Test For Two-sample Location Problem Research Articles

Permutation Tests for Two-sample Location Problem Under Extreme Ranked Set Sampling

In this paper, permutation test of comparing two-independent samples is investigated in the context of extreme ranked set sampling (ERSS). Three test statistics are proposed. The statistical power of these new test statistics are evaluated numerically. The results are compared with the statistical power of the classical independent two-sample $t$-test, Mann-Whitney $U$ test, and the usual two-sample permutation test under simple random sampling (SRS). In addition, the method of computing a confidence interval for the two-sample permutation problem under ERSS is explained. The performance of this method is compared with the intervals obtained by SRS and Mann-Whitney procedures in terms of empirical coverage probability and expected length. The comparison shows that the proposed statistics outperform their counterparts. Finally, the application of the proposed statistics is illustrated using a real life example.

Adaptive Group-combined P-values Test for Two-sample Location Problem with Applications to Microarray Data

The purpose of this article is to propose a test for two-sample location problem in high-dimensional data. In general highdimensional case, the data dimension can be much larger than the sample size and the underlying distribution may be far from normal. Existing tests requiring explicit relationship between the data dimension and sample size or designed for multivariate normal distributions may lose power significantly and even yield type I error rates strayed from nominal levels. To overcome this issue, we propose an adaptive group p-values combination test which is robust against both high dimensionality and normality. Simulation studies show that the proposed test controls type I error rates correctly and outperforms some existing tests in most situations. An Ageing Human Brain Microarray data are used to further exemplify the method.

A new nonparametric scheme for simultaneous monitoring of bivariate processes and its application in monitoring service quality

We consider a new nonparametric control chart for monitoring bivariate processes based on a distance measure. This statistic was originally introduced in context of a strictly nonparametric bivariate test for two-sample location problem and was shown to be more powerful than several competitors including Hotelling’s T2 in a large number of situations. Our proposed scheme is useful in simultaneous monitoring of the event frequency and magnitude, call centre response times and its service quality or time between the two major earthquakes and the magnitude in Richter scale, etc. Unlike most of the traditional approaches for simultaneous monitoring of event frequency and magnitude that consider event frequency and magnitude are independent, our proposed chart takes into account the dependence between two variables. We consider that the frequencies are large enough and the two variables are continuous, but we make no assumption about the mathematical form of the process distribution. We consider the availability of a Phase-I data. We discuss the design and implementation procedure in details. We conduct some Monte-Carlo simulation to examine various properties of the proposed scheme. We also illustrate our proposed scheme with a real data.

A new test for two-sample location problem based on empirical distribution function

ABSTRACTWe propose a new test for testing the equality of location parameter of two populations based on empirical distribution function (ECDF). The test statistics is obtained as a power divergence between two ECDFs. The test is shown to be distribution free, and its null distribution is obtained. We conducted empirical power comparison of the proposed test with several other available tests in the literature. We found that the proposed test performs better than its competitors considered here under several population structures. We also used two real datasets to illustrate the procedure.

Tests for Two-Sample Location Problem Based on Subsample Quantiles

This paper presents a new class of test procedures for two-sample location problem based on subsample quantiles. The class includes Mann-Whitney test as a special case. The asymptotic normality of the class of tests proposed is established. The asymptotic relative performance of the proposed class of test with respect to the optimal member of Xie and Priebe (2000) is studied in terms of Pitman efficiency for various underlying distributions.