The Methods of Statistics. by L. H. C. TippettReview by: Frederick E. CroxtonJournal of the American Statistical Association, Vol. 33, No. 202 (Jun., 1938), pp. 483-484Published by: American Statistical AssociationStable URL: http://www.jstor.org/stable/2278941 .

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* REVIEWS 483

Age Last Birthday Number of Males 29 927 30 12,294 31 652 32 2,058 33 672 34 892 35 7,723 36 1,437 37 870 38 1,362 39 467 40 10,391 41 460

The scope of a book like this may be indicated by listing both the topics it includes and some that it does not include. The following are either omitted or considered only very briefly: likelihood in Fisher's sense, fiducial limits, efficiency of statistical estimates, inverse probability, polynomials of Hermite, Pearson's curves (mentioned very briefly), frequency curve fitting, graduation by means of a normal distribution of a series which is ordered but not measured, correlation in contingency tables between ordered but not measured characters, polychoric r. The last two subjects are covered partly by a remark about tetrachoric r, but this, the authors say, involves some difficult mathematics and "is outside the scope of the book . . . The student should realize that the product-sum correlation and the tetrachoric correlation are ... two entirely different measures.... The one is in no sense an approximation to the other." This statement is very misleading, for if the distribution is exactly normal the two measures are exactly equal and mean the same thing. The mathematics for tetrachoric r is no more dif- ficult than that involved in the chi-square test. In the opinion of the re- viewer, it would have been better to have omitted the Yule "coefficient of association Q" (p. 46), which had appeared in the older book, and spent the space on an exposition of tetrachoric r; for the latter has a simple inter- pretation, and, with the tables now available, its calculation is short and easily explained.

BURTON H. CAMP

Wesleyan University

The Methods of Statistics, an Introduction Mainly f or Experimentalists, by L. H. C. Tippett. London: Williams and Norgate, Ltd. 1937 (2nd edition). 280 pp. 15s. Tippett's book is so widely and favorably known that the following com-

ments are devoted largely to a recital of some of the important respects whereby the second edition differs from the first. The revision is more than a nominal one as the book has been enlarged by some 57 pages.

The brief introduction has been rewritten. Chapters II and III of the first edition have also been rewritten and enlarged, comprising now three chapters entitled "Frequency Distributions and Constants," "Distributions Derived from Theory of Probability," and "Errors of Random Sampling

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484 AMERICAN STATISTICAL AssoCIATION*

and Statistical Inference." A few proofs have been added in the first two of these chapters. New material is most prominent in the third and includes consideration of levels of significance and rejection and acceptance of hy- potheses, standard errors of functions of statistical constants, determination of population value from sample (fiducial probability), choice of statistical constants, and method of maximum likelihood. The discussion of fiducial probability would be improved, in the reviewer's opinion, if the illustrative diagram were drawn to scale and perhaps also if it were shown how fiducial limits of p may be ascertained from

(a - P b)2 X2 q

P N, q

thus enabling the limits of p to be computed for any desired N and for vari- ous confidence coefficients.

The chapter on Goodness of Fit and Contingency Tables is essentially as before. That dealing with Small Samples includes a new section on the Neyman-Pearson L1 test for use when there are a number of estimates of vari- ance. This chapter no longer includes the chart of the t distribution for n = 4 compared with the normal distribution, a very illuminating graph for the student.

The chapter formerly treating of the sampling distribution of the correla- tion coefficient has been expanded to include regression constants. The discussion if intra-class correlation and that of correlation of ranks formerly included in the chapter on nonlinear regression are not included in the pres- ent volume. Chapter X, "The Further Theory of Errors and Principles of Experimental Arrangement" is greatly enlarged, having new portions con- cerned with economy in sampling, sampling from a limited field, the use of controls, and multiple factor experiments.

For the intermediate student this is a most valuable volume. Frequently, points which are elusive in Fisher's Statistical Methods for Research Workers are cleared up for the reader by Tippett because of more extended discus- sion, explanation, or illustration. There is, however, no adequate table of areas of the normal curve, no t table, no z (or S12/S22) table, and no table of x2. For the actual use of the principles and methods discussed the reader must therefore refer to one or more other publications. Perhaps the author will append these tables in a later printing or edition and increase the use- fulness of the book.

FREDERICK E. CROXTON Columbia University

The Treatment of Clinical and Laboratory Data, by Donald Mainland. Edin- burgh and London: Oliver and Boyd. 1938. xi, 340 pp. 15s. net. This book has been prepared for the express purpose of aiding the clinician,

untrained in statistics, in the evaluation of the significance of clinical and

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