## Tuesday, August 21, 2012

### Whose F Distribution Was It?

We use the F-distribution all of the time in our econometric work. But why is it called the "F" distribution?

A lot of students guess that the name is related to the great statistician, Sir Ronald A. Fisher. They're partly right. However, the occasionally encountered term, "Fisher's F Distribution" is somewhat misleading. The alternative terms, "Snedecor's F distribution" or the "Fisher-Snedecor Distribution" offer more accurate information.

Personally, I prefer to call it "Snedecor's F" - after George W. Snedecor. Here's why.
"The F distribution was tabulated - and the letter introduced - by G. W. Snedecor, Calculation and Interpretation of Analysis of Variance and Covariance (1934)...... For this reason it is sometimes called “Snedecor’s F distribution” of the variance-ratio. Snedecor’s goal, however, was not to introduce a new distribution but to improve the presentation of Fisher’s analysis of variance....... Fisher did not tabulate the variance-ratio, but the statistic z = ½ ln F ....... Fisher was not persuaded that it was better to tabulate the variance-ratio, nor was he happy with the choice of the letter F for the variance-ratio—even if the letter was meant as a compliment to him. See Fisher’s letter to Snedecor in 1938 and a later letter to Heckstall-Smith in Fisher’s Correspondence. (pp. 323 and 319 respectively.)"

So, in my view, Snedecor deserves the credit for the introduction of the letter, in honour of Fisher.

There's also a nice econometric connection in the history of the F distribution. Until 1982, the expression for the characteristic function that was given in all of the standard statistics texts (and used in various research papers) was wrong!

The econometrician, Peter Phillips, set things straight  (after 48 years!) with an article in Biometrika that year.

Reference

Phillips, P. C. B., 1982. The true characteristic function of the F distribution. Biometrika, 69, 261-264.