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9 Correlation and Tests of Independence > 9.1 Problems with the Product Moment ... - Pg. 441

CHAPTER 9 Correlation and Tests of Independence There are many approaches to finding robust measures of correlation and covariance (e.g., Ammann, 1993; Davies, 1987; Devlin et al., 1981; Goldberg & Iglewicz, 1992; Hampel et al., 1986, Chapter 5; Huber, 1981, Chapter 8; Li & Chen, 1985; Lupuha a, 1989; Maronna, 1976; Mosteller & Tukey, 1977, p. 211; Wang & Raftery, 2002; Wilcox, 1993b), but no attempt is made to give a detailed description of all the strategies that have been proposed. Some of these measures are difficult to compute, others are not always equal to zero under independence, and from a technical point of view, some do not have all the properties one might want. One of the main goals in this chapter is to describe some tests of zero correlation that have practical value relative to the standard test based on the usual product moment correlation, r . Some alternative methods for testing the hypothesis of independence, that are not based on some type of correlation coefficient, are described as well. (For a collection of alternative methods for detecting dependence, see Kallenberg & Ledwina, 1999.)