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Chapter 13

13-1. Chapter 13. Analysis of Variance (ANOVA). Outline. 13-2. 12-1 Analysis of Variance (ANOVA). Objectives. 13-3. Use ANOVA technique to determine a difference among three or more means. 13-1 Analysis of Variance (ANOVA). 13-4.

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Chapter 13

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  1. 13-1 Chapter 13 Analysis of Variance (ANOVA)

  2. Outline 13-2 • 12-1 Analysis of Variance (ANOVA)

  3. Objectives 13-3 • Use ANOVA technique to determine a difference among three or more means.

  4. 13-1 Analysis of Variance (ANOVA) 13-4 • When an F-test is used to test a hypothesis concerning the means of three or more populations, the technique is called analysis of variance (ANOVA).

  5. 13-1 Assumptions for the F-Test for Comparing Three or More Means 13-5 • The populations from which the samples were obtained must be normally or approximately normally distributed. • The samples must be independent of each other. • The variances of the populations must be equal.

  6. 13-1 Analysis of Variance 13-6 • Although means are being compared in this F-test, variances are used in the test instead of the means. • Two different estimates of the population variance are made.

  7. 13-1 Analysis of Variance 13-7 • Between-group variance - this involves computing the variance by using the means of the groups or between the groups. • Within-group variance - this involves computing the variance by using all the data and is not affected by differences in the means.

  8. 13-1 Analysis of Variance 13-8 • The following hypotheses should be used when testing for the difference between three or more means. • H0: =  = … = k • H1: At least one mean is different from the others.

  9. 13-1 Analysis of Variance 13-9 • d.f.N. = k – 1, where k is the number of groups. • d.f.D. = N – k, where N is the sum of the sample sizes of the groups. • Note:The formulas for this test are tedious to work through, so examples will be done in MINITAB. See text for formulas.

  10. 13-1 Analysis of Variance-Example 13-10 • A marketing specialist wishes to see whether there is a difference in the average time a customer has to wait in a checkout line in three large self-service department stores. The times (in minutes) are shown on the next slide. • Is there a significant difference in the mean waiting times of customers for each store using  = 0.05?

  11. 13-1 Analysis of Variance-Example 13-11

  12. 13-1 Analysis of Variance-Example 13-12 • Step 1: State the hypotheses and identify the claim. • H0: = H1: At least one mean is different from the others (claim).

  13. 13-1 Analysis of Variance-Example 13-13 • Step 2: Find the critical value. Since k = 3, N = 18, and  = 0.05, d.f.N. = k – 1 = 3 – 1= 2, d.f.D. = N – k = 18 – 3 = 15. The critical value is 3.68. • Step 3: Compute the test value. From the MINITAB output, F = 2.70. (See your text for computations).

  14. 13-1 Analysis of Variance-Example 13-14 • Step 4: Make a decision. Since 2.70 < 3.68, the decision is not to reject the null hypothesis. • Step 5: Summarize the results. There is not enough evidence to support the claim that there is a difference among the means. The ANOVA summary table is given on the next slide.

  15. 13-1 Analysis of Variance-Example 13-15

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