Non-parametric tests for small samples of categorized variables: A study

This paper presents a study on non-parametric tests to verify the similarity between two small samples of variables classified into multiple categories. The study shows that the only tests available for this situation are the chi-square and the exact tests. However, asymptotic tests, such as the chi-square, may not work well for small samples, leaving exact tests as the alternative. Nevertheless, if the number of classes increases, the implementation of these tests can become very difficult, in addition to requiring specific algorithms that may demand considerable computational effort. Therefore, as an alternative to the exact tests, a new test based on the difference between two uniform distributions is proposed. Computational assays are conducted to evaluate the performance of these three tests. Although non-parametric tests present numerous applications in various areas of knowledge, this study was motivated by the need to verify whether the business strategy adopted by a company is a determining factor for its competitiveness.