To make multi-sample comparisons in comparative experimental studies, multiple comparison methods are generally used. The primary aim of these methods is to test hypotheses for pairwise equality of means, but it is often difficult to extract particular features from the data. An alternative approach is to use cluster analysis to group the sample means, and then to categorize the sample means as significantly different if and only if they belong to different groups. This approach does not involve hypothesis tests for pairwise equality of means and provides a useful interpretation of sample difference based on a graphical display. In many clustering methods for multi-sample comparisons, the normality of the observations is assumed. However, real-world observations rarely satisfy this strict assumption. We therefore propose the power-normal multi-samples cluster analysis (PMC) method that assumes the distribution of the observations is power-normal. Here, the power-normal distribution is defined as the distribution before the power-normal transformation (Box and Cox, 1964). We illustrate the usefulness of the PMC method for ordinary cluster analysis for multi-sample comparisons by analyzing an example and by evaluating a small-scale simulation.

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The purpose of this study was to examine whether several aspects of personality, as measured by the Temperament and Character Inventory (i.e., novelty seeking, harm avoidance, reward dependency, persistence, self-directedness, cooperation, and self-transcendence), were determined in part by family factors (i.e., genes and/or familial environments). Analyses were conducted on a sample of 358 Japanese families (1224 individuals) using structural equation modeling (SEM). In our analysis, we operationally assumed that families with fewer than four children had missing data as a means of integrating different patterns of families simultaneously using full information maximum-likelihood (FIML) estimates. Results showed the influences of parent-offspring relationships, spouse and sibling correlations, gender differences, and heritability. Both familial environment and genetic sources of resemblance were suggested for temperament and character. Finally, future tasks were discussed.

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Asymptotic expansions of the distributions of the sample polyserial correlation coefficients and associated parameter estimators are derived up to order O(1/N) when the estimators are obtained by full maximum likelihood. The asymptotic results are given under the assumption of multivariate normality for several observed continuous variables and a single unobserved variable underlining the corresponding ordered categorical variable. Asymptotic expansions of the distributions of the pivotal statistics studentized by using the estimate of the information matrix are obtained up to the order next beyond the conventional normal approximation. Numerical examples with simulations are shown in order to illustrate the accuracy of the asymptotic results in finite samples.

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