USING SPSS: ONE-WAY ANALYSIS OF COVARIANCE (ANCOVA)1. ENTERING THE DATA:For this example, we are using the HSB500 (High School and Beyond) data file.To do a one-way analysis of covariance (ANCOVA) you have to enter the data ina manner like that shown below. The first column “subno” is the subject numberassigned to the student. The second column, “faed” is the four levels of thestudents’ father’s education, which is our independent variable (1 = Less thanHigh School, 2 = High School Graduate, 3 = Some Vocational or College, and 4 =College Graduate or More). The third column contains the students’ standardizedmathematics achievement scores (mathach, range -8.333 to 25.000) – thedependent variable. The fourth column contains the students’ mosaic score(range -28.000 to 56.000), which we will use in this example as the covariate.Note: SPSS will produce a fair amount of output as part of the ANCOVA statisticalprocess (request), of which only the applicable tables will be shown and discussed aspart of this handout.The summary data (which is generated through the Case Summaries commandin SPSS) for the four groups on both variables, MATHACH and MOSAIC areshown below:Case Summaries132 13210.86873 25.295456.186632 9.946988129 12912.44186 27.186056.448802 9.068332105 10513.21907 27.009526.283149 10.423019134 13415.83089 28.078366.494654 7.621412500 50013.09803 26.889006.604590 9.288203NMeanStd. DeviationNMeanStd. DeviationNMeanStd. DeviationNMeanStd. DeviationNMeanStd. DeviationFather's Education LevelLess than High SchoolHigh School GraduateSome Post-Secondary EducationCollege Graduate and BeyondTotalMathematicsTest ScoreMosaicTest ScoreBelow are the unadjusted means (which are part of the SPSS output generatedfrom the ANCOVA request) for MATHACH for the four groups:Descriptive StatisticsDependent Variable: Mathematics Test Score10.86873 6.186632 13212.44186 6.448802 12913.21907 6.283149 10515.83089 6.494654 13413.09803 6.604590 500Father's Education LevelLess than High SchoolHigh School GraduateSome Post-Secondary EducationCollege Graduate and BeyondTotalMean Std. Deviation NSPSS STEPS FOR ANCOVAPAGE 22. CONDUCTING THE ONE-WAY ANCOVABefore we get started – we must first conduct a test of the homogeneity-of-regression (slopes) assumption. To conduct this test, follow these steps:1. Click Analyze, click General Linear Model, then click Univariate.2. Click the dependent variable (mathach), then click ► to move it to theDependent Variable box.3. Click the independent variable (faed), then click ► to move it to the FixedFactor(s) box.4. Click the covariate (mosaic), then click ► to move it to the Covariate(s)box.5 Click Model.6 Click Custom under Specify Model.7. Click faed(F) – the independent variable under Factors & Covariates andclick ► to make it appear in the Model box.8. Click mosaic(C) – the covariate under Factors & Covariates and click ►to make it appear in the Model box.SPSS STEPS FOR ANCOVAPAGE 39. Holding down the Ctrl key, click faed(F) and mosaic(C) in the Factors &Covariates box. Check to see that the default option Interaction isspecified in the drop-down menu in the Build Term(s) box. If it is not, selectit.10. Click ► and faed*mosaic should now appear in the Model box.11. Click Continue. This will bring you back to the Univariate screen.12. Click OK.The following type of table will appear in the output screen…Tests of Between-Subjects EffectsDependent Variable: mathach Mathematics Test Score3310.890a7 472.984 12.609 .0003371.024 1 3371.024 89.866 .000290.025 3 96.675 2.577 .0531374.255 1 1374.255 36.635 .00072.562 3 24.187 .645 .58718455.792 492 37.512107545.825 50021766.682 499SourceCorrected ModelInterceptfaedmosaicfaed * mosaicErrorTotalCorrected TotalType III Sumof Squares df Mean Square F Sig.R Squared = .152 (Adjusted R Squared = .140)a. SPSS STEPS FOR ANCOVAPAGE 4Before conducting an ANCOVA – the homogeneity-of-regression (slope)assumption should first be tested. The test evaluates the interaction between thecovariate and the factor (independent variable) in the prediction of the dependentvariable. A significant interaction between the covariate and the factor suggeststhat the differences on the dependent variable among groups vary as a functionof the covariate.If the interaction is significant – the results from an ANCOVA are not meaningful –and ANCOVA should not be conducted. In our example: The interaction source islabeled faed*mosaic. Our results suggest the interaction is not significant, F(3,492) = .645, p = .587. Based on this finding, we can proceed with our ANCOVAanalysis…To conduct a one-way ANCOVA, follow these steps:1. Click Analyze, click General Linear Model, then click Univariate.2. Click Reset.If you have not exited SPSS – the prior commands will still be shown. As aprecaution for avoiding possible errors – click the reset key and begin theprocedure from the initial starting point.3. Click the dependent variable (mathach), then click ► to move it to theDependent Variable box.4. Click the independent variable (faed), then click ► to move it to the FixedFactor(s) box.5. Click the covariate (mosaic), then click ► to move it to the Covariate(s)box.6. Click on Options.7. In the Factor(s) and Factor Interactions box, click the independent variable(in our example, faed).This will provide the adjusted (Estimated Marginal) means that will beused later (if needed) in post hoc procedures.8. Click ► to move it to the Display Means for box.9. Select Descriptive statistics in the Display box.10. Select Homogeneity tests in the Display box.SPSS STEPS FOR ANCOVAPAGE 511. Click Continue.12. This will bring you back to the Univariate screen…13. Click Plots.14. Click the independent variable (faed), then click ► to move it to theHorizontal Axis: box.15. Click Add.16. Click Continue.17. This will bring you back to the Univariate screen – click OK.The following SPSS output will be produced…SPSS STEPS FOR ANCOVAPAGE 63. THE SPSS OUTPUT:Univariate Analysis of VarianceDescriptive StatisticsDependent Variable: Mathematics Test Score10.86873 6.186632 13212.44186 6.448802 12913.21907 6.283149 10515.83089 6.494654 13413.09803 6.604590 500Father's Education LevelLess than High SchoolHigh School GraduateSome Post-Secondary EducationCollege Graduate and BeyondTotalMean Std. Deviation