642 13 13-1 Basics of Nonparametric Tests 13-2 Sign Test 13-3 Wilcoxon SignedRanks Test for Matched Pairs 13-4 Wilcoxon Rank-Sum Test for Two Independent Samples 13-5 Kruskal-Wallis Test for Three or More Samples 13-6 Rank Correlation 13-7 Runs Test for Randomness Do Better Smartphones Cost More? NONPARAMETRIC TESTS Table 13-1 lists ranks and costs (dollars) of smartphones (based on data from Consumer Reports). Lower rank numbers correspond to better smartphones, based on quality scores determined by Consumer Reports. Among the smartphones included in Table 13-1, the best smartphone has a rank of 1, and its cost is $1000. Is there a correlation between ranks and cost? If so, does it appear that better smartphones cost more? Do you get what you pay for? It would be wise to begin the analysis with a basic exploration of the data. Because we want to address the issue of correlation, we create the scatterplot shown below. There appears to be a straight-line pattern, so there does appear to be a linear correlation. We could move beyond this subjective judgment and proceed to compute a linear correlation coefficient r, but let’s consider the nature of the data. Specifically, the ranks simply identify an order, and CHAPTER PROBLEM
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