Abstract: A class of statistics is proposed for the problem of testing for location difference using censored matched pair data. The class consists of linear combinations of two conditionally independent statistics where the conditioning is on the number, N, of pairs in which both members are uncensored and the number, N", of pairs in which exactly one member is uncensored. Since every member of the class is conditionally distribution-free under the null hypothesis, H: no location difference, the statistics in the proposed class can be utilized to provide an exact conditional test of H for all N. and N.. If n denotes the total number of pairs, then under suitable conditions the proposed test statistics are shown to have asymptotic normal distributions as n tends to infinity. As a result, large sample tests can be performed using any member of the proposed class. A method that can be used to choose one test statistic from the proposed class of test statistics is outlined. However, the resulting test statistic depends on the underlying distributional forms of the populations from which the bivariate data and censoring variables are sampled. Simulation results indicate that the powers of certain members in the class are as good as and, in some cases, better than the power of a test for H proposed by Woolson and Lachenbruch in their paper titled "Rank Tests for Censored Matched Paris" appearing on pages 597-606 of Biometrika in 1980. Also, unlike the test of Woolson and Lachenbruch, the critical values for small samples can be tabulated for the tests in the new class. Consequently, members of the new class of tests are recommended for testing the null hypothesis. Dissertation Discovery Company and University of Florida are dedicated to making scholarly works more discoverable and accessible throughout the world. This dissertation, "Nonparametric Analysis of Bivariate Censored Data" by Edward Anthony Popovich, was obtained from University of Florida and is being sold with permission from the author. A digital copy of this work may also be found in the university's institutional repository, IR@UF. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation.