The statistic for testing the fit of a linear model, or the statistic for testing a linear hypothesis under the model, when using probits or logits, has a central χ2-distribution for large samples if the null hypothesis is true. If it is not true, the test statistic has, asymptotically, a non-central χ2-distribution with a non-centrality parameter that depends on the alternative hypothesis, the model, and the transformation. Non-Centrality parameters associated with tests of the two types of hypotheses are derived, and the non-centrality parameters of some tests of interest in bioassay when the response is quantal are derived as special cases. Possible applications are discussed and several numerical examples are given.