Commentary on the Use of Multivariate Statistical Methods in Ant H Ropomet Ric Research the Other Side of the Story

A critical review of the increasing emphasis being placed on the use of multivariate statistical methods in anthropometric research is given. Particular attention is paid to multivariate techniques for testing hypotheses concerning mean vectors, principal components analysis and the use of discriminant functions, but some more general comments about the proper role of statistics in research are included. It is argued that multivariate techniques often do not allow the effective description and communication of the informational content of a body of data and that much additional research — both from the standpoint of theory and from the standpoint of practice — must be done before multivariate analysis can fulfill the promise it holds for the physical anthropologist.

[1]  H. Linhart.  Techniques for discriminant analysis with discrete variables , 1959 .

[2]  C. R. Rao,et al.  The Utilization of Multiple Measurements in Problems of Biological Classification , 1948 .

[3]  H. Hotelling.  The Generalization of Student’s Ratio , 1931 .

[4]  T. W. Anderson.  An Introduction to Multivariate Statistical Analysis , 1959 .

[5]  R. Gnanadesikan,et al.  A Probability Plotting Procedure for General Analysis of Variance , 1970 .

[6]  M. C. Hamilton,et al.  An analysis into age changes of the human dental arch by a multivariate technique. , 1970, American journal of physical anthropology.

[7]  P. Lachenbruch.  An almost unbiased method of obtaining confidence intervals for the probability of misclassification in discriminant analysis. , 1967, Biometrics.

[8]  C. Oxnard.  Primate evolution--a method of investigation. , 1968, American journal of physical anthropology.

[9]  G. P. Rightmire,et al.  Bushman, Hottentot and South African Negro crania studies by distance and discrimination. , 1970, American journal of physical anthropology.

[10]  L. Penrose.  Distance, size and shape. , 1954, Annals of eugenics.

[11]  O. J. Dunn,et al.  Probabilities of Correct Classification in Discriminant Analysis , 1966 .

[12]  J. Tukey.  The Future of Data Analysis , 1962 .

[13]  C. A. Smith.  Some examples of discrimination. , 1947, Annals of eugenics.

[14]  Paul Horst,et al.  Factor analysis of data matrices , 1965 .

[15]  Calyampudi R. Rao.  SOME PROBLEMS INVOLVING LINEAR HYPOTHESES IN MULTIVARIATE ANALYSIS , 1959 .

[16]  Seymour Geisser,et al.  Multivariate Analysis of Variance for a Special Covariance Case , 1963 .

[17]  M. B. Danford,et al.  ON THE ANALYSIS OF REPEATED-MEASUREMENTS EXPERIMENTS1 , 1960 .

[18]  E. H. Ashton,et al.  The descriptive use of discriminant functions in physical anthropology , 1957, Proceedings of the Royal Society of London. Series B - Biological Sciences.

[19]  S. Geisser,et al.  On methods in the analysis of profile data , 1959 .

[20]  W. Howells.  The use of multivariate techniques in the study of skeletal populations. , 1969, American journal of physical anthropology.

[21]  J. Bronowski,et al.  Statistical Methods in Anthropology , 1951, Nature.

[22]  Gould Al.  A Regression Technique for Angular Variates , 1969 .

[23]  G. P. Rightmire,et al.  Iron age skulls from Southern Africa re-assessed by multiple discriminant analysis. , 1970, American journal of physical anthropology.

[24]  H. O. Lancaster.  ZERO CORRELATION AND INDEPENDENCE , 1959 .

[25]  M. Tarter,et al.  Co-ordinate transformations to normality and the power of normal tests for independence , 1969 .

[26]  Chien-Pai Han,et al.  A note on discrimination in the case of unequal covariance matrices , 1968 .

[27]  A. Dempster.  Elements of Continuous Multivariate Analysis , 1969 .

[28]  R. Gnanadesikan,et al.  GRAPHICAL ANALYSIS OF MULTI-RESPONSE EXPERIMENTAL DATA USING ORDERED DISTANCES. , 1961, Proceedings of the National Academy of Sciences of the United States of America.

[29]  William G. Cochran,et al.  Comparison of two methods of handling covariates in discriminatory analysis , 1964 .

[30]  R. C. Elston,et al.  Estimation of Time-Response Curves and Their Confidence Bands , 1962 .

[31]  A. Gould.  A regression technique for angular variates. , 1969, Biometrics.

[32]  P. Lachenbruch.  Discriminant Analysis When the Initial Samples Are Misclassified , 1966 .

[33]  Calyampudi R. Rao,et al.  Tests of significance in multivariate analysis. , 1948, Biometrika.

[34]  M. Hills,et al.  Discrimination and Allocation with Discrete Data , 1967 .

[35]  T. W. Anderson.  Classification by multivariate analysis , 1951 .

[36]  S. P. VASWANI,et al.  A Pitfall in Correlation Theory , 1947, Nature.

[37]  Karl Pearson F.R.S..  LIII. On lines and planes of closest fit to systems of points in space , 1901 .

[38]  W. Hirschfeld.  A comparison of regression with time series-exponential smoothing predictions of craniofacial growth. , 1970, Growth.

[39]  E. S. Gilbert,et al.  The effect of unequal variance-covariance matrices on Fisher's linear discriminant function. , 1969, Biometrics.

[40]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1951 .

[41]  M. Healy.  Descriptive uses of discriminant functions , 1965 .

[42]  R. Fisher.  THE STATISTICAL UTILIZATION OF MULTIPLE MEASUREMENTS , 1938 .

[43]  N. L. Johnson,et al.  Multivariate Analysis , 1958, Nature.

[44]  W. G. Cochran,et al.  Discriminant Functions with Covariance , 1948 .

[45]  Olive Jean Dunn,et al.  The Robustness of Hotelling's T 2 , 1967 .

[46]  T. Kurczynski,et al.  Generalized Distance and Discrete Variables , 1970 .

[47]  Charles J. Kowalski,et al.  The Performance of Some Rough Tests for Bivariate Normality Before and After Coordinate Transformations to Normality , 1970 .

[48]  W. Howells.  The cranial vault: factors of size and shape. , 1957, American journal of physical anthropology.

[49]  A. Linder.  Trennverfahren bei qualitativen Merkmalen , 1963 .

[50]  C. Harris.  Problems in measuring change , 1965 .

[51]  Karl Pearson,et al.  ON THE COEFFICIENT OF RACIAL LIKENESS , 1926 .

[52]  J. Healy.  Rao''s paradox concerning multivariate tests of significance , 1969 .

[53]  R. Gnanadesikan,et al.  Graphical Methods for Internal Comparisons in Multiresponse Experiments , 1964 .

[54]  Robert R. Sokal,et al.  Distance as a Measure of Taxonomic Similarity , 1961 .

[55]  M. Kendall.  A course in multivariate analysis , 1958 .

[56]  G. Box.  NON-NORMALITY AND TESTS ON VARIANCES , 1953 .

[57]  J. G. Skellam,et al.  Multivariate Statistical Analysis for Biologists , 1965 .

[58]  C. Radhakrishna Rao,et al.  Tests with discriminant functions in multivariate analysis , 1946 .

[59]  E. S. Gilbert.  On Discrimination Using Qualitative Variables , 1968 .

[60]  H. Harman.  Modern factor analysis , 1961 .

[61]  S. Geisser,et al.  An Extension of Box's Results on the Use of the $F$ Distribution in Multivariate Analysis , 1958 .

[62]  W. Howells,et al.  Criteria for selection of osteometric dimensions. , 1969, American journal of physical anthropology.

[63]  J. Mosimann.  Size Allometry: Size and Shape Variables with Characterizations of the Lognormal and Generalized Gamma Distributions , 1970 .

[64]  R. Potthoff,et al.  A generalized multivariate analysis of variance model useful especially for growth curve problems , 1964 .

[65]  G. M. Tallis.  Some extensions of discriminant function analysis , 1970 .

[66]  J. Elashoff,et al.  On the choice of variables in classification problems with dichotomous variables. , 1967, Biometrika.

[67]  William J. Schull,et al.  On the robustness of the T02 test in multivariate analysis of variance when variance-covariance matrices are not equal , 1964 .

[68]  Elisa T. Lee,et al.  Graphical techniques for internal comparisons amongst equal degree of freedom groupings in multiresponse experiments , 1970 .

[69]  H. Hotelling.  Analysis of a complex of statistical variables into principal components. , 1933 .

[70]  Hirschfeld Wj.  A comparison of regression with time series-exponential smoothing predictions of craniofacial growth. , 1970 .

[71]  M. R. Mickey,et al.  Estimation of Error Rates in Discriminant Analysis , 1968 .

[72]  T. P. Burnaby.  Growth-Invariant Discriminant Functions and Generalized Distances , 1966 .

[73]  M. M. Barnard.  THE SECULAR VARIATIONS OF SKULL CHARACTERS IN FOUR SERIES OF EGYPTIAN SKULLS , 1935 .