Adaptive Choice of Resampling Tests for Scale in Flexible Two Stage Designs

The two sample scale problem is addressed within the rank framework which does not require to specify the underlying distribution. However, since the power of a rank test depends on the underlying distribution, it would be very useful for the researcher to have some information on it in order to use the possibly most suitable test. A two stage adaptive design is used with adaptive tests where the data from the first stage are used to compute a selector statistic to select the test statistic for stage two. More precisely an adaptive scale test due to Hall and Padmanabhan and its components are considered in one stage and several adaptive and non adaptive two stage procedures. A simulation study shows that the two stage test with the adaptive choice in the second stage and with Liptak combination when it is not more powerful than the corresponding one stage test shows however a quite similar power behavior. The tests procedures are illustrated using an ecological application.