The Median is the Message

I've written two brief historical notes about the role of median; the first was written for Journal de la Société Française de Statistique as one of several comments commemorating the reprinting of a paper by Maurice Frechet. The note is available in pdf. The second paper, which was an offshoot of the first, is about an analysis by Wilson and Hilferty of some experiments conducted by C.S. Peirce in 1872. This note is forthcoming in American Statistician and available in pdf.

A detailed description of the experiment can be found in Peirce (1873). A young man of about 18 with no prior experience was employed to respond to a signal ``consisting of a sharp sound like a rap, the answer being made upon a telegraph-operator's key nicely adjusted.'' The response times, made with the aid of a Hipp cronoscope were recorded to the nearest millisecond. The data was analyzed by Peirce who concluded that after the first day, when the the observer was entirely inexperienced, the curves representing the densities of the response times ``differed very little from that derived from the theory of least squares,'' i.e. from the Gaussian density.

The data was subsequently analysed in a diploma thesis supervised by Maurice Frechet, who reported briefly the findings in Frechet (1924), and by Wilson and Hilferty (1929). In both instances the reanalysis showed that Laplace's first law of error, the double exponential distribution, was a better representation for the data than was the Gaussian law. A compressed tar archive of the data and software required to reproduce the analysis in "The Median is the Message" is available as MiM.tar.gz.

Comments are, of course, always welcome.