13-6 Rank Correlation 677 Listed below are performance (non-verbal) IQ scores from samples of subjects with low blood lead level, medium blood lead level, and high blood lead level (from Data Set 11 “IQ and Lead” in Appendix B). For the test of equal medians, find the value of the test statistic H using the methods of this section, and then find the corrected value of H using the above correction factor. Does the corrected value of H differ substantially from the uncorrected value? Low 85 90 107 85 100 97 101 64 Medium 78 97 107 80 90 83 High 93 100 97 79 97 Key Concept This section describes the nonparametric method of the rank correlation test, which uses ranks of paired data to test for an association between two variables. In Section 10-1, paired sample data were used to compute values for the linear correlation coefficient r, but in this section we use ranks as the basis for computing the rank correlation coefficient rs. As in Chapter 10, we should begin an analysis of paired data by exploring with a scatterplot so that we can identify any patterns in the data as well as outliers. 13-6 Rank Correlation DEFINITION The rank correlation test (or Spearman’s rank correlation test) is a nonparametric test that uses ranks of sample data consisting of matched pairs. It is used to test for an association between two variables. We use the notation rs for the rank correlation coefficient so that we don’t confuse it with the linear correlation coefficient r. The subscript s does not refer to a standard deviation; it is used in honor of Charles Spearman (1863–1945), who originated the rank correlation approach. In fact, rs is often called Spearman’s rank correlation coefficient. Key components of the rank correlation test are given in the following Key Elements box, and the procedure is summarized in Figure 13-4 on page 679. Rank Correlation Objective Compute the rank correlation coefficient rs and use it to test for an association between two variables. The null and alternative hypotheses are as follows: H0: rs = 0 (There is no correlation.) H1: rs ≠ 0 (There is a correlation.) Notation rs = rank correlation coefficient for sample paired data (rs is a sample statistic) rs = rank correlation coefficient for all the population data (rs is a population parameter) n = number of pairs of sample data d = difference between ranks for the two values within an individual pair KEY ELEMENTS continued
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