Classification by Multivariate Analysis with Objectives of Minimizing Risk, Minimizing Maximum Risk, and Minimizing Probability of Misclassification

Johnson, M. Clemens

doi:10.1080/00220973.1955.11010512

Cited by 4 publications

(2 citation statements)

References 8 publications

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“…Tests of the effectiveness of the LDF in classifying individuals correctly were presented by Lubin (7). For complete and comprehensive discussions of the techniques employed in this study the reader is referred to Christensen (2), Lockman (6), and Johnson (5).…”

Section: The School Studymentioning

confidence: 99%

The use of multivariate statistical analysis of Minnesota Multiphasic Personality Inventory scores in the classification of delinquent and nondelinquent high school boys.

Rempel¹

1958

Journal of Consulting Psychology

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The research worker in psychology and education is frequently confronted with the problem of analyzing differences between two or more groups of individuals with respect to several variables. The problem of differentiating certain selected groups in terms of MMPI scores, for instance, is a good case in point. However, the kinds of statistical procedures commonly used may be subject to criticism on several grounds. Briefly, the several empirical methods of approach which have been developed lack the rigidity of a strictly mathematical model, while such univariate procedures as the t test or analysis of variance, when applied to separate keys of the MMPI, fail to take into account the amount of correlation that exists between scores on these keys. These procedures, in short, have failed to provide methods for obtaining mathematically rigid statements of profile or pattern differences.It is one of the purposes of this paper to provide an illustration of the application of more recently developed statistical procedures, namely the generalized distance function (D 2 ) and Fisher's discriminant function (LDF) to the solution of problems involving the comparison of MMPI profiles. These techniques have been employed to find answers to the following questions:1. To what extent can groups of nondelinquent and delinquent-prone ninth-grade high school boys be differentiated in terms of

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Section: The School Studymentioning

confidence: 99%

The use of multivariate statistical analysis of Minnesota Multiphasic Personality Inventory scores in the classification of delinquent and nondelinquent high school boys.

Rempel¹

1958

Journal of Consulting Psychology

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show abstract

“…This type of analysis serves as the basis for building models aimed at predicting group membership as well as for determining the relative importance of various characteristics (geographic, economic, socio/psychologic, etc.) as they contribute to the accuracy of the prediction (15) .…”

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confidence: 99%

The Relative Classificatory Ability of the Linear Discriminant Function and the Bayesian Taxonomic Procedure

Pohl

1974

The Journal of Experimental Education

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The purpose of this study was to compare the relative classificatory ability of the Linear Discriminant Function (LDF) and the Bayesian Taxonomic Procedure (BTP) when these techniques are applied to multivariate normal and nonnormal data with differing degrees of overlap in the distributions of the predictor variables. The findings and test results led to the conclusion that the LDF is an extremely robust classificatory technique. In general, the LDF should be used in solving discriminatory problems involving continuous univariate data. Only when the data are extremely skewed should a researcher consider using the BTP in preference to the LDF.DISCRIMINANT ANALYSIS is widely used in educational research. This type of analysis serves as the basis for building models aimed at predicting group membership as well as for determining the relative importance of various characteristics (geographic, economic, socio/psychologic, etc.) as they contribute to the accuracy of the prediction (15) .The most popular type of discriminant analysis is the 2-group Linear Discriminant Function (LDF). After an extensive review of educational and psychological research, Phillip stated in 1972 (25) that the-LDF was often used when its underlying assumption of multivariate normality of the predictor variables was violated. Phillip went on to outline an alternate nonparametric approach which he labeled the Bayesian Taxonomic Procedure (BTP); and subsequently he applied both methods to the same set of multivariate nonnormal data. Phillip reported no significant difference in the classificatory ability of the two techniques, but hypothesized that the results were due to the uniqueness of his data and suggested that, under certain conditions, one of the techniques should be a better predictor than the other. THE PROBLEMThe general problem investigated by the present research was the detection of significant differences in the performance of the LDF and the BTP as classification tools under varying conditions of multivariate nonnormality. RELATED RESEARCHThe Linear Discriminant Function was developed in 1935 by R.A. Fisher (1, 8). Since then it has become a standard classificatory technique in all disciplines. The LDF was popularized for educational researchers by Rulon (28) , Tiedeman (32), and Tatsuoka (31) and Chen (4).As is true for any statistical technique, the LDF is based on certain assumptions. The two basic assumptions of the LDF are 1. ) that the predictor variables used to determine the probable group membership of an object be multivariate normally distributed, and 2. ) that the predictor variables have equal or near equal variances and that the covariances among predictor variables be similar from group to group (6:ll6, 13:179, 17:166, 21). While these assumptions seemed to be fairly well met in earlier anthropological and biological studies, the same cannot be said for the more recent applications of the LDF in educational-related situations (26) .While critics have repeatedly pointed out violations of the assumptions of the LD F...

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A Bibliography of Discriminant Analysis

Cacoullos

Styan

1973

Discriminant Analysis and Applications

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Classification by Multivariate Analysis with Objectives of Minimizing Risk, Minimizing Maximum Risk, and Minimizing Probability of Misclassification

Cited by 4 publications

References 8 publications

The use of multivariate statistical analysis of Minnesota Multiphasic Personality Inventory scores in the classification of delinquent and nondelinquent high school boys.

The use of multivariate statistical analysis of Minnesota Multiphasic Personality Inventory scores in the classification of delinquent and nondelinquent high school boys.

The Relative Classificatory Ability of the Linear Discriminant Function and the Bayesian Taxonomic Procedure

A Bibliography of Discriminant Analysis

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