Rank Correlation Access tech supplements, videos, and data sets at www.TriolaStats.com TECH CENTER continued 13-6 Rank Correlation 683 R R command: cor.test(x, y, method=“spearman”) A complete list of R statistical commands is available at TriolaStats.com Excel XLSTAT Add-In 1. Click on the XLSTAT tab in the Ribbon and then click Correlation, Association tests. 2. Select Correlation tests from the dropdown menu. 3. For Observations, Quantitative variables enter the cell range for the data values. If the data range includes a data label, check the Variable labels box. 4. For Type of correlation select Spearman. 5. Enter the desired significance level. 6. Click OK. The rank correlation coefficient is displayed in the Correlation Matrix. If the value displayed is in bold font, we can reject the claim of no correlation. Excel Excel does not have a function that calculates the rank correlation coefficient from the original sample values, but the following procedure can be used. 1. Replace each of the original sample values with its corresponding rank. 2. Click Insert Function ƒx, select the category Statistical, select the function CORREL, and click OK. 3. For Array1 enter the data range for the first variable. For Array2 enter the data range for the second variable. 4. Click OK for the rank correlation coefficient rs. Statistical Literacy and Critical Thinking 1.Lottery Tickets Sold and Jackpot Amounts The following table includes the same paired data used for the Chapter Problem at the beginning of Chapter 10. The table lists paired data consisting of Powerball lottery jackpot amounts (millions of dollars) and numbers of lottery tickets sold (millions). Convert the data to ranks that would be used for finding the rank correlation coefficient. Jackpot 334 127 300 227 202 180 164 145 255 Tickets 54 16 41 27 23 18 18 16 26 2.Rank Correlation Use the ranks from Exercise 1 to find the value of the rank correlation coefficient. Also, use a 0.05 significance level and find the critical value of the rank correlation coefficient. What do you conclude about correlation? 3. Notation What do r, rs, r, and rs denote? Why is the subscript s used? Does the subscript s represent the same standard deviation s introduced in Section 3-2? 4. Efficiency Refer to Table 13-2 on page 645 and identify the efficiency of the rank correlation test. What does that value tell us about the test? 13-6 Basic Skills and Concepts
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