The analysis of variance (ANOVA) is a flexible statistical procedure that can be used when the researcher wishes to compare differences among more than two means. Two different ANOVA models will be described in this handout: the simple one-way ANOVA and the two-way factorial ANOVA. The one-way ANOVA is analogous to the t-test except that more than two means can be tested for differences simultaneously. For example, to investigate GPA in college students, a researcher may wish to conduct a t-test between mean GPAs for first-year and senior students. However, why restrict the data to only two levels of class membership? It would make more sense to look at average GPAs for first-year, sophomore, junior, and senior students. Since more than two means are being tested, a one-way analysis of variance would be the appropriate test. The end result of an ANOVA is an F-ratio which can be interpreted in the same way as the t-ratio. However, a significant F-ratio only indicates that some difference exists among the tested means. In order to determine what mean, means, or combination of means differs, it is necessary to employ subsequent tests which can either be planned ahead of time (a priori) or after the results have been seen (post hoc). The main issue in selecting exactly which test to use is to prevent Type I errors that would result if a number of dependent tests were conducted without adjusting the alpha level. SPSS has several flexible options for selecting a subsequent test.

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