1. Pretest/Posttest/Group ANCOV The Univariate Approach

2. Airport Search Data Passengers at RDU in Sept., 2004 Race: 1 = Caucasian, 2 = Arab Sex: 1 = Male, 2 = Female Pre = Prior to 9/11, how many times searched on 10 international flights. Post = same, but after 9/11.

3. Posttest Only Scores Independent t comparing the groups. Less powerful that other techniques

4. Mixed Factorial ANOVA Y = Time Race Time x Race Tests of Within-Subjects Contrasts Measure:MEASURE_1 SourcePostPre Type III Sum of SquaresdfMean SquareFSig. PostPreLinear 288.3641 84.676.000 PostPre * raceLinear 76.3641 22.424.000 Error(PostPre)Linear 180.491533.405 The interaction is of greatest importance, and it is significant

5. Simple Effects of Time, Arabs Paired Differences 95% Confidence Interval of the Difference tdf Sig. (2- tailed) Post-9-11 - Pre-9-11 LowerUpper 3.3976.6986.37920.000 Paired Samples Statistics a MeanNStd. Deviation Std. Error Mean Pair 1Post-9-11 7.67213.512.766 Pre-9-11 2.62211.161.253

6. Caucasians Paired Samples Statistics a MeanNStd. Deviation Std. Error Mean Pair 1Post-9-11 2.82341.290.221 Pre-9-11 1.21341.572.270 Paired Samples Test a Paired Differences 95% Confidence Interval of the Difference tdf Sig. (2- tailed) LowerUpper Post-9-11 - Pre-9-111.0162.2195.47333.000

7. Independent t on Difference Scores Diff = Post minus Pre Group Statistics raceNMeanStd. Deviation Std. Error Mean Post Minus PreArab 215.04763.62596.79125 Caucasian 341.61761.72354.29558 Independent Samples Test t-test for Equality of Means tdfSig. (2-tailed) Post Minus PreEqual variances assumed4.73553.000

8. Equivalent to F test of Interaction t test on difference scores is absolutely equivalent to F test of interaction t(53) = 4.735, p <.001 Square that t: 4.735**2 = 22.42 F(1, 53) = 22.42 The t will always have the same p as does the F.

9. Analysis of Covariance Post = Pre Group Dependent Variable:Post-9-11 Source Type III Sum of SquaresdfMean SquareFSig. Corrected Model 310.064 a 2155.03227.231.000 Intercept 437.2051 76.795.000 pre 5.5631.977.327 race 214.3781 37.655.000 Error 296.045525.693 Total 1807.00055 Corrected Total 606.10954 Notice that the F for race is even larger than obtained earlier for the interaction. The ANCOV is more powerful.

10. Least Squares Means Race Dependent Variable:Post-9-11 Race Mean Std. Error 95% Confidence Interval Lower Bound Upper Bound Arab7.469.5586.3508.588 Caucasian2.946.4272.0883.803 The two groups differ significantly on posttest scores after adjusting for the pretest scores.

11. Which Procedure Should I Use? Monte Carlo work has shown that the ANCOV will give more power than will the Time x Groups ANOVA. But you may still want to look at the magnitude of the pre/post difference within each group.