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of more advanced aspects is sketchy, somewhat jargonized, and some sectionsserve only to point out the existence of reference material, so that the utilityof the book is reduced greatly if one does not have access to the literature cited,most of it due to the authors and their colleagues.The book concludes with about forty pages of printout of computer programs

used for solving example problems in the text. These pages could have beenbetter used to convey additional theoretical information, or omitted to reducethe price of the book, at least presumably.Here is the list of chapters: 1. The Riccati Equation, 2. Two-Point Boundary-

Value Problems for Second-Order Differential Equations, 3. Monotone Behaviorand Differential Inequalities, 4. Systems of Differential Equations, Storageand Differential Approximations, 5. Partial Differential Equations, 6. Applica-tions in Physics, Engineering, and Biology, 7. Dynamic Programming andQuasilinearization.

L. B. RALLMathematics Research Center, U. S. ArmyUniversity of Wisconsin

Statistics and Experimental Design in Engineering and the Physical Sciences. ByIORMAN L. JOHNSON AND FRED C. LEONE. John Wiley, New York, 1964.xiv 523 pp., $10.95 (Vol. I), $11.50 (Vol. II).Reviews of scientific texts are intrinsically unjust. The authors have spent

years writing, testing, and revising their book. The editor-publisher has spentanother year getting the manuscript refereed, revised, and printed. Then theeditors of the technical iournals try to find a competent reviewer, who is in-evitably extremely busy, to take a week off and to write a review that may wellbe the only one seen by many readers. As often as not, the editor’s fourth choiceis the first who can be persuaded. To add injury to injustice, the present reviewerlost track of this request and is now complying a year late. It seems to me thatall this inefficiency can be partly remedied if the reader will give little weight tothis review except for the recommendation which follows, and if the authors canbe persuaded to comment in an accompanying note.

I advise any teacher, statistician, or experimentalist who is considering teach-ing or learning about statistics and experimental design in engineering and thephysical sciences, to get a copy of this workboth volumesand to spend thebetter part of a week looking it over. It is an excellent and courageous summaryof the whole field. No later comments should be taken as a major reduction ofthis estimate.

One’s first reaction is that the work is too long. After reading and reflection,one is astonished that so much ground is covered in the space available. Volume Istarts with the most elementary notions of descriptive statistics, sampling, andprobability. It goes through the standard developments of distribution theory,tests of significance, point- and intervM-estimation. But the volume also containsunusual and valuable chapters on order statistics and on nonparametric tests.On third thoughts, it appears to me that all statistics texts should be at least this

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long. The experimentalist or student who wants "only a little statistics" shouldbe urged not to start, at least until he realizes that there is no royal road toknowledge, and that a short course is nearly always worse than none at all.The second volume takes us quite a long way into the analysis of variance, and

into discussion of the corresponding balanced experimental plans. The 2 and 3series and their fractions are handled well, as are split-plot and nested factorials.(Of course this reviewer was pleased to see a clear treatment of the use of half-normal plots for studying 2 data. It is lamented, though that after this exposi-tion, the authors revert to squaring all contrasts and using F-tests.) There is agood chapter on sequentiul analysis and a long one on Multivariate observations.A good treatment of response surface methodology is included, anomalously, inthis chapter. Both volumes contain hundreds of problems and exercises, many ofthem using real data, many with answers. These exercises alone would make thework unique in its field.Two apparent inconsistencies in the general treatment should be mentioned.

Both are discrepancies between stated theory and recorded practice. The firstconcerns the conditions for the validity of significance tests and of confidenceinterval statements. Without exception these require that a fair sample from adefined population or set of populations be available. Fairness requires randomsampling of some sort. In experimental situations fairness requires some degreeof randomness in the assignment of "treatments" (experimental conditions) to"experimental units" (batches of raw material, time order of performance ofruns, etc.). These requirements are mentioned on p. II-107, but not again in thelengthy chapters on experimental design and analysis. The commonest cause offailure of factorial experiments is defective sampling of the universe about whichknowledge is desired. Many methods of getting better samples of data are known.For example, the use of widely separated blocks should be recommended, not togain more precision, and not because of batch-size limitations, but to broadenthe basis of the inferences to be made.

Close readers will note another maior discrepancy between the strictness ofthe requirements for validity of tests of significance (Chaps. 7 and 8), and thelooseness of language and judgment in the actual interpretations of data (Chaps.13-15). We are told earlier that levels of significance and statements of hy-potheses must be decided before the data are taken. But conclusions from eachof the 2 factorial experiments shown are given in terms of three (or sometimesfive) levels of "significance." These are called significant (.01 to .05), highly sig-nificant (.001 to .01), and very highly significant (less than .001) when definedon p. II-15, although the terms used later are strongly, etc. In discussing theresults of actual experiments, several weaker terms are added. Some effects"seem" significant, and "should not be completely disregarded." In one place(p. II-185) two interactions "show some slight evidence of significance." This isfaint praise indeed, and a far cry from the crisp requirements of vol. I. It appearsthat in all these years, no one has thought to consider the operating characteristiccurves of three-, or five-, level significance tests.A few omissions that strike the eye should be recorded. I can find one forward

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reference promising some discussion of the analysis of covariance, and one back-ward reference, but no actual discussion or example. There is no description ofthe reverse Yates algorithm for computing fitted values from a set of effectsiudged real. This is needed repeatedly in studying the simultaneous impact of anumber of factors especially if they "interact" as the examples show that they do.There are quite a few omissions of references to pioneer works that I believe

are still very useful. The excellent treatment of mixed and partially hierarchalarrangements could be made even more useful by referencing the fundamentalpapers of Wilk and Kempthorne, and the valuable tables of expected values ofmean squares by L. H.. Barter and his associates. No mention is made of J. W.Tukey’s "single degree of freedom for removable nonadditivity," or of the ac-companying transformations to more nearly additive scales. The detailed treat-ment of robust tests for comparison of variances should surely mention thepioneer work of Box and Andersen. Of the 17 references to R. A. Fisher, 14 areto the tables of Fisher and Yates, and the remaining three are to a card-playingparadox, to his z’-transformation, and to his improvement of the derivation ofStudent’s distribution. There is no reference to any of his books or to his col-leered papers. There is no indication of his creation of most of the ideas andlanguage of hypothesis testing, of statistical in.ferenee, and of the statistical designof experiments.In my experience most experimenters welcome any compact summary of their

dataand of its odditieseven if this takes an unexpected form. It must beadmitted, though, that what one man takes as a clever application of Oeeam’srazor may be taken by another as merely sharp practice. Here is one examplefrom many suggested by the examples of Chaps. 13-15. The replicated 2 ofExample 15.3 is seen to produce ten significant effects of which five are three-starred interactions. It may well be that a repetition of this experiment wouldreproduce all the "strongly significant" effects shown. But it might also be of

interest to the experimenter to know: (a) that there is something odd about thereplication error in his data since three of the pairs shown have differences far toolarge for the clear pattern set by the other 13, and (b) that most of the largeinteractions found are due to the two sets of conditions designated as xx4 andxxz4. If these two are interchanged, then most of the complexity disappears.I am not suggesting that three of the data points be dropped and that two pairsbe interchanged. I am suggesting that these two circumstances should be pointedout to the experimenter. He may want to go over his notebooks.

In conclusion, this is a valuable book for experimenters and for teaching stat-isticians. It seems well suited for self-teaching as well. I look forward to an earlyand enlarged second edition.

CUTHBERT DANIELNew York, New York

Two-Dimensional Problems in Hydrodynamics and Aerodynamics. By L. I.SEDOV. Interscience, New York, 1965, xv + 427 pp. $16.50.The Russian edition of this book was originally published in 1950 and its

contents have long been familiar to research workers in hydrodynamics. However,Dow

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