Solving Two-Factor ANOVA ProblemsLevel of Measurement and Sample Size RequirementThe Assumption of NormalityThe Assumption of Homogeneity of VarianceThe Existence of an Interaction EffectInterpretation of Main EffectsInappropriate application of the statisticWe should not use analysis of variance if we violate the level of measurement requirement, the minimum sample size requirement, or the assumption of homogeneity of variance when the ratio of largest to smallest group variance is larger than 3.0.Solving Problems in SPSSCreating Two-Factor ANOVA Output with Univariate General Linear Model - 1Creating Two-Factor ANOVA Output with Univariate General Linear Model - 2Creating Two-Factor ANOVA Output with Univariate General Linear Model – 3Creating Two-Factor ANOVA Output with Univariate General Linear Model – 4Creating Two-Factor ANOVA Output with Univariate General Linear Model – 5Creating Two-Factor ANOVA Output with Univariate General Linear Model – 6Creating Two-Factor ANOVA Output with Univariate General Linear Model – 7Creating Two-Factor ANOVA Output with Univariate General Linear Model – 8Creating Two-Factor ANOVA Output with Univariate General Linear Model – 9Sample Size RequirementMarking the Statement for the Level of Measurement and Sample Size RequirementThe Assumption of NormalityThe Assumption of Normality - 1The Assumption of Normality - 2The Assumption of Normality - 3Marking the Statement for the Assumption of NormalityAssumption of Homogeneity of VarianceAssumption of Homogeneity of Variance - 1Assumption of Homogeneity of Variance - 2Assumption of Homogeneity of Variance - 3Marking the Statement for the Assumption of Homogeneity of VarianceThe Interaction EffectInteraction Effect - 1Interaction Effect – 2Interaction Effect – 3Marking the Statement for the Interaction EffectThe Main Effect for Computer UseMain Effect for Computer UseInterpreting the Main Effect for Computer Use - 1Interpreting the Main Effect for Computer Use - 2Marking the Statement for Main Effect for Computer UseThe Main Effect for Satisfaction with Financial SituationMain Effect for Satisfaction with Financial SituationInterpreting the Main Effect for Satisfaction with Financial Situation – 2Interpreting the Main Effect for Satisfaction with Financial Situation – 3Interpreting the Main Effect for Satisfaction with Financial Situation – 4Interpreting the Main Effect for Satisfaction with Financial Situation – 51 of 28Solving Two-Factor ANOVA ProblemsHomework problems are multiple answer rather than multiple choice. The format for multiple answer questions is shown in the examples below.The directions for the problems instruct you to mark the check boxes for all of the statements that are true. One or more answers must be marked for each problem. Full or partial credit is computed for each question. To receive full credit, you must mark all of the correct answers and not mark any of the incorrect answers. Partial credit is computed by summing the points for each correct response and subtractingpoints for each incorrect answer. If the computation for partial credit results in a negative number, zero credit is assigned.Level of Measurement and Sample Size RequirementIn a two-way analysis of variance, the level of measurement for the independent variables can be any level that defines groups (dichotomous, nominal, ordinal, or grouped interval) and the dependent variable is required to be interval level. If the dependent variable is ordinal level, we will follow the common convention of treating ordinal variables as interval level, but we should note the use of an ordinal variable in the discussion of our findings.I have imposed a minimum sample size requirement of 5 cases per cell for these problems. The cells are the possible combinations of categories for the two factors. If factor one contained 2 categories and the factor two contained three categories, the total number of cells would be 6, as shown in the following table:Factor oneFactor twoCategory A Category B Category CCategory 1 Cell 1 Cell 2 Cell 32 of 28Category 2 Cell 4 Cell 5 Cell 6If the sample size requirement and the level of measurement requirement are satisfied, the check box “The level of measurement requirement and the sample sizerequirement are satisfied” should be marked. If the level of measurement or sample size requirement is not satisfied, the correct answer to the problem is “Inappropriate application of the statistic.” The Assumption of NormalityAnalysis of variance assumes that the dependent variable is normally distributed, but there is general consensus that violations of this assumption do not seriously affect the probabilities needed for statistical decision making.The problems evaluate normality based on the criteria that the skewness and kurtosis of the dependent variable fall within the range from -1.0 to +1.0. If the dependent variable satisfies these criteria for skewness and kurtosis, the check box “The skewness and kurtosis of income satisfy the assumption of normality” should be marked. If the criteria for normality are not satisfied, the check box should remain unmarked and we should consider including a statement about the violation of this assumption in the discussion of our results.In these problems we will not test transformations or consider removing outliers to improve the normality of the variable.The Assumption of Homogeneity of VarianceAnalysis of variance assumes that the variance of the dependent variable is homogeneous across all of the cells formed by the factors (independent variables). We will use the significance of Levene’s test for equality of variance as our criteria for satisfying the assumption, which SPSS provides as part of the output.Levene’s test is a diagnostic statistic that tests the null hypothesis that the variance is homogeneous or equal across all cells. The desired outcome, and support for satisfying the assumption, is to fail to reject the null hypothesis.If the significance for the Levene test is greater that the alpha for diagnostic statistics, we fail to reject the null hypothesis and the check box “The assumption of homogeneity of variance is supported by Levene's test for equality of variances” should be marked. If the criterion for homogeneity of variance is not satisfied, the check box should remain unmarked. Analysis of variance is robust to violations of the assumption of homogeneity of variances provided the ratio