Letter to the Editor
I write to draw attention to an odd error in the January issue of Amstat News. The statement is made that Karl Pearson used Weldon’s data “… when developing the chi-square statistic.” I have not checked early issues of Biometrika, but I am almost certain that KP never mentioned “the chi-square statistic.” He would always have written the Greek character, and not a representation as a pseudo-English word, but, in speech, he would certainly have said “chi squared”!
When some 70 years ago I first encountered North American statistical texts, I was surprised by the use of “square,” where British usage is always “squared,” but of course I had to learn that, in mathematical speech, generally USA practice is always to say “x square” for what my earliest algebra lessons had taught me to call “x squared.”
I have written semi-facetiously about something of no deep importance to statistics, but I think we can be sure that KP followed English educational custom. I knew Egon Pearson quite well and would certainly have noticed if his usage had differed. I suggest that Amstat News could spare a paragraph to comment on historic origins. What is the practice in other modern European languages? I am almost certain that French is equivalent to my side of the English Channel, but I cannot answer for German or Spanish, etc. I expect that Stephen Stigler would know.
David J. Finney
Response from Michael D. Larsen, CHANCE editor
I would like to thank Dr. Finney for his attention to detail. Indeed, he appears to be exactly correct. I examined two articles [written] by Karl Pearson in 1900 and 1934 [“On the Criterion That a Given System of Deviations from the Probable in the Case of Correlated System of Variables Is Such That It Can Be Reasonably Supposed to Have Arisen from Random Sampling,” Philosophical Magazine, and “On a New Method of Determining ‘Goodness of Fit,’” Biometrika] and one by Egon Pearson in 1965 [“Some Incidents in the Early History of Biometry and Statistics, 1890-94,” Biometrika], and they use the symbol X2. In Biometrika, the words “chi-squared” are used consistently. Searching online in Web of Science for “chi-square” produced nothing in recent years, but “chi-squared” produced several articles.
Robin Plackett, in her 1983 article in the International Statistical Review, “Karl Pearson and the Chi-Squared Test,” also used “chi-squared.” However, I regret to inform Dr. Finney that it is not difficult to find prominent sources, such as the NIST/SEMATECH e-Handbook, using “chi square.”
Michael D. Larsen