born : being a lecture delivered at the Galton laboratory, University College, London, March 17, 1914 / by Karl Pearson.

Pearson, Karl, 1857-1936.

Date:: 1914

Licence: Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)

Credit: On the handicapping of the first-born : being a lecture delivered at the Galton laboratory, University College, London, March 17, 1914 / by Karl Pearson. Source: Wellcome Collection.

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$This (b) gives the hypothetical number of families of the size recorded in {a). Add up continuously from the bottom and we obtain the number of children of each order of birth in (e). Multiply by 1-8652888—i.e. 1000/536-11—and we obtain (d) the number of children of each order of birth permille, adjusted in our case to units. The reciprocal of 188, the first entry in (d), multiplied by 1000, gives the average size of family. We are now prepared for the ‘ Short Table’ method, which treats each size of family independently, and asks whether the marked members are distributed equally throughout the family. It is con venient to put this in the following form : TABLE III. DISTRIBUTION OF H-MARKED MEMBERS IN FAMILIES OF DIFFERENT SIZES. Size of Family. Total observed and expected in Row. I 2 3 4 5 6 7 8 9 IO 4*7 II 12 *3 H o'5 Expected No. 11 -o 10*0 11-3 I3-5 12-0 8*o 10-3 7' 8 6*0 2*1 1-9 First-born . Second-born Average of Inter- ) mediates ^ Average of two ) Last-born $ I I I I 9 10 11 14 11 I 4'5 9 12 w II-O 7 7 9-0 8-o 6 10 II-O 11- 5 6 8 8-i 7'5 8 5 5'4 7-0 4 5 5-o 4 -o 5 1 i-6 3 -o 4 2-0 1-5 1 i- 4 2‘5 I I *4 *5 \ 9 2 \ IOI S 85 l go j 61 1 55 5 7 1 j 68 It will be seen at once that there is no systematic deviation from the Expected Number —i.e. the row of H-Totals of Table II divided by the number in family—in the rows of first-borns, second-borns, average of last two born, or in the average of intermediates. This ‘ Short Table ’ method has the advantage of illustrating whether there is special weighting of late-borns as well as, or apart from, first-borns. It misses, however, the point already referred to, that weighting of first-borns may be due to bias against small families. (3) We are now armed with two methods of approaching the problem—that of the ‘Long Table’ and that of the ‘Short Table’. But to deduce results from the ‘ Long Table’, we must have some standard of reference of what the distribution of first- to ^ tb -borns in any community is. I was very early convinced that this is$