Maximization of the ratio of the quadratic forms V' AV/V' WV effected by simultaneous diagonalization of the pooled within-group, W, and pooled among-group, A, matrices of these environments using roundness statistics of quartz grains yields optimal multigroup discrimination. The discriminant scores projected onto the retained discriminant space are in dependent among group means as well as within each of these groups so th at the discriminant space can be partitioned by using simple Euclidean distance between the group-mean scores. It is concluded that the main discriminating variables are roundness-standard deviation and roundness-skewness, which affect about 99.37 percent of the total discrimination, whereas the second discriminant function, inclined at 75 degrees to the first, is statistically significant for classification and is largely loaded on roundness-mean.

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