Assumption of HomoscedasticitySlide 2Evaluating homoscedasticityTransformationsWhen transformations do not workProblem 1Request a boxplotSpecify the type of boxplotSpecify the dependent variableSpecify the independent variableComplete the request for the boxplotThe boxplotRequest the test for homogeneity of varianceSlide 14Slide 15The homogeneity of variance test is an optionSpecify the homogeneity of variance testComplete the request for outputInterpreting the homogeneity of variance testThe assumption of homoscedasticity scriptSelecting the assumption of homoscedasticity scriptSpecifications for homoscedasticity scriptThe test of homogeneity of varianceProblem 2Computing the logarithmic transformationSpecifying the variable name and functionAdding the variable name to the functionPreventing illegal logarithmic valuesThe transformed variableSlide 30The homogeneity of variance testHomogeneity of variance test from the scriptOther problems on homoscedasticity assumptionSteps in answering questions about the assumption of homoscedasticity – question 1Steps in answering questions about the assumption of homoscedasticity – question 2SW388R7Data Analysis & Computers IISlide 1Assumption of HomoscedasticityHomoscedasticity(also referred to as homogeneity of variance)(also referred to as uniformity of variance)TransformationsAssumption of normality scriptPractice problemsSW388R7Data Analysis & Computers IISlide 2Assumption of HomoscedasticityHomoscedasticity refers to the assumption that that the dependent variable exhibits similar amounts of variance across the range of values for an independent variable.While it applies to independent variables at all three measurement levels, the methods that we will use to evaluation homoscedasticity requires that the independent variable be non-metric (nominal or ordinal) and the dependent variable be metric (ordinal or interval). When both variables are metric, the assumption is evaluated as part of the residual analysis in multiple regression.SW388R7Data Analysis & Computers IISlide 3Evaluating homoscedasticity Homoscedasticity is evaluated for pairs of variables.There are both graphical and statistical methods for evaluating homoscedasticity .The graphical method is called a boxplot.The statistical method is the Levene statistic which SPSS computes for the test of homogeneity of variances.Neither of the methods is absolutely definitive.SW388R7Data Analysis & Computers IISlide 4TransformationsWhen the assumption of homoscedasticity is not supported, we can transform the dependent variable variable and test it for homoscedasticity . If the transformed variable demonstrates homoscedasticity, we can substitute it in our analysis.We use the sample three common transformations that we used for normality: the logarithmic transformation, the square root transformation, and the inverse transformation.All of these change the measuring scale on the horizontal axis of a histogram to produce a transformed variable that is mathematically equivalent to the original variable.SW388R7Data Analysis & Computers IISlide 5When transformations do not workWhen none of the transformations results in homoscedasticity for the variables in the relationship, including that variable in the analysis will reduce our effectiveness at identifying statistical relationships, i.e. we lose power.SW388R7Data Analysis & Computers IISlide 6Problem 1In the dataset GSS2000.sav, is the following statement true, false, or an incorrect application of a statistic? Use 0.01 as the level of significance.Based on a diagnostic hypothesis test for homogeneity of variance, the variance in "highest academic degree" is homogeneous for the categories of "marital status.“1. True2. True with caution3. False 4. Incorrect application of a statisticSW388R7Data Analysis & Computers IISlide 7Request a boxplotThe boxplot provides a visual image of the distribution of the dependent variable for the groups defined by the independent variable.To request a boxplot, choose the BoxPlot… command from the Graphs menu.SW388R7Data Analysis & Computers IISlide 8Specify the type of boxplotFirst, click on the Simple style of boxplot to highlight it with a rectangle around the thumbnail drawing.Second, click on the Define button to specify the variables to be plotted.SW388R7Data Analysis & Computers IISlide 9Specify the dependent variableFirst, click on the dependent variable to highlight it.Second, click on the right arrow button to move the dependent variable to the Variable text box.SW388R7Data Analysis & Computers IISlide 10Specify the independent variableFirst, click on the independent variable to highlight it.Second, click on the right arrow button to move the independent variable to the Category Axis text box.SW388R7Data Analysis & Computers IISlide 11Complete the request for the boxplotTo complete the request for the boxplot, click on the OK button.SW388R7Data Analysis & Computers IISlide 1256114220138N =MARITAL STATUSNEVER MARRIEDSEPARATEDDIVORCEDWIDOWEDMARRIEDRS HIGHEST DEGREE543210-1918291051321422562342171128169664023619768635887892142432031341811711631009026214178The boxplotEach red box shows the middle 50% of the cases for the group, indicating how spread out the group of scores is. If the variance across the groups is equal, the height of the red boxes will be similar across the groups. If the heights of the red boxes are different, the plot suggests that the variance across groups is not homogeneous.The married group is more spread out than the other groups, suggesting unequal variance.SW388R7Data Analysis & Computers IISlide 13Request the test for homogeneity of varianceTo compute the Levene test for homogeneity of variance, select the Compare Means | One-Way ANOVA… command from the Analyze menu.SW388R7Data Analysis & Computers IISlide 14Specify the independent variableFirst, click on the independent variable to highlight it.Second, click on the right arrow button to move the independent variable to the Factor text box.SW388R7Data Analysis & Computers IISlide 15Specify the dependent variableFirst, click on the dependent variable to highlight it.Second, click on the right arrow button to move the dependent variable to the Dependent List text box.SW388R7Data Analysis & Computers IISlide 16The homogeneity of variance test is an optionClick on the Options… button to open the options dialog box.SW388R7Data Analysis & Computers IISlide 17Specify the