Small sample sizes : A big data problem in high-dimensional data analysis

Acknowledgements The authors are grateful to the Editor, Associate Editor and three anonymous referees for their helpful suggestions, which greatly improved the manuscript. Funding The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The research is supported by the German Science Foundation awards number DFG KO 4680/3-2 and PA 2409/3-2.Peer reviewedPublisher PD

GFD: An R Package for the Analysis of General Factorial Designs

Factorial designs are widely used tools for modeling statistical experiments in all kinds of disciplines, e.g., biology, psychology, econometrics and medicine. For testing null hypotheses in this framework, ANOVA methods are widely used. However, the corresponding F tests are only valid for normally distributed data with equal variances, two assumptions which are often not met in practice. The R package GFD provides an implementation of the Wald-type statistic (WTS), the ANOVA-type statistic (ATS) and a studentized permutation version of the WTS. Both the WTS and the permuted WTS do not require normally distributed data or variance homogeneity, whereas the ATS assumes normality. All methods are available for general crossed or nested designs and all main and interaction effects can be plotted. Additionally, the package is equipped with an optional graphical user interface to facilitate application for a wide range of users. We illustrate the implemented methods for a range of different designs