Migraciones Internas: Teoria, Metodo y Factores Sociologicos. by Juan C. Elizaga; John J.Macisco,Review by: George PoveyJournal of the American Statistical Association, Vol. 74, No. 365 (Mar., 1979), pp. 253-254Published by: American Statistical AssociationStable URL: http://www.jstor.org/stable/2286780 .

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Book Reviews 253

Statistical Reasoning in Sociology, 3rd Edition. J.H. Mueller, K.F. Schuessler, and H.L. Costner. Boston: Houghton-Mifflin Company, 1977. xvi + 544 pp. $13.95.

A revision and enlargement of a well-known text, Statistical Reasoning is designed for a one- or two-semester course for sociology undergraduates. There are no prerequisites. Some algebraic manipu- lations are presented but are optional. The reader usually is led step by step through the substitutions necessary to employ stan- dard formulas. But the "volume is intended to foster a statistical conception of social knowledge as well as to guide the student toward proficiency in statistical manipulations." To this end, a leisurely exposition features historical and etymological notes on the development of statistics, the statement of commonsense rationales for the procedures illustrated, and instructive discussions of the substantive implications of numerical examples. Many of these examples use published sociological data; where contrived data appear, this fact is so stated and the data are usually designed to simulate published studies.

The first 10 of the 15 chapters expound descriptive statistics, so that averages, variation, the normal curve, association of quali- tative variables, correlation, partial correlation, bivariate and multiple regression, and path analysis are presented before proba- bility, sampling, and statistical inference are introduced. This gives the work an old-fashioned quality, as do the priority given to the concept of correlation over regression, the questionable emphasis on measures of association for contingency tables, and the quotation of S.S. Stevens's obsolete and stultifying classification of scales of measurement. I believe a "statistical conception of social knowledge" requires greater emphasis on the stochastic component of models used to analyze quantitative data and on statistical inference as a pervasive and inescapable problem. In this work, the binomial distribution gets short shrift, the Central Limit Theorem is not cited by name, and it is claimed that "de- scriptive statistics have a validity and importance in their own right." This is not to fault the chapters on estimation and hy- pothesis testing, which contain standard material, but to protest their subordination to the earlier topics.

The revision makes a serious effort to respond to the trends of the discipline of sociology. This accounts for the inclusion of the section on path analysis and a treatment of the three-way contingency table. Comments on the sociological import of exam- ples are judicious and informative. Technical errors are infrequent or are innocuous at the level where the book will be used, although one regrets the lapse that allowed the hypothesis of no three-way interaction to be stated in terms of the sample counts. Altogether, this book makes a solid case for the statistical method in social inquiry, a remark that does not apply to most of the numerous works on introductory social statistics that have come along in recent years.

OTIS DUDLEY DUNCAN University of Arizona

Applied Statistics in Atmospheric Science. Part A: Frequencies and Curve Fitting.

0. Essenwanger. Amsterdam: Elsevier Scientific Publishing Company, 1976. xi + 412 pp. $53.95.

This book should prove easy to read for those who have a good knowledge of the material usually covered in junior-senior level mathematical statistics courses, a classical course in matrix theory, and a course in advanced calculus for engineers. The tone and style of the book are those of a good advanced engineering text. The theme and purpose are to present various applications of statistical methods and theory to data analysis problems occurring in meteorology.

The material is presented precisely enough and the references are complete. The examples are all based on meteorological data and are on the whole interesting. It is a good source of data for those teaching basic statistical methods courses. Interval scale data abound and real life examples involving these data are not contrived and exhibit the problems associated with real data.

Two attractive features of the book are the selection of topics not usually found in statistics methods books and the bibliography.

The references give the statistician a brief historical list of statis- tical applications involving meteorological data. The unusual list of topics reflects the need of the meteorologist for data analyst techniques not usually encountered by most statisticians in academia.

The book is divided into four chapters, two of which are very long. In Chapter 1, the author introduces topics which include the mathematics of moments, expectations, significance, and con- fidence; the central limit theorem; and the concept of "persistence." The second chapter is a series of definitions and discussions of the properties of a large number of distribution functions. Among these are the U-distribution, the log-normal, the logistic, and the three- and four-parameter Wiebull. Important variations include the truncated distributions and mixtures of normal distributions. The material on mixed distributions is indeed thorough and the important aspects of existing methodology are summarized. This is the best part of the book.

The third chapter is entitled "Curve Fitting," but includes factor analysis, the mathematics of transformations, and a little quality control. The chapter also includes spectral analysis, Bessel functions, orthogonal polynomials, and analysis of time series.

The fourth chapter includes the mathematics of matrices, de- terminants and eigenvalues. It emphasizes computational aspects and is tedious to read.

Briefly, the book has real value as a reference book for statis- ticians and is an excellent complement to the Handbook of Statis- tical Methods in Meteorology by C.E.P. Brooks and N. Carruthers (1953). The latter includes an excellent bibliography of earlier references, some of which are not contained in the book of Essen- wanger. These two books would be an excellent and nearly com- plete reference set of statistical methodology in meteorology.

One modern topic, which unfortunately was not covered, is the statistics and the design of experiments involved in weather modi- fication and inadvertent climate change due to human intervention and pollutants. These topics are of such current importance that the statistical literature associated with these topics would have significantly increased the value of the book. The quoted price of the book is over fifty dollars, which is exceedingly overpriced for the statistics, but could be worth it to a researcher needing the bibliography.

PATRICK L. ODELL University of Texas at Dallas

Migraciones Internas: Teoria, Metodo y Factores Sociologicos.

Juan C. Elizaga and John J. Macisco, Jr. Santiago, Chile: Centro Latino-Americano de Demografia, 1975. 615 pp. $10.00.

This is a collection, in Spanish, of 26 papers, most of which were puiblished or delivered in the 1960's, 22 of them originally in English and the rest in Spanish.

The material is grouped in six sections titled: Concepts, Defini- tions and Theory; Methodology; Influential Factors in Migration; Selective and Differential Migrations; Consequences of Adaptation; and Special Approaches.

The first section is concerned with the clarification of notions fundamental to the study of migration, such as the definition of migration, migratory interval, migratory current, and turnover. It considers the sources of data (censuses, surveys, registration) and forces responsible for migration (push-pull theory, inertia). Classes of migration are identified (primitive, forced, free, massive), and assimilation is discussed in terms of adaptation, participation, and acculturation.

The section on methodology considers the problems of data collection and analysis, complicated in the study of internal migra- tion with difficulties in definition, sampling, and interpretation.

Concerning influential factors, a series of papers considers such forces as regional differences, ecologic forces, modernization, family size, and upward mobility.

"Selective and Differential Migration" deals with such deter- minants as completed primary education, occupation, and fertility. "Consequences of Adaptation" considers community of origin, integration, upward mobility and acculturation. "Special Ap- proaches" is concerned with more theoretical considerations, such as the principle of least effort, demographic gravitation, and dimensional analysis theory.

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254 Journal of the American Statistical Association, March 1979

For those who have followed the English language literature concerning migration, this book offers little new information. For Spanish readers, and particularly for those who teach Spanish- reading students, it constitutes a useful collection of material which will provide rapid access to the world literature in this field.

GEORGE POVEY University of British Columbia

Techniques de la Description Statistique. L. Lebart, A. Morineau, and N. Tabard. Paris: Bordas, Dunod, Gauthier-Villars, 1977. viii + 351 pp. $25.20.

Within the last 15 years there has been a great upsurge of interest and activity among French statisticians in the field of data analysis. Much work has been done to develop suitable multivariate tech- niques and computer programs to handle great masses of data, such as often arise in large-scale socioeconomic surveys. For such data, a priori models are often hard to formulate, and the appro- priate models are often hidden by the very profusion of the data.

The first two authors are professors at the Statistical Institute of the Universities of Paris, and all three are affiliated with the CNRS and/or other public research organizations doing large-scale socioeconomic surveys. The first three chapters present the basic techniques and have formed the basis, several times revised, of a course for students in applied statistics at the Institute. The book as a whole presupposes a knowledge of linear algebra and statistics. Calculus is invoked only once, and hard analysis occurs only in certain sections of Chapter V, which can be skipped without loss of understanding of the rest of the book. The format for the chapters usually is first to explain the methodology, then to discuss an application in some detail, and finally to document and present suitable computer programs in Fortran. There are 7 principal programs, 75 subprograms in all, taking up 75 pages.

Chapter I deals with principal components analysis. Given n individuals and p characters, they derive not only a principal components analysis of characters in RP but also such an analysis of individuals in Rn. They urge that graphs of both analyses be superimposed to discover various relationships. However, this must be done with caution.

One section of Chapter III deals with one method of non- hierarchical clustering. Aside from the above topics, almost the entire book concerns itself with correspondence analysis and its multiple-way generalization. "Correspondence analysis" is a new name for an old but neglected technique going back to 1935. It trans- lates Professor J.-P. Benzecri's term "l'analyse des correspondances."

Consider a two-way contingency table with p rows and q columns. Assign scores to the rows and columns of the table. Choose the two sets of scores so that the correlation between rows and columns is maximized. This gives rise to a typical eigen-analysis. To each eigenvalue Pa with 0 < pa < 1, there correspond two eigenvectors of scores with suitable norms, one with p components, the other with q. The authors achieve the same vectors of scores by first defining a chi-squared type distance function between rows (columns) of the table and then finding the direction in the column space (row space) in which the sum of squares of the rojections of such distances of the first space onto the second space is maximized. They show by examples that much can be learned about the struc- ture of the data by superimposing on one graph the factors of the row space and the factors of the column space. Correspondence analysis can also be applied to certain other rectangular arrays of nonnegative numbers besides actual frequencies.

Chapter II takes up the basic theory of correspondence analysis, while Chapter III introduces Hotelling's canonical correlation analysis and Fisher's linear discriminant analysis, not primarily for their own sakes but rather to place correspondence analysis in its proper context. Let Zi (n X p) denote the incidence matrix of the n individuals with the p rows of the contingency table: the jth element of the ith row of Z, is one if the ith individual belongs to the jth row category of the contingency table, and is zero otherwise. Similarly, let Z2 denote the incidence matrix of the individuals with the columns of the contingency table. Then the contingency table is Z1,Z2. Discriminant analysis is a special type of canonical analysis in which the data matrix for one of the two sets of variables is an incidence matrix. Correspondence anal- ysis can be set up as a double discriminant analysis in which the

data matrices for the two sets of variables are the row and column incidence matrices Z1 and Z2, respectively.

R.A. Fisher gave an example of correspondence analysis in the last section of a 1940 paper on discriminant functions. In 1942 Khint Maung, then also at Galton Laboratory, applied correspond- ence analysis to a large subset of data from J.F. Tocher's pig- mentation survey of eye and hair color of Scottish school children. Meanwhile in 1941 Louis Guttman derived correspondence analysis as a method of constructing suitable scales for categorical data. However, they were all anticipated by a paper which went almost unnoticed for many years. H.O. Hirschfeld, a youthful emigre from Germany newly arrived in England, published a short paper in 1935 which derived almost all of the mathematical theory. This was within months of Hotelling's first short paper on canonical correlation in an American psychology journal and the year before Fisher's first paper on discriminant analysis. Hirschfeld went on to achieve an international reputation under the anglicized form of his name.

Chapter IV introduces multiple correspondence analysis for Q-way contingency tables. Kettenring (1971) lists five ways of generalizing canonical correlation analysis for when there are more than two sets of variables. Thus, here in the analogous problem, the authors have several options. They first consider the two-way case and show that its analysis is equivalent to the eigen-analysis of Z'Z, where Z = [Z1, Z2] in the earlier notation above. The eigenvectors for the two ways are subvectors of the eigenvectors of Z'Z and are constrained to be suitably normed. In the general case, take Z = [Z1, ..., ZQ]. An eigenvector of Z'Z now consists of Q subvectors, all constrained to be suitably normed. The re- sulting analysis is analogous to the maximum sum of correlations method in Kettenring's list of generalizations of canonical analysis. In a typical application, n individuals are asked Q questions which have multiple choice answers. Corresponding to any eigenvalue, the score of an individual is proportional to the average of the scores of all of the answers he gave, and the score for a particular answer is proportional to the average of the scores of all individuals who gave that answer.

Chapter V considers various iterative algorithms to shorten computations and cut down on the demands on the computer. Some of the analysis of rates of convergence demands a higher level of mathematics than the rest of the book. Chapter VI dis- cusses the validity of results. The most immediately useful part here is a study of what percentage of their sum the successive eigenvalues of correspondence analysis can be expected to be. Charts give the upper 0.05 points of such proportions of total variability under the null hypothesis for the first five eigenvalues and quite a range of sizes of contingency tables.

Chapter VII is devoted to a careful discussion in some depth of three large socioeconomic surveys. Much supplementary infor- mation is easily incorporated into the analysis. The examples are one of the best features of the book and in the book as a whole take up about 65 pages.

Every reviewer is expected to find some faults. The number of misprints is happily relatively small. At the bottom of page 105, the Mahalanobis squared distance is not X = c'T-'c, but rather is proportional to X/(1 - X) = c'D-Tc. The second example of Chapter VII uses a multiple correspondence analysis to get a factor based on social status and education to predict personal income. Figure 6 on pages 272 to 273 shows professional people and highly educated people at the left, while unskilled workers and poorly educated people are at the right. Thus the first factor is negatively correlated with personal income. Surely it would have been just as easy and less confusing to the reader to have changed the sign of the first factor beforehand. (The same criticism applies to the first example of Chapter VII.) Figure 8a on page 278 shows the distributions of the factor predicting income and of the logarithm of income. But now, without any warning, the data are for 1,773 families instead of 1,681, the range of the predictive factor is much narrower, and Figure 8b on page 279 shows that it now has a posi- tive correlation with income. These are matters which can easily be set right, but which are vexing for the reader.

To sum up: this book presents methods for bringing into more tractable form large arrays of data, especially when they are divided categorically in two or more ways. The level of mathematics pre- supposed is relatively modest. The presentation is generally quite clear. Two of the best features of the book are the extended dis- cussion of real examples from large socioeconomic surveys and

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