Introducing a cross-variance concept and its application

Abstract

Cross-variance is a variance concept between two samples, where it is defined by using the second sample average to compute the first sample variance and reversely. In this paper we introduce a cross-variance, a new statistical test, and a new probability statistics distribution based on the cross-variance concept. The concept leads to an alternative test for the equality of means of two normal populations. A simulation study is conducted to show the performance of the new proposed test in comparison to the t test when the variances are equal.