Journal of Clinical Epidemiology 54 (2001) 1191–1194 0895-4356/01/$ – see front matter © 2001 Elsevier Science Inc. All rights reserved. PII: S0895-4356(01)00420-6 COMMENTARY Francis Galton and the invention of terms for quantiles Jeffrey K. Aronson Department of Clinical Pharmacology, Radcliffe Infirmary, Woodstock Road, Oxford OX2 6HE, UK Received 2 May 2001; revised 7 July 2001; accepted 12 July 2001 When one of the highly respected Editors of the Journal of Clinical Epidemiology writes to ask you which of tertile and tercile is the correct form, you jump to it and reply. The answer to this question, posed by Professor Feinstein, is rel- atively simple, and I discuss it at the end of this article. However, in formulating the answer I started to question the origins of all the statistical words that describe quantiles. Here I describe those origins, and in particular the role that Francis Galton played in their invention. Let’s start with quantile itself. It comes from the Latin word quantus (how much or how great), and is defined in the Oxford English Dictionary (OED) as “each of any set of values of a variate which divide a frequency distribution into equal groups, each containing the same fraction of the total population; also, any one of the groups so produced, e.g. a quartile, decile, or percentile.” Well that expresses the general concept. The more specific term percentile is defined in the OED as “each of a series of values obtained by dividing a large number of quantities into a hundred equal groups in order of magnitude; that value which is not exceeded by the lowest group is the first percentile; that not exceeded by the lowest two, the second percentile; and so on.” Similarly, quartiles divide the distribution into four parts, quintiles into five parts, and so on. Now you would think that the general term quantile would have been the first of these words to have been coined and that all the rest would have followed. But words do not always evolve as logically as they ought, and in fact quantile did not appear until as late as 1940 [1], although the idea of a general term of this sort was enunciated by Francis Galton when he used the term equi-postile in 1902 [2]. The order of appearance of the others was first quartile and oc- tile [3], then decile [4], and then percentile [5], all of which appeared in the late 19th century. Other –iles, of which there is now a veritable archipelago, did not appear until the 20th century: centile in 1902 [2], sextile in 1920 [6], tertile in 1931 [7], vigintile in 1936 [8], quintile in 1951 [9], nonile in 1968 [10], quadragintile in 1976 [11], and septile in 1993 [12]. The names for the various quantiles, derived from the ordinal forms of the medieval Latin number words, are shown in Table 1, along with the dates of the earliest cita- tions that I have found in the OED, or in JSTOR (a digitally copied database of scholarly journals), or elsewhere. Of course, earlier citations may exist, and if anyone knows of any I should be pleased to hear about them. Since mis- citations may have occurred in secondary sources, for ex- ample through the introduction of typos by optical character reading in JSTOR [16], I have checked all citations in their primary sources. Although the whole idea of dividing a range of values into groups of equal size originated with Francis Galton [17,18], the OED gives first credit for the use of the word quartile to one Donald McAlister in a paper on “the law of the geometric mean” presented to the Royal Society in 1879 [3]: “As these two measures, with the mean, divide the curve of facility into four equal parts, I propose to call them the ‘higher quartile’ and the ‘lower quartile’ respectively. It will be seen that they correspond to the ill-named ‘probable errors’ of the ordinary theory.” Now McAlister was not a Fellow of the Royal Society—in order to present his paper he had to be introduced, and it was Francis Galton who in- troduced him with a paper of his own [19], in which he said that he would “communicate a memoir by Mr Donald McAlister, who, at my suggestion, has mathematically in- vestigated the subject [of the Law of Error, based on the geometric mean].” In turn, McAlister ended his paper by ac- knowledging Galton: “In conclusion, I desire to acknowl- edge my indebtedness to Mr. Galton, not only for suggest- ing the problem I have here attempted to solve, but also for many valuable practical hints in the working.” “McAlister” was Donald (later Sir Donald) MacAlister, a brilliant young mathematician, a Fellow of St John’s Col- lege Cambridge, who only two years earlier had been Senior Wrangler, the term given to the top student in mathematics in the final year at Cambridge. However, he later switched careers and studied medicine at Cambridge, St Bartho- lomew’s Hospital in London, and briefly in Leipzig, gradu- ating in 1884. Among his many distinctions, he was Princi- pal of Glasgow University from 1907 to 1929 and later its * Corresponding author. Tel.: +44-(0)-1865-224626; fax: +44-(0)- 1865-791712. E-mail address: jeffrey.aronson@clinpharm.ox.ac.uk.