Statistical testing

The final GLM fit and dispersion estimate allows us to calculate the total likelihood of the model given the data, and the uncertainty on each fitted coefficient. The two statistical tests each make use of one of these values.

Wald test
Tests whether a given coefficient is non-zero. This test is used in the All group pairs and Against control group comparisons. For example, to test whether there is a difference between patients treated with a placebo, and those treated with drugB, we would use the Wald test to determine if the $ \mathrm{drugB}$ coefficient is non-zero.
Likelihood Ratio test
Fits two GLMs, one with the given coefficients and one without. The more important the coefficients are, the greater the ratio of the likelihoods of the two models. This test is used in the Across groups (ANOVA-like) comparison. If we wanted to test whether either drug had an effect, we would compare the likelihoods of the GLM described in equation 26.1 with those in the reduced GLM $ \log{y_i} = \mathrm{(Male)} + \mathrm{Female} + \mathrm{constant_i}$.