We consider Markov basis arising from fractional factorial designs with threelevel factors. Once we have a Markov basis, p values for various conditional tests are estimated by the Markov chain Monte Carlo procedure. For designed experiments with a single count observation for each run, we formulate a generalized linear model and consider a sample space with the same sufficient statistics to the observed data. Each model is characterized by a covariate matrix, which is constructed from the main

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... and the interaction effects we intend to measure. We investigate fractional factorial designs with 3 p−q runs noting correspondences to the models for 3 p−q contingency tables.