Hierarchical Cluster Analysis for Multi-Sample Comparisons Based on the Power-Normal Distribution

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.