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1 Repeated-measures data in educational research trials – how should it be analysed? Ben Styles Senior Statistician National Foundation for Educational Research

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3 Two sweeps example Cluster randomised trial of reading materials Baseline reading test, 10 week intervention, follow-up reading test Two parallel versions of the Suffolk Reading Scale

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4 Using baseline data as a covariate in a multi- level (pupil, school) regression model Different analysis, different results OutcomeBackgroundCoefficientSEp Post-test scoreConstant10.950.68760.000*** Intervention0.6720.57420.242NS Pre-test score0.77080.01670.000***

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Different analysis, different results Using time as a level in a repeated measures multi-level (time, pupil, school) regression model 5 OutcomeBackgroundCoefficientSEp Total scoreConstant32.351.2060.000*** Time3.3870.35930.000*** Intervention-1.6821.6840.318NS Time*intervention1.2380.49160.012*

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Interaction 6

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Six sweeps example Mentoring scheme for struggling readers Pupil-level randomisation Questionnaire administered once at baseline and then every four months for the next two years 7

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Six sweeps example Using time as a level in a repeated-measures multi-level (time, pupil, school) regression model 8 OutcomeBackgroundCoefficientSEp Aspirations for the futureConstant 22.650.1310.000*** Time -0.073580.026250.005** Intervention -0.27960.16940.099NS Time*intervention 0.081310.038010.032*

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Reading Two-waves studies cannot describe individual trajectories of change and they confound true change with measurement error (Singer and Willett, 2002) ANCOVA is valid even with pre-test measurement error (Senn, 2004) Unconditional change models described in text books have three or more time-points The ANCOVA will almost always provide a more powerful test of the hypothesis of interest than will the repeated measures ANOVA approach (Dugard and Todman, 1995) 9

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Change model assumption violation (2 sweeps) 10

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Change model assumption OK (six sweeps) 11 Correlations r1r2r3r4r5r6 r1Pearson Correlation 1.000-0.002 0.023-0.002-0.003 Sig. (2-tailed) 0.0000.957 0.5490.9690.957 N 843680675674656347 r2Pearson Correlation -0.0021.000-0.0020.016 0.121 -0.039 Sig. (2-tailed) 0.9570.0000.9680.700 0.003 0.490 N 680 610606 591 315 r3Pearson Correlation -0.002 1.0000.047-0.002-0.003 Sig. (2-tailed) 0.9570.9680.0000.2370.9680.955 N 675610675622603316 r4Pearson Correlation 0.0230.0160.0471.000-0.0190.065 Sig. (2-tailed) 0.5490.7000.2370.0000.6360.237 N 674606622674612331 r5Pearson Correlation -0.002 0.121 -0.002-0.0191.000-0.003 Sig. (2-tailed) 0.969 0.003 0.9680.6360.0000.956 N 656 591 603612656321 r6Pearson Correlation -0.003-0.039-0.0030.065-0.0031.000 Sig. (2-tailed) 0.9570.4900.9550.2370.9560.000 N 347315316331321347

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Measurement error problematic 12

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Measurement error problematic 13

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Measurement error not a problem 14

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A better repeated measures model 15

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A (slightly) better conditional model 16

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Conclusion No consensus but it is probably safer to use a conditional model for a pre-test post-test design Designs with three or more sweeps will benefit from a repeated measures multi- level model Care with level 1 residual autocorrelation Try a few models and check assumptions Don’t get hung up on significance 17

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Questions and advice 18

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Acknowlegements Pearson Business in the Community and Queen’s University, Belfast Tom Benton Dougal Hutchison NFER 19

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