Section 9-2 includes methods for testing equality of means from two independent populations, but this chapter presents a method for testing equality of three or more population means. Here are the chapter objectives: 12-1 One-Way ANOVA • Apply the method of one-way analysis of variance to conduct a hypothesis test of equality of three or more population means. The focus of this section is the interpretation of results from technology. 12-2 Two-Way ANOVA • Analyze sample data from populations separated into categories using two characteristics (or factors), such as gender and eye color. • Apply the method of two-way analysis of variance to the following: (1) test for an interaction between two factors, (2) test for an effect from the row factor, and (3) test for an effect from the column factor. The focus of this section is the interpretation of results from technology. CHAPTER OBJECTIVES w S Key Concept In this section we introduce the method of one-way analysis of variance, which is used for tests of hypotheses that three or more populations have means that are all equal, as in H0: m1 = m2 = m3. Because the calculations are very complicated, we emphasize the interpretation of results obtained by using technology. F Distribution The analysis of variance (ANOVA) methods of this chapter require the F distribution, which was first introduced in Section 9-4. In Section 9-4 we noted that the F distribution has the following properties (see Figure 12-1): 1. There is a different F distribution for each different pair of degrees of freedom for numerator and denominator. 2. The F distribution is not symmetric. It is skewed right. 3. Values of the F distribution cannot be negative. 4. The exact shape of the F distribution depends on the two different degrees of freedom. 12-1 One-Way ANOVA Value of F5 s1 2 2s 2 0 Not symmetric (skewed to the right) F Nonnegative values only a FIGURE 12-1 F Distribution 612 CHAPTER 12 Analysis of Variance
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