A Note on the Test of Equality Between Two Bivariate Groups: An Analogue to Kolmogorov-Smirnov Test Statistic

Abstract

This study developed parametric and nonparametric test statistic, an analogue to Kolmogorov-Smirnov two sample test, for the testing of the equality between bivariate groups. We also established the performance of the developed test statistic in achieving accurate separation and classification. The concept layout model, which is based on Cartesian interaction between discrete random variables (rv's) xₘ and yₖ arranged in rows and columns respectively for m, k ∈ ℕ, has a behavioural pattern with bivariate cumulative distribution function (cdf) F(x,y). We assumed that the content within the matrix m × k frame followed log-logistic distribution (LLD) and is distribution free. The test statistic t' is the absolute difference between two bivariate cdf, |F₁(x,y) - F₂(x,y)|, under the two distribution scenarios. We then optimize the test statistic which is a function of relationship matrices from the two groups and established its significance at optimal parameter value, from a newly introduced multivariate test significance, before investigating its performance analysis. This analysis enhances the understanding of the profiled content in the two groups, whether they are from the same group or not. In addition, we established the discrimination accuracy of the relationship matrix model towards perfect classification (diagnostic). Application to the discrimination and classification of Bumpus, cancer and mode of delivery data were established.