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Testing hypotheses concerning frequency tables using the χ 2 distribution

In: Introduction to Biometry

Author

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  • Pierre Jolicoeur

    (University of Montreal, Department of Biological Science)

Abstract

The distribution of χ 2 (chapter 7) has many uses in statistics. In the case where a continuous variate X follows a normal distribution (chapter 5), the χ 2distribution may be used to test hypotheses or to determine confidence intervals exactly about the parametric variance σ x 2 of the population (chapter 10). When the hypothesis that within-groups variances are equal must be tested in an analysis of variance, Bartlett’s criterion follows the χ 2distribution approximately (section 12.7). Moreover, the hypotheses that the distribution of a set of data has the same skewness index (γ 1= 0) and the same peakedness index (γ 2= 0) as a normal distribution can be tested jointly by using the χ 2distribution (section 13.5). But the most common application of the χ 2distribution, which was discovered by Karl Pearson (1900), is perhaps its approximate use to test hypotheses about frequency tables (also called contingency tables),one of the oldest among the so-called nonparametricmethods.

Suggested Citation

  • Pierre Jolicoeur, 1999. "Testing hypotheses concerning frequency tables using the χ 2 distribution," Springer Books, in: Introduction to Biometry, chapter 0, pages 94-101, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4615-4777-8_16
    DOI: 10.1007/978-1-4615-4777-8_16
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