PAIRED OR PARTIALLY PAIRED TWO-SAMPLE TESTS WITH MISSING IDENTITIES

Abstract

In paired or partially paired two-sample data, it is common to encounter unordered samples in which subject identities are not observed or unobservable. The absence of subject identities masks the correspondence between the two samples, rendering existing testing methods inapplicable. In this thesis, we propose two novel methods to test the mean equality based on unordered samples. The first method splits one of the two unordered samples into blocks and approximates the population mean using the average of the other sample. The second method is a variant of the first, in which subsampling is used to construct an incomplete U-statistic. Asymptotic null distributions of the proposed test statistics are derived and the local powers of the tests are studied. Four real examples are used to illustrate the proposed methods, in which we demonstrate that naive methods can yield misleading conclusions.