Rank-based multiple test procedures and simultaneous confidence intervals

We study simultaneous rank procedures for unbalanced designs with independent observations. The hypotheses are formulated in terms of purely nonparametric treatment effects. In this context, we derive rank-based multiple contrast test procedures and simultaneous confidence intervals which take the correlation between the test statistics into account. Hereby, the individual test decisions and the simultaneous confidence intervals are compatible. This means, whenever an individual hypothesis has been rejected by the multiple contrast test, the corresponding simultaneous confidence interval does not include the null, i.e. the hypothetical value of no treatment effect. The procedures allow for testing arbitrary purely nonparametric multiple linear hypotheses (e.g. many-to-one, all-pairs, changepoint, or even average comparisons). We do not assume homogeneous variances of the data; in particular, the distributions can have different shapes even under the null hypothesis. Thus, a solution to the multiple nonparametric Behrens-Fisher problem is presented in this unified framework.DFG/Br 655/16-1DFG/HO 1687/9-

The nonparametric Behrens-Fisher problem in small samples

While there appears to be a general consensus in the literature on the definition of the estimand and estimator associated with the Wilcoxon-Mann-Whitney test, it seems somewhat less clear as to how best to estimate the variance. In addition to the Wilcoxon-Mann-Whitney test, we review different proposals of variance estimators consistent under both the null hypothesis and the alternative. Moreover, in case of small sample sizes, an approximation of the distribution of the test statistic based on the t-distribution, a logit transformation and a permutation approach have been proposed. Focussing as well on different estimators of the degrees of freedom as regards the t-approximation, we carried out simulations for a range of scenarios, with results indicating that the performance of different variance estimators in terms of controlling the type I error rate largely depends on the heteroskedasticity pattern and the sample size allocation ratio, not on the specific type of distributions employed. By and large, a particular t-approximation together with Perme and Manevski's variance estimator best maintains the nominal significance leve

Robustness considerations in selecting efficient two-color microarray designs

The main goal of microarray experiments is to select a small subset of genes that are differentially expressed among competing mRNA samples. For a given set of such mRNA samples, it is possible to consider a number of two-color cDNA microarray designs with a fixed number of arrays. Appropriate criteria can be used to select an efficient design from such a set of alternative experimental designs. In practice, however, microarray expression data often contain missing observations and the most efficient design (with complete observations) for a specific setup may not be efficient in the presence of missing observations. In this article, we propose two criteria to address the robustness of microarray designs against missing observations. We demonstrate the simultaneous use of efficiency and robustness criteria to select good microarray designs for both one-factor and multi-factor experiments. Contact: [email protected]

Are multiple contrast tests superior to the ANOVA?

Multiple contrast tests can be used to test arbitrary linear hypotheses by providing local and global test decisions as well as simultaneous confidence intervals. The ANOVA-F-test on the contrary can be used to test the global null hypothesis of no treatment effect. Thus, multiple contrast tests provide more information than the analysis of variance (ANOVA) by offering which levels cause the significance. We compare the exact powers of the ANOVA-F-test and multiple contrast tests to reject the global null hypothesis. Hereby, we compute their least favorable configurations (LFCs). It turns out that both procedures have the same LFCs under certain conditions. Exact power investigations show that their powers are equal to detect their LFCs. © 2013 Elsevier BV