Nonparametric tests for the simple tree alternative on both the mean and variance

Two new nonparametric tests are proposed to test for differences in the location or scale between the control population and at least one level of the treatment population. The new tests are combinations of the Hollander Test for Extreme Reaction and the Fligner-Wolfe test. They are compared on the basis of power under a variety of underlying distributions with two existing tests proposed by Alsubie and Magel (2020a). It is found that at least of the new tests has higher powers than the existing tests when there are differences in location and scale between the control population and the combined treatment population.