The analysis of categorical data often leads to the analysis of a contingency table. For large samples, asymptotic approximations are sufficient when calculating p-values, but for small samples the tests can be unreliable. In these situations an exact test should be considered. This bases the test on the exact distribution of the test statistic. Sampling techniques can be used to estimate the distribution. Alternatively, the distribution can be found by complete enumeration. This thesis develops a number of new algorithms for complete enumeration of various models. Recursive algorithms are developed to test for independence in r × c tables. The algorithm is extended for multi-dimensional tables. One algorithm is extended to enumerate tables under the model of quasi-independence, and a rejection stage enables testing of models such as quasi-symmetry and uniform association. A new algorithm is developed that enables a model to be defined by a model matrix, and all tables that satisfy the model are found. This provides a more efficient enumera-tion mechanism for complex models and extends the range of models that can be tested. The technique can lead to large calculations and a distributed version of the algorithm is developed that enables a number of machines to work efficiently on the same problem.

this paper, is the hypothesis of QI for the off-diagonal cells of a r \Theta r square table, where the sufficient statistics for the nuisance parameters are x i+ ; x +j and x ii , for i; j = 1; : : : ; r.

s on a heterogeneous network. For these reasons, LISP-STAT is an ideal basis for the development of a statistical computing environment for heterogeneous networks. LISP-STAT provides dynamic, interactive graphics. Under the X-windows system, LISP-STAT processes running on one workstation can use another for their display and user interaction. These facilities alone are sufficient to allow one user to run LISP-STAT processes on multiple computers, each having its display set to the user's workstation. However, to harness the full potential of such an environment, mechanisms for communication between those processes must be provided---and these mechanisms need to be supported within the LISP-STAT language so that they are available to a user writing LISP-STAT programs. 3 Distributed Lisp To establish an environment for distributed statistical computing, it is essential to specify standard interfaces between the components of the system. This will enable the con