- Nahm, S. and Choi, Y.S.(2017). A Permutation test for the Differences between Groups
Using the Dissimilarity Measure of the Multidimensional Scaling, The Korean Journal of Applied Statistics, DOI: http://dx.doi.org/10.5351/KJAS.2017.27.1.001.

Abstract
In general, grouped multivariate data can be tested for the differences between two or more groups using multivariate analysis of variance (MANOVA). However, if several assumptions of MANOVA are violated, this method cannot be used. In this case, multidimensional scaling(MDS) and analysis of distance(AOD) can be applied to the grouped dissimilarities based on the various distances. And permutation test is available to test the differences between groups. MDS is used to calculate the coordinates of observations from dissimilarities and AOD is useful for finding group structure using these coordinates. In particular, if using the euclidean distance when computing dissimilarities, AOD is associated with MANOVA mathematically. In this paper, we study the between and within group structure by applying MDS and AOD to the grouped dissimilarities. In addition, we propose a new test statistic using this group structure for permutation test. Finally, we investigate the relationship between AOD and MANOVA from dissimilarities based on the euclidean distance.

Keywords: dissimilarity, multidimensional scaling, analysis of distance, permutation test, analysis of variance