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

Klawonn F, Jayaram B, Crull K, Kukita A, Pessler F - Health Inf Sci Syst (2013)

Bottom Line: 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.It explains the contingency table in terms of an overall effect, row and columns effects and residuals.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.

View Article: PubMed Central - PubMed

Affiliation: Bioinformatics and Statistics, Helmholtz Centre for Infection Research, Inhoffenstr. 7, Braunschweig, D-38124 Germany ; Ostfalia University of Applied Sciences, Salzdahlumer Str. 46/48, Wolfenbuettel, D-38302 Germany.

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.

No MeSH data available.


Related in: MedlinePlus

IQRoQ plot for the row (left) and column effects (right) for the exponential artificial example data set.
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Fig2: IQRoQ plot for the row (left) and column effects (right) for the exponential artificial example data set.

Mentions: As a second artificial example we consider the same contingency table, but apply the exponential function to each of its entries. The IQRoQ plots shown in Figure 2 have their maximum at λ = 0 and therefore suggest to use the logarithmic transformation before applying median polish. So this power transformation reverses the exponential function and we retrieve the original data which were generated by the additive model.Figure 2


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

Klawonn F, Jayaram B, Crull K, Kukita A, Pessler F - Health Inf Sci Syst (2013)

IQRoQ plot for the row (left) and column effects (right) for the exponential artificial example data set.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4340119&req=5

Fig2: IQRoQ plot for the row (left) and column effects (right) for the exponential artificial example data set.
Mentions: As a second artificial example we consider the same contingency table, but apply the exponential function to each of its entries. The IQRoQ plots shown in Figure 2 have their maximum at λ = 0 and therefore suggest to use the logarithmic transformation before applying median polish. So this power transformation reverses the exponential function and we retrieve the original data which were generated by the additive model.Figure 2

Bottom Line: 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.It explains the contingency table in terms of an overall effect, row and columns effects and residuals.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.

View Article: PubMed Central - PubMed

Affiliation: Bioinformatics and Statistics, Helmholtz Centre for Infection Research, Inhoffenstr. 7, Braunschweig, D-38124 Germany ; Ostfalia University of Applied Sciences, Salzdahlumer Str. 46/48, Wolfenbuettel, D-38302 Germany.

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.

No MeSH data available.


Related in: MedlinePlus