13-5 The Kruskal-Wallis Test

Transcription

1 13-5 The Kruskal-Wallis Test luman, hapter

2 13-5 The Kruskal-Wallis Test The NOV uses the F test to compare the means of three or more populations. The assumptions for the NOV test are that the populations are normally distributed and that the population variances are equal. luman, hapter

3 The Kruskal-Wallis Test When these assumptions cannot be met, the nonparametric Kruskal-Wallis test, sometimes called the H test, can be used to compare three or more means. luman, hapter

4 The Kruskal-Wallis Test When these assumptions cannot be met, the nonparametric Kruskal-Wallis test, sometimes called the H test, can be used to compare three or more means. Each sample size must be 5 or more. luman, hapter

5 The Kruskal-Wallis Test When these assumptions cannot be met, the nonparametric Kruskal-Wallis test, sometimes called the H test, can be used to compare three or more means. Each sample size must be 5 or more. In these situations, the distribution can be approximated by the chi-square distribution with k 1 degrees of freedom. luman, hapter

6 Formula for the Kruskal-Wallis Test luman, hapter

7 hapter 13 Nonparametric Statistics Section 13-5 Example 13- Page #92 luman, hapter

8 Example 13-: reakfast Drinks researcher tests three different brands of breakfast drinks to see how many milliequivalents of potassium per quart each contains. These data are obtained. t α = 0.05, is there enough evidence to reject the hypothesis that all brands contain the same amount of potassium? luman, hapter

9 Example 13-: reakfast Drinks Step 1: State the hypotheses and identify the claim. luman, hapter 13

10 Example 13-: reakfast Drinks Step 1: State the hypotheses and identify the claim. H 0 : There is no difference in the amount of potassium contained in the brands (claim). luman, hapter 13

11 Example 13-: reakfast Drinks Step 1: State the hypotheses and identify the claim. H 0 : There is no difference in the amount of potassium contained in the brands (claim). H 1 : There is a difference in the amount of potassium contained in the brands. luman, hapter 13

12 Example 13-: reakfast Drinks Step 1: State the hypotheses and identify the claim. H 0 : There is no difference in the amount of potassium contained in the brands (claim). H 1 : There is a difference in the amount of potassium contained in the brands. Step 2: Find the critical value. Use Table G, with d.f. = 2 and α = 0.05, to find the critical value of luman, hapter 13

13 Example 13-: reakfast Drinks Step 3: Find the test value. a. rrange lowest to highest, and rank each value. b. Sum the ranks of each brand: rand : = 15 rand : = 53 rand : = 52 luman, hapter 13

14 Example 13-: reakfast Drinks Step 3: Find the test value. a. rrange lowest to highest, and rank each value. mount rand Rank b. Sum the ranks of each brand: rand : = 15 rand : = 53 rand : = mount rand Rank luman, hapter 13

15 Example 13-: reakfast Drinks Step 3: Find the test value. a. rrange lowest to highest, and rank each value. mount rand Rank mount rand Rank luman, hapter 13

16 Example 13-: reakfast Drinks Step 3: Find the test value. a. rrange lowest to highest, and rank each value. mount rand Rank b. Sum the ranks of each brand: mount rand Rank luman, hapter 13

17 Example 13-: reakfast Drinks Step 3: Find the test value. a. rrange lowest to highest, and rank each value. mount rand Rank b. Sum the ranks of each brand: rand : = mount rand Rank luman, hapter 13

18 Example 13-: reakfast Drinks Step 3: Find the test value. a. rrange lowest to highest, and rank each value. mount rand Rank b. Sum the ranks of each brand: rand : = 15 rand : = 53 rand : = mount rand Rank luman, hapter 13

19 Example 13-: reakfast Drinks luman, hapter

20 Example 13-: reakfast Drinks Step 3: Find the test value. c. Substitute in the formula. luman, hapter

21 Example 13-: reakfast Drinks Step 3: Find the test value. c. Substitute in the formula. luman, hapter

22 Example 13-: reakfast Drinks Step 4: Make the decision. luman, hapter

23 Example 13-: reakfast Drinks Step 4: Make the decision. Since the test value 9.38 is greater than the critical value 5.991, the decision is to reject the null hypothesis. luman, hapter

24 Example 13-: reakfast Drinks Step 4: Make the decision. Since the test value 9.38 is greater than the critical value 5.991, the decision is to reject the null hypothesis. Step 5: Summarize the results. There is enough evidence to reject the claim that there is no difference in the amount of potassium contained in the three brands. Hence, not all brands contain the same amount of potassium. luman, hapter