Skip to main content

Analysis of Multi-way Tables

  • Chapter
  • First Online:
Contingency Table Analysis

Part of the book series: Statistics for Industry and Technology ((SIT))

  • 3918 Accesses

Abstract

Issues discussed in Chap.2 for two-way tables are extended to multi-way contingency tables. Emphasis is given to clarifying the concepts of partial and marginal association. Further on, stratified 2 × 2 tables are analyzed by the Mantel–Haenszel and the Breslow–Day–Tarone tests. Types of independence for three-way tables are introduced. Graphs are presented for multi-way contingency tables while fourfold plots are used to visualize stratified 2 × 2 tables. All examples are implemented in R.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Agresti, A.: Categorical Data Analysis, 3rd edn. Wiley, Hoboken (2013)

    MATH  Google Scholar 

  • Birch, M.W.: The detection of partial association II: the general case. J. Roy. Stat. Soc. Ser. B 27, 111–124 (1965)

    MATH  MathSciNet  Google Scholar 

  • Breslow, N., Day, N.E.: Statistical Methods in Cancer Research, vol. I. IARC, Lyon (1980)

    Google Scholar 

  • Cochran, W.G.: Some methods for strengthening the common X 2 tests. Biometrics 10, 417–451 (1954)

    Article  MATH  MathSciNet  Google Scholar 

  • Cox, D.R.: Some remarks on overdispersion. Biometrika 70, 269–274 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  • Davison, A.C.: Treatment effect heterogeneity in paired data. Biometrika 79, 463–474 (1992)

    Article  MATH  Google Scholar 

  • Fienberg, S.E.: Perspective canada as a social report. Soc. Indicat. Res. 2, 153–174 (1975)

    Article  Google Scholar 

  • Friendly, M.: Mosaic displays for multiway contingency tables. J. Am. Stat. Assoc. 89, 190–200 (1994)

    Article  Google Scholar 

  • Friendly, M.: Conceptual and visual models for categorical data. Am. Stat. 49, 153–160 (1995)

    Google Scholar 

  • Friendly, M.: Extending mosaic displays: marginal, conditional, and partial views of categorical data. J. Comput. Stat. Graph. 8, 373–395 (1999)

    Google Scholar 

  • Friendly, M.: Visualizing Categorical Data. SAS Institute, Cary (2000)

    Google Scholar 

  • Friendly, M.: A brief history of the mosaic display. J. Comput. Graph. Stat. 11, 89–107 (2002)

    Article  MathSciNet  Google Scholar 

  • Friendly, M.: Working with categorical data with R and the vcd and vcdExtra packages. http://cran.r-project.org/web/packages/vcdExtra/vignettes/vcd-tutorial.pdf (2013)

  • Gart, J.J., Nam, J.: Approximate interval estimation of the ratio of binomial parameters: a review and correction for skewness. Biometrics 44, 323–338 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  • Glassman, A.H., Helzer, J.E., Covey, L.S., Cottler, L.B., Stetner, F., Tipp, J.E., Johnson, J.: Smoking, smoking cessation, and major depression. J. Am. Med. Assoc. 264, 1546–1549 (1990)

    Article  Google Scholar 

  • Goodman, L.A.: On partitioning chi-square and detecting partial association in three-way contingency tables. J. Roy. Stat. Soc. Ser. B 31, 486–498 (1969)

    MATH  Google Scholar 

  • Hartigan, J.A., Kleiner, B.: Mosaics for contingency tables. In: Eddy, W.F. (ed.) Computer Science and Statistics: Proceedings of the 13th Symposium on the Interface, pp. 268–273. Springer, New York (1981)

    Chapter  Google Scholar 

  • Hartigan, J.A., Kleiner, B.: A mosaic of television ratings. Am. Stat. 38, 32–35 (1984)

    Google Scholar 

  • Jones, M.P., O’Gorman, T.W., Lemke, J.H., Woolson, R.F.: A Monte Carlo investigation of homogeneity tests of the odds ratio under various sample size configurations. Biometrics 45, 171–181 (1989)

    Article  MATH  Google Scholar 

  • Landis, J.R., Heyman, E.R., Koch, G.G.: Average partial association in three-way contingency tables: a review and discussion of alternative tests. Int. Stat. Rev. 46, 237–254 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  • Liang, K.Y., Self, S.G.: Tests for homogeneity of odds ratio when the data are sparse. Biometrika 72, 353–358 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  • Liu, Q., Pierce, D.A.: Heterogeneity in Mantel-Haenszel-type models. Biometrika 80, 543–556 (1993)

    MATH  MathSciNet  Google Scholar 

  • Mantel, N.: Chi-square tests with one degree of freedom: extensions of the Mantel-Haenszel procedure. J. Am. Stat. Assoc. 58, 690–700 (1963)

    MATH  MathSciNet  Google Scholar 

  • Mantel, N., Byar, D.P.: Marginal homogeneity, symmetry and independence. Commun. Stat. Ser. A 7, 953–976 (1978)

    Article  Google Scholar 

  • Mantel, N., Haenszel, W.: Statistical aspects of the analysis of data from retrospective studies of disease. J. Natl. Cancer Inst. 22, 719–748 (1959)

    Google Scholar 

  • Mehta, C.R., Walsh, S.J.: Comparison of exact, mid-p, and Mantel-Haenszel confidence intervals for the common odds ratio across several 2 × 2 contingency tables. Am. Stat. 46, 146–150 (1992)

    Google Scholar 

  • Meyer, D., Zeileis, A., Hornik, K.: The strucplot framework: Visualizing multi-way contingency tables with vcd. J. Stat. Software 17(3), 1–48 (2006)

    Google Scholar 

  • Riedwyl, H., Schüpbach, M.: Siebdiagramme: Graphische Darstellung von Kontingenztafeln. Technical Report No. 12. Institute for Mathematical Statistics, University of Bern, Bern, Switzerland (1983)

    Google Scholar 

  • Riedwyl, H., Schüpbach, M.: Parquet diagram to plot contingency tables. In: Faulbaum, F. (ed.) Softstat’93: Advances in Statistical Software, pp. 293–299. Gustav Fischer, New York (1994)

    Google Scholar 

  • Tarone, R.E.: On heterogeneity tests based on efficient scores. Biometrika 72, 91–95 (1985)

    Article  MathSciNet  Google Scholar 

  • Woolf, B.: On estimating the relation between blood group and disease. Ann. Hum. Genet. 19, 251–253 (1955)S

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer Science+Business Media New York

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Kateri, M. (2014). Analysis of Multi-way Tables. In: Contingency Table Analysis. Statistics for Industry and Technology. Birkhäuser, New York, NY. https://doi.org/10.1007/978-0-8176-4811-4_3

Download citation

Publish with us

Policies and ethics