13-6 Rank Correlation 679 Yes Yes No Yes No No Start Does either variable have ties among its ranks? Calculate rs using Formula 10-1 with the ranks: rs 5 nΣxy – (Σx) (Σy) Ïn(Σx2) – (Σx)2 Ïn(Σy2) – (Σy)2 Find the negative and positive critical values of rs from Table A-9. Calculate the difference d for each pair of ranks by subtracting the lower rank from the higher rank. Square each difference d and then find the sum of those squares to get Σ(d2). • If rs is between the negative and positive critical values, fail to reject the null hypothesis rs 5 0 (no correlation). • If rs is not between the negative and positive critical values, reject the null hypothesis rs 5 0 and conclude that there is sufficient evidence to support a claim of a correlation. Are the n pairs of data in the form of ranks? Calculate the critical values where z corresponds to the significance level. Is n ◊ 30? Complete the computation of to get the test statistic. rs 5 1 2 6Σd2 n(n2 – 1) rs 5 6 Ïn – 1 z Convert the data of the first sample to ranks from 1 to n and then do the same for the second sample. FIGURE 13-4 Rank Correlation Procedure for Testing H0: Rs = 0
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