Changes in Variance and the Detection of Trends

Background: Tests for a trend in location are appropriate when there is an ordered alternative such as, for example, when it is assumed that the effect does not decrease with increasing doses of a drug or fertilizer. Classical trend tests for normally distributed data as well as the nonparametric Jonckheere trend test can have inflated type I error rates when variances differ between groups. Here, different approaches suggested to handle heterogeneous variances are investigated in combination with the Williams trend test. Methods: A simulation study was performed to compare the Jonckheere trend test with competing tests. The different tests were investigated for normal and non-normal data and also applied to a data set on sizes of walnuts opened by birds in various stages of a winter. Results: With one exception, all investigated trend tests can have an inflated type I error rate when variances differ. Only a nonparametric multiple contrast test based on relative effects showed an acceptable type I error rate in all scenarios considered in the simulation. Conclusions: The Williams trend test in combination with the nonparametric multiple contrast test based on relative effects can be suggested for routine use. With this procedure, an increase in variance cannot cause a significant result in the test for trend.