Soviet Economic Statistics. by Vladimir G. Treml; John P. HardtReview by: Judith A. ThorntonJournal of the American Statistical Association, Vol. 68, No. 342 (Jun., 1973), pp. 496-497Published by: American Statistical AssociationStable URL: http://www.jstor.org/stable/2284116 .

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496 Journal of the American Statistical Association, June 1973

may be generated under many of the conditions examined here sug- gests that . . . Duncan and Newman-Keuls are unsuitable. By contrast, the methods of Scheffe and Tukey seem appropriate to use on any data appropriate for analysis of variance." To that, this reviewer would add the methods of Dunn [1] or Bonferroni as described by Miller [4] and Kirk [2]. The author gives a passing comment to these tremendously important multiple test procedures, but they are never illustrated.

Unfortunately, there is a tradition in the behavioral sciences to emphasize hypothesis testing almost to the complete exclusion of estimation and, in particular, to interval estimation. Winer, having roots in psychology, tends to follow this pattern and thereby creates a number of confusing situations for his readers. For example, one finds the author testing an omnibus hypothesis based on K means with K - 1 degrees of freedom and finding that the differences are significant at the .05 or .01 level. While most researchers would per- form a post hoc Scheff6 or Tukey type analysis, the author fre- quently performs a number of post hoc one degree of freedom tests on contrasts of interest at an unspecified alpha level, occasionally at a specified .05 level, or occasionally at a specified .01 level. There appears to be no uniform model for a new researcher or student to follow. Sometimes decisions are made on the basis of the size of the significance probability, and sometimes on a strict adherence to a preassigned decision rule. If a student follows the procedures de- scribed a number of times in the text, it is possible to obtain a non- significant F-test based on K - 1 degrees of freedom, and then find that a number of post hoc comparisons are significant when based on one degree of freedom tests using .05 or even .01 as a level of significatnce. The author warns the reader on page 175 that, "When a large number of comparisons are made following a significant over- all F, some of the decisions which reject HI may be due to Type I errors." Yet he goes on and makes the error he advises against. Fortunately, the problem is solvable. One could select a, count the numbei of comparisons that are of interest, partition a, and then apply the Bonferroni-Dunn procedures. But as stated, Winer does not describe these methods.

While much of this inconsistency can be traced to the greater interest behavioral scientists have in significance testing, part of the problem is also related to the inability of the author to choose betweeni preassigned decision rule methods and the use of decision making methods based on after the fact examination of the level or magnitude of significance probabilities. As stated on page 160, "The formal method for testing statistical hypotheses requires that the level of significance of a test be set in advance of obtaining the data. Convention in the analysis of variance is somewhat opposed to this procedure. The value of Fobs iS generally compared with tabled critical values, and the outcome is described in terms of the state- ment: F.b, exceeds a specified percentile point (usually the 95 or 99 percentile points). The choice of the level of significance is thus in part determined by the observed data. This procedure is not objec- tionable, for purposes of estimating the probability of the observed outcome in terms of an assumed underlying sampling distribution." However, this reviewer finds the procedure objectionable since it confounds the post hoc analysis of rejected hypotheses. It is hard to know where the author stands on this important issue. Sometimes he uses a decision theory model in which a hypothesis is or is not rejected at a preassigned probability level and at times one finds the author stating that the differences are significant at the observed level of significance. For the novice this creates problems, especially when it comes to a post hoc investigation of the data. If an F-ratio leads to a rejection of Ho beyond the .001 level of significance, one does not know how to select a type I error level if Tukey's or Scheffe's methods are to be used to investigate possible sources for the high F-value. Without doubt, the final decisions depend upon whether or not .05, .01, .001, or any other significance probability level is emnployed.

Finally, this reviewer is not satisfied with the way Winer handles the problem of significant interactions in fixed effect designs. For example, on page 435 one reads, "Should the interaction term in the analysis of variance prove to be statistically significant, it is generally desirable to analyze the simple main effects rather than the overall main effects." This statement is void of meaning since contrasts based on row, column, or row by column effects are spanned by vectors that lie in subspaces that are mutually orthogonal to onle another. Thus, statements about row or column effects are also orthogonal to statements about interaction effects. Later, on page 529, he repeats, "If the AB interaction were significant, tests on

simple main effects would be called for, rather than direct tests on main effects," and even later, on page 562, one reads, "It should be noted that a difference between two simple main effects is a mixture of main effects and interaction effects." Certainly, this last comment should warn one that such an analysis is not warranted under the assumed linear model.

For example, if it is assumed that Xijk = I + ai.. + /.j + Yij. + ei k

then a simple pairwise contrast in the cell means of any specific row actually estimates

VI = lAi -j Aij = (ai.. -

ci,..) + (yij -yi'j).

This contrast is therefore not worthy of examination in a fully crossed design, but with another model this same contrast is interpretable. If the mathematical model is a nested model in which Factor A is nested in B so that

Xijk = I + Cea(j). + 3.j. + tijk, then

Ai= -Lj -itjj = ai(j). -ai,(j).

Here, clear decisions can be made concerning the differences between each level of the A factor in a specified level of the B factor.

With the appropriate model, it will not be necessary to lhange techniques or models as the author does on page 461 when discussing the appearance of a significant interaction between levels of in- struction A and methods of training B. As stated, "Because of the significant AB interaction, care must be taken in interpreting the main effects due to Factor B. The manner in which educational level is related to method of training is most readily shown by the profiles of the simple effects for the methods at each of the levels of educa- tion." At the same time, it should be noted that one could switch A and B and say that the manner in which education level is related to methods of training is most readily shown by the profiles of the simple effects for the levels of education at each of the levels of train- ing. In any case, as shown by Marascuilo and Levin [3], both models can be analyzed with ease, and in a clear and simple fashion with either simple pairwise or complex contrasts.

As a closing note, readers of this review should not view the pre- ceedinig criticisms as a condemnation of this book. On the contrary, the book is outstanding and is a must as a standard work in the library of all serious behavioral scientists and teachers of experi- mental design. It is a book of significant value for both reference and use. It is also an important book. It is often quoted and referenced, and for that reason what Winer says is important.

LEONARD A. MARASCUILO University of California, Berkeley

REFERENCES

[1] Dunn, O.J., "Multiple Comparisons Among Means," Journal of the American Statistical Association, 56 (1961), 52-64.

[2] Kirk, R.E., Experimental Design: Procedures for the Behavioral Sciences, Monterey, California: Brooks/Cole Publishing Company, 1971.

[3] Marascuilo, L.A. and Levin, J., "Appropriate Post Hoc Comparisons for Interaction and Nested Hypotheses in Analysis of Variance Designs: The Elimination of Type IV Errors," American Educational Research Journal, 7 (1970), 397-421.

[4] Miller, R.G., Jr., Simultaneous Statistical Inference, New York: MIcGraw-Hill Book Company, 1966.

[5] Petrinovich, L.F. and Hardyck, C.D., "Error Rates for Multiple Comparison Methods: Some Evidence Concerning the Frequency of Erroneous Con- clusions," Psychological Bulletin, 71 (1969), 43-54.

[6] Scheffe, H.A., The Analysis of Variance, New York: John Wiley and Sons, Inc., 1959.

Soviet Economic Statistics, Vladimir G. Treml and John P. Hardt (eds.). Durham, North Carolina: Duke University Press, 1972. x + 457 pp., $14.75.

This is one of the most useful books to come out of the Soviet field. Any economist doing research on the Soviet economy will want to have this book on his shelf for reference. The volume contains a collection of papers on Soviet statistics and on the Soviet statistical system by some of the most knowledgeable scholars in the Soviet field. The papers are concerned with the subject of statistics as data collection rather than with statistics as science. They discuss the

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Book Reviews 497

problerns of availability and reliability of statistical data both for internal planning purposes and for evaluating the performance of the Soviet economy from outside. And they provide an organized comprehensive survey of Soviet data on national income, industry, agriculture, labor arid wages, income and consumption, money and prices (but, alas, not on foreign trade or fiscal policy).

There are some common themes that run through many papers. One is the existence of major gaps in information caused by selective concealment of data by the Central Statistical Administration. The disparity between information collected by the Central Statistical Administration and that published is documented by Michael Kaser in "Publication of Soviet Statistics." His point acquires weight as each of the separate contributors comments on the paucity of pertinent dtata available from official sources in his own field. Abra- ham Becker writes that a manual of the Soviet national accounts has not been published in over thirty years. Morris Bornstein con- cludes that the Soviet government has released only a small portion of the price statistics that have been complied for official use. Eber- hard Schinke draws similar conclusions in the case of agricultural statistics. Writing on wages and income, Gertrude Schroeder com- plains, "From 1937 until 1965 the USSR was unique among indus- trialized countries in that its current official statistical publications contained not a single figure in the country's own currency about the wages of its work force" (p. 287). And Itaymond Powell writes,

.the most startling observation to be made about Soviet mone- tary statistics is how fragmentary they are. Indeed, it is doubtful whether any other area of the economy, not closely related to military or security affairs, has been treated by the authorities with equlal secretiveness" (p. 397).

While substantially more data is available on the Soviet economy now than ten years ago, the second theme that recurs in most of the papers is the continued low reliability of official Soviet series due to unclear methodology and a variety of technical deficiencies such as changing coverage and incomplete deflation of constant-price quantity indices. For that reason, the papers collected here serve as guides to the peculiarities of the Soviet series, and, in some cases, they provi(le independent alternative estimates of some series.

Several of the papers serve as guides to the statistics of an area: Gertrude Schroeder's study of wage series; Eberhard Schinke's detailing of various agricultural output and input definitions; Morris Bornstein's discussion of the methodology of Soviet price indices; Abraham Becker's survey of various Soviet income concepts in an input-output framework; and Murray Feshbach's impressive job of reconciling inconsistencies in Soviet official labor series by tracing changes in coverage.

A number of the papers also provide independent estimates of certain statistical series. Notable is Raymond Powell's compilation of Gosbank balance sheets for 1928-67. There are summaries of Abraham Becker's estimates of Soviet gross social product and national income, of Stanely Cohn's measures of growth of national income, and a detailing of U.S. Government methodology for the estimation of Soviet industrial production by Rush Greenslade. Marshall Goldman's survey of consumption provides some data from Soviet sources, including the average operating life of Soviet consumer durables (ten years for a washing machine, seven years for a wrist watch).

Balancing the criticism in the other chapters, Robert Campbell provides a somewhat more charitable evaluation of the Central Statistical Administration, arguing that shortcomings in the statis- tical systemn follow from conceptual flaws in the decision making system.

In sum, this is a consistently strong collection of papers.

JUDITH A. THORNTON University of Washington

Posterior Probabilities of Alternative Linear Models, F.B. Lempers. Rotterdam: Rotterdam University Press, 1971. 110 pp., Dfl 33.65.

This book is intended to acquaint the reader with the Bayesian approach t,o an old econometric problem-namely, the problem of comnparing or choosing among alternative linear models of a stochastic process. Its theme rests upon the idea that the relative importance of each model of a process under study can be measured by the model's posterior Drobability of being correct. In other words, the

posterior probability of a linear hypothesis takes over the role usually played by the R2 statistic in problems of this type.

The book is divided into six chapters. In the first three chapters, the author motivates, reviews and extends the theory of the Bayesian comparison procedure. For those readers who are unfamiliar with the Bayesian train of thought, Lempers also provides an excellent summary of the statistical concepts needed for the book's theoretical development.

In Chapter 3, Lempers derives and analyzes most of the expressions used to compute the posterior probabilities. It is especially gratifying to find that considerable attention has been given to the various ways of specifying the prior distribution of the models, and to the implications that each of these bears upon the computation of the posterior probabiltiies. This is, indeed, a critical aspect of the tech- nique; and the author is to be commended for bringing these issues into sharp focus.

The remainder of the book is devoted to applying the procedure to several different problems. In the first application, Lempers shows how the comparison of alternative error structures for a linear model can be cast into the model comparison framework. To me, these examples seem rather contrived. Why anyone would want, for in- stance, to use this approach to handle autocorrelated disturbances is a mystery, particularly since so many other more natural ap- proaches to the problem are available.

In Chapter 5, Lempers discusses the procedure's application to the important problem of comparing alternative linear models which have the same dependent variable, but different matrices of expla- natory variables. Here, he introduces a new two-phase sampling tech- nique which, according to him, is void of certain difficulties inherent in earlier approaches adopted by other authors. To what extent this new technique offers an advantage over the earlier ones still remains to be determined.

On the whole, the book is well-written. If it has any annoying features at all, it would be in the author's choice of notation, which many economists will undoubtedly find alien. But this is a minor criticism. The fact that the book brings to print for the first time a comprehensive introduction to a body of research, mostly unpub- lished, is sufficient to warrant its purchase by those interested in the topic.

KENNETH M. GAVER University of Rochester

An Introduction to Applied Probability and Random Processes,

John B. Thomas. New York: John Wiley and Sons, Inc., 1971. x + 338 pp., $13.95.

This is a well-written introduction to probability and random processes written primarily for engineering students at the senior or first year graduate level. It begins with an introductory chapter on such preliminary concepts as set theory, combinatorial analysis, and the relative frequency approach to defining probabilities. Chapter 2 is a short chapter on the axiomatic foundation of prob- ability theory. One important omission in this chapter is a proof (or statement) about the continuity of a probability measure, as this result is implicitly used many times in the text (for instance, in proving the right continuity of a distribution function). Chapters 3 and 4 deal with random variables and their distribution functions, and Chapter 5 is concerned with expectations and characteristic functions. Included in this chapter are sections on the Chernoff bound and on least mean squared error prediction. Chapter 6 is entitled "The Binomial, Poisson and Normal Distribution." Chapters 7 and 8 deal with, respectively, the multivariate normal distribution and transformations of random variables. Chapter 9, the last pure probability chapter, is concerned with the convergence of sequences of random variables. Such models of convergence as convergence in distribution, in probability, and almost sure convergence are dis- cussed (although the "equivalent statement" to almost sure con- vergence presented in (9.4-2) is not correct). The weak and strong laws of large numbers and the central limit theorem are also presented in this chapter.

Chapters 10, 11, and 12 introduce the subject matter of random processes. In Chapter 10, the idea of a point process is introduced and the Poisson process is considered. The author however defines this by such inexact expressions as the following: As the time interval

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