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2 results

  • 3 - Contingency Tables

  • Jan Lepš, University of South Bohemia, Czech Republic, Petr Šmilauer, University of South Bohemia, Czech Republic
  • Book:
    Biostatistics with R
    Published online:
    18 September 2020
    Print publication:
    30 July 2020, pp 39-54

  • Summary

    The contingency tables are used to quantify and test relationships between two or more categorical (qualitative) variables. Taking a simple example of a two-way contingency table (relating two categorical variables), we illustrate the process of calculating the frequencies of category combinations expected under the assumption of variable independence, and show how observed and expected frequencies are compared within the chi-square test statistic. We also briefly describe the task of measuring the strength of association between two categorical variables, which is important for evaluating the co-occurrence of biological taxa. We illustrate the differences between statistical and causal relationships between variables, highlighting the essential role of manipulative experiments for revealing causality. Finally, we demonstrate the possible ways of visualising contingency tables and their test results. The methods described in this chapter are accompanied by a carefully-explained guide to the R code needed for their use, including the vcd package.

  • ASYMPTOTIC ENUMERATION OF SYMMETRIC INTEGER MATRICES WITH UNIFORM ROW SUMS

  • Part of
  • BRENDAN D. MCKAY, JEANETTE C. MCLEOD
  • Journal:
    Journal of the Australian Mathematical Society / Volume 92 / Issue 3 / June 2012
    Published online by Cambridge University Press:
    04 March 2012, pp. 367-384
    Print publication:
    June 2012
    • Article
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  • We investigate the number of symmetric matrices of nonnegative integers with zero diagonal such that each row sum is the same. Equivalently, these are zero-diagonal symmetric contingency tables with uniform margins, or loop-free regular multigraphs. We determine the asymptotic value of this number as the size of the matrix tends to infinity, provided the row sum is large enough. We conjecture that one form of our answer is valid for all row sums. An example appears in Figure 1.