Contingency tables (cross-tabulation)

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For cross-classified data, contingency tables (cross-tabulations) record the frequency for the values that fall into each possible combination of levels from two different factors. One of the factors is associated with the columns of the contingency table; the other factor is associated with the rows of the contingency table. Individual qualitative data values are simply grouped by the values of the classification variable. For individual quantitative data values, a classification may be created by defining intervals or cutpoints to bin the data into separate groups.


To properly analyze and interpret results of the contingency tables, you should be familiar with the following terms and concepts:

If you are not familiar with these terms and concepts, you are advised to consult with a statistician. Failure to understand and properly apply contingency tables may result in drawing erroneous conclusions from your data. Additionally, you may want to consult the following references:

  • Agresti, A. 1990. Categorical Data Analysis. New York: John Wiley & Sons.
  • Agresti, A. 1996. An Introduction to Categorical Data Analysis. New York: John Wiley & Sons.
  • Bishop, Y. M. M., Fienberg, S. E., and Holland, P. W. 1975. Discrete Multivariate Analysis. Cambridge, MA: MIT Press.
  • Brownlee, K. A. 1965. Statistical Theory and Methodology in Science and Engineering. New York: John Wiley & Sons.
  • Conover, W. J. 1980. Practical Nonparametric Statistics. 2nd ed. New York: John Wiley & Sons.
  • Daniel, Wayne W. 1978. Applied Nonparametric Statistics. Boston: Houghton Mifflin.
  • Daniel, Wayne W. 1995. Biostatistics. 6th ed. New York: John Wiley & Sons.
  • Everitt, B. S. 1992. The Analysis of Contingency Tables. 2nd ed. London: Chapman & Hall.
  • Rosner, Bernard. 1995. Fundamentals of Biostatistics. 4th ed. Belmont, California: Duxbury Press.
  • Sokal, Robert R. and Rohlf, F. James. 1995. Biometry. 3rd. ed. New York: W. H. Freeman and Co.
  • Zar, Jerrold H. 1996. Biostatistical Analysis. 3rd ed. Upper Saddle River, NJ: Prentice-Hall.

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