Parametric location-scale and scale trend tests based on Levenes transformation

In case of heteroscedasticity classical tests for trend in location do not control the type I error rate and have a reduced power. Since increasing locations are often accompanied by an increase in variability and apparent heteroscedasticity indicates that there are treatment differences, it is appropriate to consider an alternative involving trends in location as well as in scale. As a location-scale trend test we use the sum of a location and a scale trend test statistic. The investigated scale trend test is based on Leveneʹs transformations. According to our simulation study we suggest to construct the tests using the principle of Bartholomewʹs likelihood ratio test. The different tests are applied to the data of a biomedical study.