564 CHAPTER 10 Chi-Square Tests and the F -Distribution Two-Way ANOVA When you want to test the effect of two independent variables, or factors, on one dependent variable, you can use a two-way analysis of variance test. For instance, suppose a medical researcher wants to test the effect of age and type of medication on the mean length of time it takes pain relievers to provide relief. To perform such an experiment, the researcher can use the two-way ANOVA block design shown below. Adults ages 18–64 taking type I Adults ages 18–64 taking type II Adults ages 18–64 taking type III I II III Adults ages 65+ taking type I Adults ages 65+ taking type II Adults ages 65+ taking type III 18–64 65+ Type of medication Age A two-way ANOVA test has three null hypotheses—one for each main effect and one for the interaction effect. A main effect is the effect of one independent variable on the dependent variable, and the interaction effect is the effect of both independent variables on the dependent variable. For instance, the hypotheses for the pain reliever experiment are listed below. Hypotheses for main effects: H0: Age has no effect on the mean length of time it takes a pain reliever to provide relief. Ha: Age has an effect on the mean length of time it takes a pain reliever to provide relief. H0: The type of medication has no effect on the mean length of time it takes a pain reliever to provide relief. Ha: The type of medication has an effect on the mean length of time it takes a pain reliever to provide relief. Hypotheses for interaction effect: H0: There is no interaction effect between age and type of medication on the mean length of time it takes a pain reliever to provide relief. Ha: There is an interaction effect between age and type of medication on the mean length of time it takes a pain reliever to provide relief. To test these hypotheses, you can perform a two-way ANOVA test. Note that the conditions for a two-way ANOVA test are the same as those for a one-way ANOVA test with the additional condition that all samples must be of equal size. Using the F@distribution, a two-way ANOVA test calculates an F@test statistic for each hypothesis. As a result, it is possible to reject none, one, two, or all of the null hypotheses. The statistics involved with a two-way ANOVA test is beyond the scope of this course. You can, however, use technology such as Minitab to perform a two-way ANOVA test. Study Tip If age and type of medication have no effect on the length of time it takes a pain reliever to provide relief, then there will be no significant difference in the means of the relief times.
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