# Analysis of contingency tables based on generalised median polish with power transformations and non-additive models

Klawonn, F and Jayaram, Balasubramaniam and Crull, K and Kukita, A and Pessler, F (2014) Analysis of contingency tables based on generalised median polish with power transformations and non-additive models. Health Information Science and Systems, 1 (11). pp. 1-14. ISSN 2047-2501

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## Abstract

Contingency tables are a very common basis for the investigation of effects of different treatments or influences on a disease or the health state of patients. Many journals put a strong emphasis on p-values to support the validity of results. Therefore, even small contingency tables are analysed by techniques like t-test or ANOVA. Both these concepts are based on normality assumptions for the underlying data. For larger data sets, this assumption is not so critical, since the underlying statistics are based on sums of (independent) random variables which can be assumed to follow approximately a normal distribution, at least for a larger number of summands. But for smaller data sets, the normality assumption can often not be justified. Robust methods like the Wilcoxon-Mann-Whitney-U test or the Kruskal-Wallis test do not lead to statistically significant p-values for small samples. Median polish is a robust alternative to analyse contingency tables providing much more insight than just a p-value. Median polish is a technique that provides more information than just a p-value. It explains the contingency table in terms of an overall effect, row and columns effects and residuals. The underlying model for median polish is an additive model which is sometimes too restrictive. In this paper, we propose two related approach to generalise median polish. A power transformation can be applied to the values in the table, so that better results for median polish can be achieved. We propose a graphical method how to find a suitable power transformation. If the original data should be preserved, one can apply other transformations – based on so-called additive generators – that have an inverse transformation. In this way, median polish can be applied to the original data, but based on a non-additive model. The non-linearity of such a model can also be visualised to better understand the joint effects of rows and columns in a contingency table.

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IITH Creators:
IITH CreatorsORCiD
Jayaram, Balasubramaniamhttp://orcid.org/0000-0001-7370-3821
Item Type: Article
Additional Information: This study was co-financed by the European Union (European Regional Development Fund) under the Regional Competitiveness and Employment objective and within the framework of the Bi2 SON Project Einsatz von Informations- und Kommunikationstechnologien zur Optimierung der biomedizinischen Forschung in Südost-Niedersachsen. This work was partly carried out during the visit of the second author to the Department of Computer Science, Ostfalia University of Applied Sciences under the fellowship provided by the Alexander von Humboldt Foundation.
Subjects: Mathematics
Divisions: Department of Mathematics
Depositing User: Team Library
Date Deposited: 26 Nov 2014 09:54