Abstract

The analysis of contingency tables is a powerful statistical tool used in experiments with categorical variables. This study improves parts of the theory underlying the use of contingency tables. Specifically, the linkage disequilibrium parameter as a measure of two-way interactions applied to three-way tables makes it possible to quantify Simpson's paradox by a simple formula. With tests on three-way interactions, there is only one that determines whether the partial interactions of all variables agree or whether there is at least one variable whose partial interactions disagree. To date, there has been no test available that determines whether the partial interactions of a certain variable agree or disagree, and the presented work closes this gap. This work reveals the relation of the multiplicative and the additive measure of a three-way interaction. Another contribution addresses the question of which cells in a contingency table are fixed when the first- and second-order marginal totals are given. The proposed procedure not only detects fixed zero counts but also fixed positive counts. This impacts the determination of the degrees of freedom. Furthermore, limitations of methods that simulate contingency tables with given pairwise associations are addressed.

Highlights

  • Categorical variables are observed in many branches of science

  • B gained from the finding that five partial correlations could be set to zero

  • It could be possible that the five partial correlations agree but are not zero

Read more

Summary

Introduction

Contingency table theory serves to infer such data. A great spectrum of analytical methods was presented by Agresti [1]. Some parts of the theory are improved and some methods are added. In their historical overview, Fienberg and Rinaldo [2] recognized Bartlett’s [3] important contribution to the theory of contingency tables. Simpson [4] clarified some remaining questions from Bartlett’s‘paper on the three-way interaction in a 2×2×2 table. If the data were merged, no effect was seen. Blyth [5] showed that the merged data might even indicate a strong negative effect of the drug.

Methods
Findings
Discussion
Conclusion
Full Text
Published version (Free)

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call