Testing Mean Differences among Groups: Multivariate and Repeated Measures Analysis with Minimal Assumptions

• Published in: Multivariate behavioral research Vol. 53; no. 3; pp. 348 - 359
• Main Authors: Bathke, Arne C., Friedrich, Sarah, Pauly, Markus, Konietschke, Frank, Staffen, Wolfgang, Strobl, Nicolas, Höller, Yvonne
• Format: Journal Article
• Language: English
• Published: United States Taylor & Francis Ltd 01.05.2018; Routledge
• Subjects: Age Factors; Aged; Alzheimer Disease - diagnosis; Alzheimer Disease - physiopathology; Alzheimer's disease; Between-subjects design; Brain - diagnostic imaging; Brain - physiopathology; Computed tomography; Computer Simulation; Covariance matrix; Data Interpretation, Statistical; Electroencephalography; Female; Humans; Male; Multivariate Analysis; Normality; Photon emission; Sex Factors; Single Photon Emission Computed Tomography Computed Tomography; Within-subjects design; Bootstrap; closed testing; MANOVA; factorial designs; repeated measures
• ISSN: 0027-3171; 1532-7906; 1532-7906
• DOI: 10.1080/00273171.2018.1446320

To date, there is a lack of satisfactory inferential techniques for the analysis of multivariate data in factorial designs, when only minimal assumptions on the data can be made. Presently available methods are limited to very particular study designs or assume either multivariate normality or equal covariance matrices across groups, or they do not allow for an assessment of the interaction effects across within-subjects and between-subjects variables. We propose and methodologically validate a parametric bootstrap approach that does not suffer from any of the above limitations, and thus provides a rather general and comprehensive methodological route to inference for multivariate and repeated measures data. As an example application, we consider data from two different Alzheimer's disease (AD) examination modalities that may be used for precise and early diagnosis, namely, single-photon emission computed tomography (SPECT) and electroencephalogram (EEG). These data violate the assumptions of classical multivariate methods, and indeed classical methods would not have yielded the same conclusions with regards to some of the factors involved.