The development of modern statistics Author(s): Dale E. Varberg Source: The Mathematics Teacher, Vol. 56, No. 4 (APRIL 1963), pp. 252-257 Published by: National Council of Teachers of Mathematics Stable URL: http://www.jstor.org/stable/27956805 . Accessed: 22/10/2014 15:44 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. National Council of Teachers of Mathematics is collaborating with JSTOR to digitize, preserve and extend access to The Mathematics Teacher. http://www.jstor.org This content downloaded from 146.186.124.59 on Wed, 22 Oct 2014 15:44:00 PM All use subject to JSTOR Terms and Conditions HISTORICALLY SPEAKING,? Edited byHoward Eves, University ofMaine, Orono, Maine The development of modern statistics* by Dale E. Varberg, H aniline University, St. Paul, Minnesota That area of study which we now call evoke some notion of the procedures which statistics has only recently come of age. are used to condense and interpret a col While its origins may be traced back to lection of data, such as the computing of the eighteenth century, or perhaps earlier, means and standard deviations. But to the first really significant developments in the practitioner of the craft, statistics is the theory of statistics did not occur until the art ofmaking inferences from a body of the late nineteenth and early twentieth data, or, more generally, the science of centuries, and it is only during the last making decisions in the face of uncer thirty years or so that it has reached a tainty. fullmeasure of respectability. It was ante Statisticians concern themselves with dated by the theory of probability and has answering such questions as: Is this par its roots embedded in this subject. In fact, ticular lot of manufactured items defec any serious study of statistics must of tive? Is there a connection between smok necessity be preceded by a study of prob ing and cancer? Will Kennedy win the ability theory, for it is in the latter sub next election? In answering these ques ject that the theory of statistics finds its tions, it is necessary to reason from the foundation and fountainhead. specific to the general, from the sample to The word Statistik was first used by the population. Therefore, any conclu Gottfried Achenwall (1719-72), a lecturer sions reached by the statistician are not to at the University of G?ttingen [l].** He be accepted as absolute certainties. It is, is sometimes referred to as the "Father of in fact, one of the jobs of the statistician Statistics"?perhaps mistakenly, since he to give some measure of the certainty of was mainly concerned with the description the conclusions he has drawn. of interesting facts about his country. It should not be inferred from this lack Our English word "statistic" means dif of certainty that the mathematics of sta ferent things to different people. To the tistics is nonrigorous. The mathematics man on the street, statistics is the mass of that forms the basis of statistics stems figures that the expert on any subject uses from probability theory and has a firm to support his contentions?it's "what axiomatic foundation and rigorously you use to prove anything by." To the proved theorems. more sophisticated person, the word may If we conceive of statistics as the science * of drawing inferences and deci This is the first of two lectures on the history of making statistics given by Professor Varberg at a National sions, it is appropriate to date its begin Science Foundation Summer Institute for High with the work of Sir Francis Galton School Mathematics Teachers held at Bowdoin Col nings lege during the summer of 1962. Notes were taken by (1822-1911) and Karl Pearson (1857 Alvin K. Funderburg. in the late nineteenth ** Numerals in brackets refer to the notes at the 1936) century. end of this article. Starting here, modern statistical theory 252 The Mathematics Teacher | April, 1963 This content downloaded from 146.186.124.59 on Wed, 22 Oct 2014 15:44:00 PM All use subject to JSTOR Terms and Conditions has developed in four great waves of ideas, smaller than the other. I wonder if she " in four periods, each of which was intro could be lying to me.' duced by a pioneering work of a great We have here in this simple story, as statistician [2], Helen Walker points out, "rejection of The first period was inaugurated by the constituted authority, appeal to empiri publication of Galton's Natural Inheri cal evidence, faith in his own interpreta tance in 1889. If for no other reason, this tion of the meaning of observed data, and book is justly famous because it sparked finally imputation of moral obliquity to a the interest of Karl Pearson in statistics. person whose judgment differed from his Until this time, Pearson had been an ob own." These were to be prominent charac scure mathematician teaching at Uni teristics throughout Pearson's whole life. versity College in London. Now the idea This first period, then, was marked by a that all knowledge is based on statistical change in attitude toward statistics, a foundations captivated his mind. Moving recognition of its importance by the scien to Gresham College in 1890 with the tificworld. But, in addition to this, many chance to lecture on any subject that he advances were made in statistical tech wished, Pearson chose the topic: "the nique. Among the technical tools invented scope and concepts of modern science." and studied by Galton, Pearson, and In his lectures he placed increasingly their followers were the standard devia stronger emphasis on the statistical foun tion, correlation coefficient, and the chi dation of scientific laws and soon was de square test. voting most of his energy to promoting the About 1915, a new name appeared on study of statistical theory. Before long, the statistical horizon, R. A. Fisher his laboratory became a center in which (1890-). His paper of that year on the men from all over the world studied and exact distribution of the sample correla went back home to light statistical fires. tion coefficients ushered in the second pe Largely through his enthusiasm, the sci riod of statistical history and was followed entific world was moved from a state of by a whole series of papers and books disinterest in statistical studies to a situa which gave a new impetus to statistical in tion where large numbers of people were quiry. One author has gone so far as to eagerly at work developing new theory and credit Fisher with half of the statistical gathering and studying data from all theory that we use today. Among the sig fields of knowledge. The conviction grew nificant contributions of Fisher and his that the analysis of statistical data could associates were the development of meth provide answers to a host of important ods appropriate for small samples, the dis questions. covery of the exact distributions of many An anecdote, related by Helen Walker sample statistics, the formulation of logi [3], of Pearson's childhood illustrates in cal principles for testing hypotheses, the a vivid way the characteristics which invention of the technique known as an marked his adult career. Pearson was alysis of variance, and the introduction of asked what was the first thing he could re criteria for choice among various possible member. "Well," he said, "I do not know estimators for a population parameter. how old I was, but I was sitting in a high The thirdperiod began about 1928with chair and I was sucking my thumb. Some the publication of certain joint papers by one told me to stop sucking it and said Jerzy Neyman and Egon Pearson, the lat that unless I do so the thumb would ter a son of Karl Pearson. These papers wither away. I put my two thumbs to introduced and emphasized such concepts gether and looked at them a long time. as "Type II" error, power of a test, and 'They look alike to me/ I said to myself, confidence intervals. It was during this can't see that the thumb I suck is any period that industry began to make wide Historically speaking,? 253 This content downloaded from 146.186.124.59 on Wed, 22 Oct 2014 15:44:00 PM All use subject to JSTOR Terms and Conditions spread application of statistical tech Frequency diagram niques, especially in connection with quality control. There was increasing in terest in taking of surveys with consequent attention to the theory and technique of taking samples. We date the beginning of the fourth pe riod with the first paper of Abraham Wald mm i?it (1902-50) on the now often used statisti ?4 cal procedure-sequential sampling. This paper of 1939 initiated a deluge of papers by Wald, ended only by his untimely 2 death in an airplane crash when at the Figure height of his powers. Perhaps Wald's most contribution was his introduc significant the data pictorially. William Playfair tion of a new of at statistical way looking (1759-1823) of England is usually given what is known as statistical de problems, credit for introducing the idea of graphi cision From this of theory.