Small Sample Validation of Discriminant Analysis of Motor Proficiency

Abstract

Discriminant analysis has been used to describe the physiology of good and elite distance runners, to indicate the personality and body-image differences of adult females high and low in body fat and to examine movement characteristics of mildly mentally retarded and nonhandicapped children. To evaluate discriminative power, studies have used the resubstitution method presented in many computer packages to estimate percent of correct classification. That method yields optimistically biased estimates of correct classification. This study describes the use of a less biased method, called the jackknife, and contrasts the classification results obtained with those from the resubstitution method. Gross and fine motor proficiency data, obtained from four ( n = 67) intact physical education classes (Grade 1, kindergarten, mildly mentally retarded, and moderately mentally retarded), were analyzed and classified by the resubstitution method. The over-all correct classification was 74.6%. Using the jackknife method, which is particularly suitable for small samples, the corresponding percentage was 59.7%. This more realistic jackknife estimate highlights differences among the four classes, showing that the over-all reduction in percentage correct classification was especially noticeable with the two mentally retarded classes.