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

2.50
Hdl Handle:
http://hdl.handle.net/10033/620715
Title:
Analysis of contingency tables based on generalised median polish with power transformations and non-additive models
Authors:
Klawonn, Frank; Jayaram, Balasubramaniam; Crull, Katja; Kukita, Akiko; Pessler, Frank
Abstract:
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.
Citation:
Health Information Science and Systems. 2013 May 30;1(1):11
Issue Date:
30-May-2013
URI:
http://dx.doi.org/10.1186/2047-2501-1-11; http://hdl.handle.net/10033/620715
Type:
Journal Article
Appears in Collections:
publications of the research group biomarker in infection and immunity [[TC] BIOM)

Full metadata record

DC FieldValue Language
dc.contributor.authorKlawonn, Franken
dc.contributor.authorJayaram, Balasubramaniamen
dc.contributor.authorCrull, Katjaen
dc.contributor.authorKukita, Akikoen
dc.contributor.authorPessler, Franken
dc.date.accessioned2017-01-17T09:49:01Z-
dc.date.available2017-01-17T09:49:01Z-
dc.date.issued2013-05-30en
dc.identifier.citationHealth Information Science and Systems. 2013 May 30;1(1):11en
dc.identifier.urihttp://dx.doi.org/10.1186/2047-2501-1-11en
dc.identifier.urihttp://hdl.handle.net/10033/620715-
dc.description.abstractAbstract 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.en
dc.titleAnalysis of contingency tables based on generalised median polish with power transformations and non-additive modelsen
dc.typeJournal Articleen
dc.language.rfc3066enen
dc.rights.holderKlawonn et al.; licensee BioMed Central Ltd.en
dc.date.updated2015-09-04T08:29:46Zen
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