Report

Building Evidence in Education: Workshop for EEF evaluators 2nd June: York 6th June: London www.educationendowmentfoundation.org.uk The EEF by numbers 2,300 schools participating in projects 34 topics in the Toolkit 14 6,000 members of EEF team 500,000 pupils involved in EEF projects heads presented to since launch £210 16 m estimated spend over lifetime of the EEF 10 reports published independent evaluation teams 83 evaluations funded to date Session 1: Design Adapting Design Carole Torgerson (Durham) David Torgerson (York Trials Unit) Calculating effect sizes Adetayo Kasim (Durham) Calculating Effect Sizes for Cluster Randomized Trials Adetayo Kasim Main Points • Over estimation of effect size when CLUSTER LEVEL ANALYSIS is used. • Disconnection between hypothesis testing and effect size from MULTILEVEL MODELS Calculating Effect Size Calculating Effect Size • Cluster level analysis (CLA) - Two stage approach • Summarise data to cluster level • Calculate effect size using summarised data • Multilevel models (MLM) • Analyse pupils level data, but accounts for intra cluster correlation • Calculate effect size using WITHIN cluster variability Calculating Effect Size Illustration 1: Simulation study Calculating Effect Size Simulation 1: MEAN, SE and SD Value Mean SE SD Method MLM 0.41(0.4) 0.39(0.59) 0.41(0.75) 0.39(0.91) 0.4(1.11) 0.38(1.33) CLA 0.41(0.4) 0.39(0.59) 0.41(0.75) 0.39(0.91) 0.4(1.11) 0.38(1.33) MLM 0.43(0.06) 0.57(0.13) 0.73(0.18) 0.89(0.22) 1.07(0.27) 1.28(0.33) CLA 0.39(0.10) 0.56(0.14) 0.73(0.18) 0.89(0.22) 1.07(0.27) 1.28(0.33) MLM - W 1.98(0.15) 1.99(0.15) 1.99(0.15) 2.00(0.15) 1.99(0.15) 2.00(0.15) MLM - T 2.00(0.14) 2.10(0.16) 2.23(0.20) 2.38(0.24) 2.56(0.31) 2.80(0.39) CLA 0.62(0.15) 0.89(0.23) 1.15(0.29) 1.40(0.35) • MEAN(SD) from 10,000 simulated data 1.69(0.43) 2.03(0.52) Calculating Effect Size Simulation 2: Calculating effect size assuming within cluster variance Effect size 0.2 0.3 0.4 Method 0 0.1 0.2 0.3 0.4 0.5 MLM - W 0.20(0.20) 0.20(0.26) 0.21(0.30) 0.20(0.36) 0.2(0.42) 0.19(0.49) MLM - T 0.20(0.20) 0.18(0.23) 0.17(0.26) 0.15(0.28) 0.13(0.29) 0.11(0.28) CLA 0.64(0.69) 0.50(0.67) 0.43(0.68) 0.36(0.66) 0.31(0.67) 0.25(0.66) MLM - W 0.30(0.20) 0.3(0.25) 0.3(0.36) 0.3(0.42) 0.31(0.49) MLM - T 0.29(0.20) 0.28(0.23) 0.25(0.26) 0.22(0.28) 0.20(0.29) 0.17(0.29) CLA 0.95(0.72) 0.76(0.68) 0.63(0.69) 0.52(0.67) 0.46(0.67) 0.39(0.67) MLM - W 0.41(0.21) 0.40(0.40) 0.40(0.31) 0.40(0.36) 0.40(0.42) 0.40(0.50) MLM - T 0.39(0.20) 0.37(0.24) 0.34(0.26) 0.30(0.28) 0.26(0.29) 0.22(0.30) CLA 1.26(0.74) 1.00(0.72) 0.84(0.70) 0.71(0.69) 0.61(0.69) 0.52(0.67) • 0.3(0.30) MEAN(SD) of Hedges Effect Size from 10,000 simulated data Calculating Effect Size • Cluster level analysis may overestimates effect size when between variability is negligible and there is substantial variability within clusters • Effect sizes based on within cluster variance and total variance from multilevel model are comparable when between cluster variance is negligible • Using only within cluster variance could result in different conclusions based on effect sizes and hypothesis testing when there is a substantial variability between clusters Discussion Cluster level analysis OR Within cluster Variance from multilevel model OR Total variance from multilevel model ? References Tymms P., Merrell C. and Henderson B. (1997) The first year at school: a quantitative investigation of the attainment and progress of pupils. Educational research and Evaluation, 3(2), pp. 101 - 118 Larry V. Hedges (2007) Effect sizes in cluster-randomized designs. Journal of Educational and Behavioural Statistics, 32(4), pp. 341-370 A. Brand, M.T. Bradley, L.A. Best, G. Stoica (2008) Accuracy of effect size estimates from published psychological research. Perceptual and Motor Skills, 106 (2) (2008), pp. 645–649