conclusion can be reached based on the Q-Q plot (on the log scale) comparison in Figure 3. From Table 4, the over-dispersion factor is positively correlated with empirical type I errors under various considered significant levels. The over-dispersion factor is indeed a good summary indicating the level of inflation in type I error, as well as the extent of confounding effect. This justifies the use of over-dispersion factor in the permutation procedure.
