Answering Questions in BlackBoard Homework 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 subtracting points for each incorrect answer. If the computation for partial credit results in a negative number, zero credit is assigned. Level of Measurement Requirement In 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. If the level of measurement requirement (along with the sample size requirement) is satisfied, the check box “The level of measurement requirement and the sample size requirement are satisfied” should be marked. If the level of measurement requirement isnot satisfied, the correct answer to the problem is “Inappropriate application of the statistic.” All other answers should be unmarked when the answer about level of measurement and sample size is “Inappropriate application of the statistic.” Sample Size Requirement 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 the 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 two Factor one Category A Category B Category C Category 1 Cell 1 Cell 2 Cell 3 Category 2 Cell 4 Cell 5 Cell 6 If the sample size requirement (along with the level of measurement requirement) is satisfied, the check box “The level of measurement requirement and the sample size requirement are satisfied” should be marked. If the sample size requirement is not satisfied, the correct answer to the problem is “Inappropriate application of the statistic.” All other answers should be unmarked when the answer is “Inappropriate application of the statistic.” The Assumption of Normality Analysis 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 Variance Analysis 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 of the largest group variance is not more than 3 time the smallest group variance. If we violate this assumption, but the ratio is less than or equal to 3.0, we should consider including a statement about the violation of this assumption in the discussion of our results. If we violate this assumption and the ratio of largest to smallest variance is 3.0 or greater, we should not use analysis of variance for the data for these variables and we mark the checkbox , “Inappropriate application of the statistic.” The check boxes for level of measurement and sample size, and the assumption of normality should remain marked if these conditions are satisfied. The Existence of an Interaction Effect Interaction effects represent the effects associated with combinations of the independent variables that are not detected when each independent variable is analyzed by itself. An interaction effect is generally understood to contradict the interpretation of the main effects, such that main effects are not interpreted when there is a statistically significant interaction effect. The pattern that we might ascribe to a single independent variable changes when we take into account the pattern that is exhibited when we look at it jointly. If the interaction effect is statistically significant, the check box “The relationship between income and sex cannot be interpreted independent of self-employment’ is marked. If the interaction effect is not statistically significant, the check box is left blank. If the interaction effect is statistically significant, none of the statements about main effects are marked, even though they might be statistically significant. The problem statement does not include a statement interpreting the interaction effect because the interpretation is complex. However,