Re: Galton

[Jan de Leeuw]

Title: Re: Galton

"Natural Inheritance" summarizes Galton's earlier work. The section on

regression is taken mainly from the presidential address

"Regression towards mediocrity in hereditary stature", Journal of the Anthropological Institute 15 (1886), 246-263

The table on p 203 in NH is the same as Table 1 in this address. With supporting material (regression line, pulley models) it is at

http://www.stat.ucla.edu/history/regression.gif

and the regression ellipse based on the table is at

http://www.stat.ucla.edu/history/regression_ellipse.gif

Of course Galton introduced the term "co-relation" in another 1888

paper.

"Co-relations" and their measurement, chiefly from antropometric data

RS Proc, 45, 1888, 135-145

It is instructive to read Pearson, Notes on the History

of Correlation, Biometrika, 13, 1920, 25-45. This paper is remarkable

because in an earlier historical account in 1895 Pearson attributed

correlation to an 1846 memoir of Bravais -- he takes this back in 1920

and gives Galton's work between 1877 and 1888 all the credit.

Summarizing, the bivariate normal was studied first by Bravais, the

notion of correlation (and its wide applicability) is due to Galton

around 1885, the term "coefficient of correlation" is due to Edgeworth

in 1892.

At 21:37 -0700 05/25/2000, David A. Heiser wrote:

I have been waiting until everybody was through throwing their stuff into the pot.

 

Dennis refers to Galton's works on inheritance, which is in his book "Natural Inheritance" published in 1889. Galton is credited with starting the idea of correlations and bivariate relationships. The table is on page 208. I made a jpg image of it and sent it to DR.

 

Jan de Leeuw's UCLA website picture is a pretty poor representation of what Galton did and of his table on page 208, and what was his insight on the relationships. Galton at least put in the units. How Galton got the data is very interesting. No professor today would do what he did to get his data.

 

Dickson did the math on Galton's data, and established a curve of probable error in the form of the equation of an ellipse. He does not use the term bivariate or correlation or any such terms. He refers to his work as a discussion of the surface of frequency of p.The terms we use today were not yet developed back then. (1880's). Galton does not use modern terms. He describes the effect in terms of regression and on the means of the populations and the ellipse on page 101 as the law of errors.

 

Also floating around in the responses to Dennis's request was Fisher's discussion of correlation in his book "Statistical Methods for Research Workers", and his use of a table of heights of fathers and daughters on page 180 to introduce the concept of correlation. The data was from K. Pearson and A. Lee, "Inheritance of Physical Characters" in Biometrika, 1903, 357 I think this was the first issue). Fisher introduces the bivariate normal distribution and calculates a correlation coefficient of +0.5157 for the data (which includes Sheppard's correction for grouped data).

 

I have these pages in jpg image format, but can't attach it here. If you send me an Email requesting them I will send them.

 

DAHeiser 

--
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Jan de Leeuw; Professor and Chair, UCLA Department of Statistics;
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