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159 a) The test statistic for ANOVA is an F -ratio, which is a ratio of two sample variances. b) In the context of ANOVA, the sample variances are called mean squares, or MS values. c) The top of the F-ratio MS between measures the size of mean differences between samples. d) The bottom of the ratio MS within measures the magnitude of differences that would be expected without any treatment effects. e) A large value for the F -ratio indicates that the obtained sample group mean differences are greater than would be expected if the treatments had no effect. At its simplest (there are extensions) ANOVA tests the following hypotheses: a. H 0 : The means of all the groups are equal. b. H a : Not all the means are equal However, the ANOVA does not tell how or which of the three variables differ, and in such cases, further analyses using “multiple comparisons” or posthoc comparisons are applied. Performing ANOVA in SPSS The following instructions are divided into three sets of steps before performing an ANOVA. The first step is to ensure that all descriptives show that data presented enables an ANOVA to be performed. Conduct an exploratory analysis to (a) examine descriptive statistics, (b) check for outliers, (c) check that the normality assumption is met, and d) verify that there are mean differences between groups to justify ANOVA. In performing ANOVA it is important to a) Conduct the actual one-way ANOVA to determine whether group means are different from one another (warranting planned or post-hoc comparison tests, as described in step 3). Also, check that the homogeneity of variance assumption is met. b) Conduct planned or post-hoc comparisons if warranted. For illustration purposes, instructions are provided for both planned and post-hoc comparisons. ANOVA in SPSS 1. Go to Analyse 2. Compare Means. 3. One-Way ANOVA. 4. Highlight the Dependent variable and move it to the Dependent List box. 5. Highlight the independent variables and move them to the Factor box.