Building Evidence in Education: Workshop for EEF evaluators 2 nd June: York 6 th June: London

The EEF by numbers 83 evaluations funded to date 2,300 schools participating in projects 34 topics in the Toolkit 16 independent evaluation teams 500,000 pupils involved in EEF projects 14 members of EEF team £210 m estimated spend over lifetime of the EEF 6,000 heads presented to since launch 10 reports published

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

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

ValueMethod Mean MLM0.41(0.4)0.39(0.59)0.41(0.75)0.39(0.91)0.4(1.11)0.38(1.33) CLA0.41(0.4)0.39(0.59)0.41(0.75)0.39(0.91)0.4(1.11)0.38(1.33) SE MLM0.43(0.06)0.57(0.13)0.73(0.18)0.89(0.22)1.07(0.27)1.28(0.33) CLA0.39(0.10)0.56(0.14)0.73(0.18)0.89(0.22)1.07(0.27)1.28(0.33) SD MLM - W1.98(0.15)1.99(0.15) 2.00(0.15)1.99(0.15)2.00(0.15) MLM - T2.00(0.14)2.10(0.16)2.23(0.20)2.38(0.24)2.56(0.31)2.80(0.39) CLA0.62(0.15)0.89(0.23)1.15(0.29)1.40(0.35)1.69(0.43)2.03(0.52) Calculating Effect Size Simulation 1: MEAN, SE and SD MEAN(SD) from 10,000 simulated data

Calculating Effect Size Simulation 2: Calculating effect size assuming within cluster variance Effect sizeMethod MLM - W0.20(0.20)0.20(0.26)0.21(0.30)0.20(0.36)0.2(0.42)0.19(0.49) MLM - T0.20(0.20)0.18(0.23)0.17(0.26)0.15(0.28)0.13(0.29)0.11(0.28) CLA0.64(0.69)0.50(0.67)0.43(0.68)0.36(0.66)0.31(0.67)0.25(0.66) 0.3 MLM - W0.30(0.20)0.3(0.25)0.3(0.30)0.3(0.36)0.3(0.42)0.31(0.49) MLM - T0.29(0.20)0.28(0.23)0.25(0.26)0.22(0.28)0.20(0.29)0.17(0.29) CLA0.95(0.72)0.76(0.68)0.63(0.69)0.52(0.67)0.46(0.67)0.39(0.67) 0.4 MLM - W0.41(0.21)0.40(0.40)0.40(0.31)0.40(0.36)0.40(0.42)0.40(0.50) MLM - T0.39(0.20)0.37(0.24)0.34(0.26)0.30(0.28)0.26(0.29)0.22(0.30) CLA1.26(0.74)1.00(0.72)0.84(0.70)0.71(0.69)0.61(0.69)0.52(0.67) 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 Total variance from multilevel model Cluster level analysis Within cluster Variance from multilevel model OR ?

References 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 Larry V. Hedges (2007) Effect sizes in cluster-randomized designs. Journal of Educational and Behavioural Statistics, 32(4), pp 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