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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 scoreConstant *** Intervention NS Pre-test score ***

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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 scoreConstant *** Time *** Intervention NS Time*intervention *

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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 *** Time ** Intervention NS Time*intervention *

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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 Sig. (2-tailed) N r2Pearson Correlation Sig. (2-tailed) N r3Pearson Correlation Sig. (2-tailed) N r4Pearson Correlation Sig. (2-tailed) N r5Pearson Correlation Sig. (2-tailed) N r6Pearson Correlation Sig. (2-tailed) N

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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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