Pretest/Posttest/Group ANCOV The Univariate Approach

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.

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

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 PostPre * raceLinear Error(PostPre)Linear The interaction is of greatest importance, and it is significant

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

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

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

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 = F(1, 53) = The t will always have the same p as does the F.

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

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

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.