Testing hypotheses concerning frequency tables using the χ 2 distribution

Pierre Jolicoeur
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Pierre Jolicoeur: University of Montreal, Department of Biological Science

Chapter Chapter 15 in Introduction to Biometry, 1999, pp 94-101 from Springer

Abstract: 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.

Keywords: Marginal Probability; Total Frequency; Finite Population; Frequency Table; Compound Event (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1007/978-1-4615-4777-8_16

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