Godfrey H. Thomson

Methods of Estimating Mental Factors

MR. M. S. BARTLETT has proposed1 formulæ for the estimation of mental factors as alternatives to formulæ I have given2. My formulæ were arrived at by the ordinary regression method. Bartletts estimates and the regression estimates attain different ends, and it is agreed that each method is correct in the right place. The regression estimates minimize the squares of the discrepancies between the estimates and the true values, summed over the population of persons. Bartletts estimates minimize the squares of a mans specific factors, summed over the tests. If the scores expressed in matrix notation as linear functions of the true factors are the two sets of estimates, for the common factors only, are . The regression method has the quality that if factors estimated by it are inserted in the specification equation which defines a vocation in terms of factors, the result is the same as a direct regression estimate of vocational ability from the tests.

Charles Spearman, 1863-1945

Charles Spearman was born in London on 10 September 1863, and died there on 17 September 1945. He was survived by Mrs Spearman and their daughters; But their only son was killed in Crete in 1941. Even in his schooldays, he has told us, he was ambitious to follow an academic career. But, yielding to ‘the mouthful delusion that life is long’, he tried first a spell in the army as a regular officer of Engineers, went through the Burma campaign of that time, and then, mourning the lost years and fired by zeal for the developing science of experimental psychology, he resigned his commission and went to study under Wundt at his newly founded laboratory at Leipzig. There he came into contact with Krueger and Wirth, both of whom he much admired. His stay in Germany was interrupted by further military service during the Boer War. He served as the Staff Officer for Guernsey, and met there his future wife. They were married in 1901.

Boundary conditions in the common-factor-space, in the factorial analysis of ability

The author arrives at a simple rule for ascertaining when a matrix of correlations, with communalities reducing it to minimum rank, cannot be analyzed into factors such that every column of loadings has at least as many zeros as the number of common factors, as required by Thurstone. A more exact but arithmetically tedious rule is also deduced from Ridley Thompsons boundary conditions, and a correction is made to the latter.

Mathematical Methods of Statistics A First Course in Mathematical Statistics

THESE two books at once invite comparison with A Maurice Kendalls “Advanced Theory of Statistics” and A. C. Aitkens “Statistical Mathematics”. All four are mathematically flawless, and they all require from the reader some mathematical training and ability, but not to the same extent, nor are they all addressed to quite the same category of scientific workers. Kendall, in his preface, called his “a book on statistics, not on statistical mathematics” and declared his intention “to keep the mathematics to heel”. Cramers book (based on his Stockholm lectures since 1930) is very definitely for the mathematician, and its avowed purpose is to join the two lines of development due on one hand to the British and American schools of statisticians, and on the other to the rigorous work of French and Russian mathematicians in developing the calculus of probability. The first twelve chapters are a purely mathematical introduction, dealing with the properties of sets, Lebesque integrals, Fourier integrals, matrices and quadratic forms, and the like, preparatory to the later chapters on random variables, probability distributions, and statistical inference. The author advises the reader to jump to Chapter 13 after reading the first three chapters and a few other paragraphs, and thereafter to use this earlier part only as needed. The advice is good, and for my part I would say jump to Chapter 13 at once. Many who ought to read the book would be highly discouraged by the apparent irrelevance of those first three chapters, yet might turn to them without dismay later after seeing their use and necessity.Mathematical Methods of StatisticsBy Prof. Harald Cramér. (Princeton Mathematical Series, 8.) Pp. xvi + 575. (Princeton, N.J.: Princeton University Press; London: Oxford University Press, 1946.) 33s. 6d. net.A First Course in Mathematical StatisticsBy Prof. C. E. Weatherburn. Pp. xv + 272, (Cambridge: At the University Press, 1946.) 15s. net.

INTRODUCTION TO CORRELATION

• How long someone will live • Whether the stock market will go up or down • Whether or not someone will become a criminal • Whether or not a surgery will prolong a cancer patient’s life • Whether or not a depressed person will commit suicide • Whether or not a person will make a productive employee • Whether or not a football team will make a first down on the next play • Whether or not somebody’s marriage will survive or end in divorce