674 CHAPTER 13 Nonparametric Tests Kruskal-Wallis Test Access tech supplements, videos, and data sets at www.TriolaStats.com TECH CENTER Statdisk 1. Click Analysis in the top menu. 2. Select Kruskal-Wallis Test from the dropdown menu. 3. Enter a significance level and select the columns to be included in the analysis. 4. Click Evaluate. StatCrunch 1. Click Stat in the top menu. 2. Select Nonparametrics in the dropdown menu and KruskalWallis in the submenu. 3. Select the columns to be used in the analysis. 4. Check Adjust for ties under Options. 5. Click Compute! TIP: Checking Adjust for ties provides more accurate results that may be different from those in this section of the textbook. Minitab 1. List all of the sample data in column C1 and identify the sample (using names or numbers) for the corresponding value in a second column C2. • For the data of Table 13-6 in this section, enter the 19 sample values in C1 and in C2 enter eight 1s followed by six 2s followed by five 3s. 2. Click Stat in the top menu. 3. Select Nonparametrics from the dropdown menu and select Kruskal-Wallis from the submenu. 4. For Response select column C1 and for Factor select column C2. 5. Click OK. Rationale: The Kruskal-Wallis H test statistic is the rank version of the F test statistic used in analysis of variance discussed in Chapter 12. When we deal with ranks R instead of original values x, many components are predetermined. For example, the sum of all ranks can be expressed as N1N + 12>2, where N is the total number of values in all samples combined. The expression H = 12 N1N + 12 Σni1Ri - R2 2 where Ri = Ri ni and R = ΣRi Σni combines weighted variances of ranks to produce the H test statistic given here, and this expression for H is algebraically equivalent to the expression for H given earlier as the test statistic. TI-83, 83 84 Plus Calculator 8 us Ca cu ato Requires programs KWTEST and ZZRANK (available at TriolaStats.com) 1. Data must be entered as columns in Matrix A: Manually enter data: Press F then Q to get to the MATRIX menu, select EDIT from the top menu, select [A], and press [. Enter the number of rows and columns needed, press [, and proceed to enter the sample values. Using existing lists: Lists can be combined and stored in Matrix A. Press F then Q to get to the MATRIX menu, select MATH from the top menu, and select the item List Smatr. Enter the list names followed by the matrix name [A], all separated by commas. Important: The matrix name must be entered by pressing F then Q, selecting [A], and pressing [. The following is a summary of the commands used to create a matrix from three lists (L1, L2, L3): List Smatr(L1, L2, L3, [A]). 2. Press N, select KWTEST, and press [ twice. The value of the H test statistic and the number of degrees of freedom will be provided. Refer to Table A-4 to find the critical value. TIP: If the samples have different sizes, some of the matrix entries will be zeros. If any of the original data values are zero, add some convenient constant to all of the sample values so that no zeros are present among the original data values.
RkJQdWJsaXNoZXIy NjM5ODQ=