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.
In this paper we discuss different ways to apply median polish to contingency tables in the context of medical data and how to interpret the results based on different examples. We also introduce a technique based on power transformations to find a suitable transformation of the data before applying median polish.
Keywords
- Additive Model
- Contingency Table
- Reporter Plasmid
- Logarithmic Transformation
- Power Transformation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References
Leek, J., Scharpf, R., Corrado Bravo, H., Simcha, D., Langmead, B., Johnson, W., Geman, D., Baggerly, K., Irizarry, R.: Tackling the widespread and critical impact of batch effects in high-throughput data. Nature Reviews|Genetics 11, 733–739 (2010)
Shaffer, J.P.: Multiple hypothesis testing. Ann. Rev. Psych. 46, 561–584 (1995)
Holm, S.: A simple sequentially rejective multiple test procedure. Scandinavian Journal of Statistics 6, 65–70 (1979)
Benjamini, Y., Hochberg, Y.: Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing. Journal of the Royal Statistical Society. Series B (Methodological) 57, 289–300 (1995)
Hoaglin, D., Mosteller, F., Tukey, J.: Understanding Robust and Exploratory Data Analysis. Wiley, New York (2000)
Berthold, M., Borgelt, C., Höppner, F., Klawonn, F.: Guide to Intelligent Data Analysis: How to Intelligently Make Sense of Real Data. Springer, London (2010)
R Development Core Team: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria (2009)
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© 2012 Springer-Verlag Berlin Heidelberg
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Klawonn, F., Crull, K., Kukita, A., Pessler, F. (2012). Median Polish with Power Transformations as an Alternative for the Analysis of Contingency Tables with Patient Data. In: He, J., Liu, X., Krupinski, E.A., Xu, G. (eds) Health Information Science. HIS 2012. Lecture Notes in Computer Science, vol 7231. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29361-0_5
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DOI: https://doi.org/10.1007/978-3-642-29361-0_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-29360-3
Online ISBN: 978-3-642-29361-0
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