Comparing mixed data

Testing the equality of two populations based on independent samples, the two-sample problem, is a classic one in Statistics. Most existing procedures assume that the entire data are categorical or numerical. The mixed data case (some components of the vector to be compared are categorical and others numerical) has received less attention in the statistical literature. Here, we propose and study a new test for comparing mixed data, which is consistent against fixed alternatives. Resampling schemes are studied to consistently approximate the null distribution of the test statistic. Moreover, it is demonstrated that their practical implementation is cheap. The performance of the test in finite samples is analysed via simulation. The proposal is applied to two real datasets.