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Correlation and Application of Statistics to Problems of Heredity 53

length, though partly for the sake of compactness, it is only those of length that will be here given as examples" (loc. cit. p. 137). Galton already saw clearly that his new method enabled comparison to be made on equal terms between variates with such intrinsic diversity as acuity of vision and head breadth*.

I have endeavoured to check Galton's work. I expect he found his medians and quartiles by plotting an "ogive curve" (see our p. 31 and Plate II) and smoothing it. The process of checking is rendered difficult by the following statements on p. 138:

"It is unnecessary to extend the limits of Table II [that of stature and cubit reproduced above] as it includes every line and column in my MS. table that contains not less than twenty entries. None of the entries lying within the flanking lines and columns of Table II were used."'

The first statement seems to suggest that the whole table has not been printed, the second leaves one in doubt as to how to find the medians of the arrays, or indeed of the marginal totals, if none of the entries in the flanking lines and columns had been used. Unfortunately I have not succeeded in discovering the original work and manuscript tables for this memoir among Galton's papers'. Putting aside the possibility of re-examining Galton's own work by more modern methods, we can, I think, indicate how closely his semigraphic median, quartile and regression slope methods accord with those obtained from much longer series by more accurate processes. First let us consider the correlation coefficients

Correlation Coefficient | ||

Character Pair |
As found by Galton from 350 Male Adults |
As found by Macdonell from 3000 Criminals |

Stature and Cubit ... ... |
0.80 {0.8290} |
0.7999 |

Stature and Head Length ... |
0.35 |
0.3399 |

Stature and Middle Finger ... |
0.70 |
0.6608 |

Cubit and Middle Finger ... |
0.85 |
0.8464 |

Head Length and Head Breadth |
0.45 |
0.4016 |

Stature and Height of Knee ... |
0.90 {0.8665} |
- |

Cubit and Height of Knee ... |
0-8010-8028} |
- |

The values in the first column of this table were the first organic correlations ever published, and on that account are of great h' orical interest.

* It is not without interest to note that more than a quarter of century later, Major Leonard Darwin could assert that the influences of environment and here 't uld not be compared, because there was no common unit of measurement applicable to them both ! He appeared still ignorant of Galton's use of Q. See Eugenics Review, Vol. v, p. 152.

t My colleague, Miss E. M. Elderton, has taken out the first 348 entries for male adults 21 years and upwards from-Galton's Laboratory records, and the resulting values from her tables, computed by modern methods, are given in brackets in the above and the following tables. Our table for stature and cubit differs somewhat from Galton's but with a probable error of

0113 the correlation is hardly significantly different from Galton's value. Both Knee Height and Cubit are measured in the Anthropometric Laboratory at University College, but the former is measured to the lowest point of the patella with the subject standing at rest, while Galton measured to the top of the knee with the subject sitting. Galton deducted the measured heel, we measure with boots off. Our correlation for male students of Knee Height and Cubit is only 0.66.

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