We propose a nonparametric criterion to test the hypothesis that the j-th largest roots of two populations are equal, in Section 2. This testing procedure is distribution free, and in Section 3 and 4 we show that it is reliable when the sample sizes increase and the population latent roots are separate, under the multivariate normal distribution. We suggest which sample sizes are necessary to rely on the above test.
Elderly cases offered Takizawa method as one of the rehabilitation techniques were evaluated statistically. Initially we clarified the characteristics of the total FIM (Functional Independent Measure) score and the relation between the number of improved items and of worsened ones. Furthermore, we investigated the multidimensional relevance of 18 FIM items to explain the characteristics of improvement or aggravation clear, and obtained four factors by factor analysis and classified into six groups by cluster analysis, and then extracted some specific cases. Finally, we statistically verified the effect about the 18 FIM evaluation items using the t-test, a sign test and the Wilcoxon signed rank sum test, and several items in the FIM were turned out to be significantly effective.
Two-sample problem is considered to test the equality of the intermediate latent roots of two covariance matrices assuming non-normal distributions.The nonparametric method known as the Moses rank-like test is proposed for principal component scores(PC-scores), and its efficiency is compared with the Ansari-Bradley test and Ftest by Monte Carlo experiments. This testing procedure turns out to be very useful when the population latent roots are sufficiently distinct and the sample sizes increase.
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