Application of Multiple Testing Procedures Based on Ordered p-Values to Separate Homogenous Groups of Means

Multiple testing procedures based on 'ordered p-values' may be found an interesting tool for simultaneous testing of more than one hypothesis at a time. Discussed methods are applicable to a broad spectrum of statistical problems since their requirements for statistical assumption are considerably less restricted than in case of classical procedures (only dependency among test statistics should be controlled). The analysis is distilled down to a collection of p-values or adjusted p-values. Depending on approach to the control of Type I error for the family of inferences these methods may be categorized into two major groups: FWE (Family-Wise Error Rate) and FDR (False Discovery Rate) procedures. In this paper the selected procedures - Bonferroni, Bonferroni-Sidak, Holm, Holm-Sidak and Hochberg-Benjamini are discussed and applied to the pair-wise comparison of means. As an example an average monthly expenditure on food and tobacco products in six groups of households is considered according to regions of Poland and search for homogenous groups of households. On the basis of these empirical examples the authoress evaluates classical procedures thus illustrating typical problems faced by researchers that use classical methods as implemented in STATISTICA software and compares them to multiple testing procedures based on 'p-values' in balanced one-way analysis of variance.