Section 25.4 Section 5.2 Summary
Whereas the previous section dealt with comparing several groups on a categorical response variable, this one introduced you to comparing several groups on a quantitative response variable. You learned how to apply analysis of variance (ANOVA) to assess the significance of the differences among several sample/treatment means. The test procedure is based upon a probability distribution known as the F-distribution. You have seen that the same ANOVA procedure applies whether the data were gathered as independent random samples from several populations or from randomization of subjects to several treatment groups. (But like always, the scope of conclusions differs depending on how the data were collected.) You have also found that ANOVA results are affected by the variability in sample means, the variability within samples/groups, and the sample sizes. Like always, you have examined technical conditions that must be satisfied in order for this procedure to be valid; in addition to random sampling or random assignment, these conditions are that each group has a normal distribution and that the standard deviations are similar across groups. Example 5.2 presents an application of the ANOVA procedure.
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