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The Statistical Legacy of William Sealy Gosset (“Student”) cdh Volume 25 Number 4 December 2008 Community Dental Health In this issue Effect of tooth loss on quality of life amongst the elderly in Sri Lanka Caries levels amongst teenagers in Milan, Italy Access to dental services for people with a physical disability in the UK The journal of the British Association for the Study of Community Dentistry and the European Association Published by of Dental Public Health FDI World Dental Press Ltd Community Dental Health Volume 25 Number 4 December 2008 Editorial 194 Original Communications Effect of tooth loss and denture status on oral health-related quality of life of older individuals from Sri Lanka C. Pallegedara and L. Ekanayake 196 The distribution of general dental practitioners with NHS contract numbers in relation to the distance of their practices from the seven dental undergraduate teaching hospitals in England outside London R. J. McCormick, R. Smith, D. Edwards, D. White and J. Langford 201 Evaluation of oral health-related quality of life questionnaires in a general child population L.G. Do and A. J. Spencer 205 Retention and effectiveness of fissure sealants in Kuwaiti school children R. Francis, A.K. Mascarenhas, P. Soparkar and S. Al-Mutawaa 211 Loss of sealant retention and subsequent caries development in a mobile dental clinic S. Tianviwat, V. Chongsuvivatwong and B. Sirisakulveroj 216 Oral health and treatment needs among 15-year-olds in Tehran, Iran R. Yazdani, M.M. Vehkalahti, M. Nouri and H. Murtomaa 221 The frequency of periodontal infrabony defects on panoramic radiographs of an adult population seeking dental care N. Dundar, T. Ilgenli, B. Ilhan Kal and H. Boyacioglu 226 Oral health problems and needs in nursing home residents in Northern Italy R. Ferro, A. Besostri, L. Strohmenger,L. Mazzucchelli, G. Paoletti, A. Senna, E. Stellini and S. Mazzoleni 231 Caries prevalence and need for dental care in 13–18-year-olds in the Municipality of Milan, Italy G. Campus, M. G. Cagetti, A. Senna, G. Sacco, L. Strohmenger, P.E. Petersen 237 Number of teeth and serum lipid peroxide in 85-year-olds K. Sonoki, Y. Takata, T. Ansai, K. Fujisawa, M. Fukuhara, M. Wakisaka, S. Akifusa, I. Soh, A. Yoshida, T. Hamasaki, S. Awano, and T. Takehara 243 Access to dental services for people with a physical disability: a survey of general dental practitioners in Leicestershire, UK W.O. Baird, C. McGrother, K.R. Abrams, C. Dugmore and R.J. Jackson 248 Short Communication: Risk indicators of dental caries in 5-year-old Brazilian children K. L. Cortellazzi, S. Márcia Pereira, E. P. da Silva Tagliaferro, C. Tengan, G. M. B. Ambrosano, M. de Castro Meneghim and A. C. Pereira 253 www.bascd.org www.Dundee.ac.uk/EADPH The cover illustration shows William Sealy Gosset (1876 – 1937), the pioneering statistician whose contribution to that branch of mathematics is amply described in the editorial of this issue. It only remains to note as an interesting aside that while the general formula for deriving the popular black stout was in common use elsewhere, a local tradition declares that the modification which made the product unique was based on a fortuitous miscalculation attributed to Richard Guinness who worked as a brewer for the Archbishop of Cashel in the south of Ireland, and whose son Arthur established the brewery at St. James’s Gate in Dublin. The 2007 Journal Citation Reports have now been published by Thomson ISI and Community Dental Health has an impact factor of 0.736. CDH December 08 Contents .indd 193 02/12/2008 11:19:31 Community Dental Health (2008) XX, 1–02 © BASCD 2008 doi:10.1922/CDH_2479Hanley02 Editorial The statistical legacy of William Sealy Gosset (“Student”) The work The Probable Error of a Mean that led to manufacturer’s imprint on the cover of “Student’s” first today’s t-distribution was the lead article in the March small sample notebook, “The Student’s Science Notebook, 1908 issue of Biometrika. Its author was William Sealy Eason and Son, Ltd., Dublin and Belfast,” 1905-1907, Gosset [1876-1937], who -- for proprietary reasons -- which “Student” used while on sabbatical at Karl Pear- wrote under the pen name “Student.” With an Oxford son’s Biometric Laboratory. His notebooks contain the degree in mathematics and chemistry, Gosset began work results of the statistical simulations, and his mathematical at the Guinness brewery in Dublin in 1899. Those who derivations. He used the simulations to check the form of still misspell his surname today –as of this writing, the his theoretical curves, since he was not entirely confident list includes the website of his own employer -- might that they were mathematically correct. find it easier to remember the correct spelling if they In Fisher’s obituary, W. S. Gosset is described as “one realized that the Gossets came from Huguenot stock, that of the most original minds in contemporary science.” the name on the family crest refers to “trois Goussés de Fisher goes on, “Without being a professional math- fèves feuillées et tigées, et rangées, en pairle de meme” ematician, he first published, in 1908, a fundamentally and that it was transmuted to Gosset when his forbears new approach to the classical problem of the theory of settled in the Channel Island of Jersey errors, the consequences of which are only still gradually The first of his more than 20 statistical papers, pub- coming to be appreciated in the many fields of work to lished in 1907 while he was on sabbatical leave at Karl which it is applicable. The story of this advance is as Pearson’s unit at University College, dealt with statistical instructive as it is interesting.” variations in the counting of (yeast) cells. In it, he inde- And indeed it is. The “different distribution curves for pendently derived the Poisson distribution. Moreover, he the behaviour of means based on different sample sizes” used statistical techniques for correlations and goodness were the impetus for Fisher to develop the idea of degrees of fit developed by Pearson in the previous ten years to of freedom, and analysis of variance. The concept of the test the fit of this theoretical distribution to several sets former is still difficult for students today; this author of experimental data. In 1935, he moved back to his likes to describe the number of degrees of freedom as native England to set up a Guinness brewery in Park the number of independent assessments of error. In the Royal in London. 1939 tribute to Gosset, Fisher upbraided Karl Pearson Gosset died at the age of 61 in 1937. His friend E S -- Gosset’s supervisor while he wrote the seminal 1908 Beaven, a barley breeder, wrote an obituary in the London paper – for his insistence on using a divisor of n, rather Times. In it, he revealed Gosset’s pen name, and described than n-1, to estimate the variance. Gosset had studied him as one of a “new generation of mathematicians who Airy’s Theory of Errors, and must have read there that were founders of theories now generally accepted for the the use of n-1 leads to an unbiased estimator. Indeed, interpretation of industrial and other statistics.” The 1939 in a letter to a Dublin colleague in May 1907, he wrote Biometrika tribute by his Guinness colleague McMullen “when you only have quite small numbers, I think the warmly described “ “Student” as a Man.” “Student” as formula with the divisor of n-1 we used to use is better” Statistician” by Egon Pearson also described his warm But Karl Pearson, scoffed that it doesn’t matter, “because personal relationship with Gosset, and reviewed Gos- only naughty brewers take n so small that the difference set’s groundbreaking statistical work, his links with Karl is not of the order of the probable error!” Pearson and Ronald Fisher, and how Gosset remained a Gosset’s limited mathematical statistics capacity and friend of both of these temperamental men. vision did not allow him to see how his table could be Fisher, who never again published in Biometrika after used for a much broader array of statistical analyses his early dealings with its editor Karl Pearson, wrote his than the simple 1-sample or paired sample situations he appreciation of Gosset in the Annals of Eugenics (now illustrated in his 1908 paper. It was Fisher who saw, and the Annals of Human Genetics). He asked Gosset’s wife in 1925 fully described, the many extensions of Gosset’s Marjory for a suitable photograph of Gosset. She replied work, not just to the familiar 2-independent-samples con- that he didn’t like to be photographed in his later years, text, but also to correlation and regression coefficients. but she could supply “one fairly good photo of him taken Fisher also convinced Gosset to leave behind the ratio, z about 1908, but I suppose that wouldn’t do.” He used it = (ȳ-µ)/s , whose sampling distribution he had originally as the frontispiece for the issue of the journal; this photo derived, for the ratio we learn today, t= (ȳ-µ)/(s/√n), is the source for the image used in this 2008 tribute. and in which – unlike the use of the divisor of n that And, thanks to Stephen Ziliak’s book, we now know that Pearson insisted on -- the standard deviation s is now Gosset’s nom-de-plume may well have derived from a estimated using the degrees of freedom n-1 as the divisor. Correspondence to: James A. Hanley, Department of Epidemiology, Biostatistics and Occupational Health, McGill University, 1020 Pine Avenue West, Montreal, Quebec, H3A 1A2, Canada.
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