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Nonparametric analysis of a multi-group incompletely ranked item response data

Nonparametric procedures to analyze multi-group ranked item response data where each subject ranks only the top p items out of t items are considered. A Durbin-type statistic with small sample adjustment for testing interactions between the groups and the items is developed. For post-hoc analysis, various multiple comparison procedures to detect which interaction contrast is responsible for rejection are proposed. Another Durbin-type statistic is also discussed in establishing no overall preference for the items, assuming there is no group and item interaction. Several multiple comparison procedures for detecting the items that are responsible for rejection are employed. A small scale simulation study is conducted for investigating small sample properties of the proposed methods. A real data example is used to illustrate the methodology.