Abstract
THE errors made in measuring the height of the head are certainly much larger in the instance given by “F. M. T.” than they should be; still they do not seem to me large enough to throw doubt on the truth of the general conclusions to which he refers. (1) As regards the difference between the means of the “products” in the high honour and the poll men. Those means are 224 and 237, and they depend on 258 and 361 observations respectively, which numbers are much the same as 162 and 192. Therefore the probable error in the determination of each of these means will be equal to the probable error of a single “product” divided by 16 in the one case and by 19 in the other. I have as yet no data to determine the probable error of a single “product,” due to faults of measurement alone, other than those given by “F. M. T.,” which suggest, though in the rudest way, that it is about 4 units. Accepting this for the moment as a basis, the probable error of the means of the two sets of “products” would be 4 divided by 16 and by 19, equal, say, to ¼ and 1/5 respectively. Now, the chance of an error exceeding 4 or 5 times the probable error is not worth regarding; therefore safety, so far as regards the effects of inaccuracy of measurement, is practically to be found in each mean value beyond a range of about 1 unit. In the differences between the mean measures, safety will be found beyond the range √2, say 1½ units. But the two means 224 and 237 differ by as much as 7 units. It should, however, be remarked that the seven observations fall into two well-marked groups, each of which is very consistent within itself, but which differ from one another by 10 units. This raises strong suspicion of some peculiarity in the shape of the head, which caused doubt as to the exact line of maximum height, and that one line was followed in three of the measurements and another line in the remaining four. (2) As regards the differences between the high honour and the poll men at different ages, the observations at each stage are, of course, much less numerous than in the sum of all of them, still they range in all cases but two between 25 (or 52) and 102 (or say 102). Each person must judge for himself, from the diagram that accompanied my little paper, how far the run of those differences confirms my conclusions. I think they do well enough to give “an approxirnately true” idea of what we should find if we had the opportunity of discussing a much larger number of observations, and this was all that I claimed.
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GALTON, F. Head Growth in Students at the University of Cambridge. Nature 40, 318 (1889). https://doi.org/10.1038/040318a0
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DOI: https://doi.org/10.1038/040318a0
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