You said:   "in testing hypothesis, the part of robustness is ability of the procedures to control Type I error rate of a test to close to the significance level α"   That's correct.  So what is question you are asking?  Is it about the robustness of some particular statistical method?  If so, what method?   The only way I know of to measure robustness is through simulation--and simulating enough datasets that violate an assumption to adequately test is difficult.   Steve Denham ... View more