Tests of fit and other nonparametric data analysis

The aims of this thesis are first, to introduce and investigate statistical tests of some common discrete data models and second, to unify and extend some well known nonparametric tests. Partitioning Pearson's classical chi-squared statistic and extending Neyman's smooth tests to discrete distributions are the main approaches used. New tests of fit are given for the ordered discrete uniform, the binomial and the univariate and bivariate Poisson distributions. Comparison of r ordered multinomial distributions is considered. New nonparametric tests for one-way and two-way layout data are introduced. The material presented extends and complements that given in the book Smooth Tests of Goodness of Fit by Rayner and Best (1989). This thesis, with its emphasis on partitioning chi-squared using orthogonal polynomials, is clearly influenced by the book of Lancaster (1969) entitled The Chi-Squared Distribution. It is hoped that others will apply the methods presented, and to that end a large Appendix of Microsoft FORTRAN Powerstation code which runs using MS-DOS in Windows 95 or Windows NT is provided. This code should compile on other FORTRAN compilers, such as the Lahey FORTRAN 77 compiler, with only a small number of changes. A large number of examples are also given to demonstrate the versatility and power of the methods presented. Many of these examples reflect the author's experience in design and analysis of sensory evaluation experiments.