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Term 3, 2008Bio753 Advanced Methods III1 Weighted Means and RE models

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Term 3, 2008Bio753 Advanced Methods III9 INFERENCE SPACE (Sanders) The choice between fixed and random effects depends in part on the reference population (the inference space) –These studies or people – Studies or people like these –

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Term 3, 2008Bio753 Advanced Methods III10 Random Effects should replace “unit of analysis” Models contain Fixed-effects, Random effects (via Variance Components) and other correlation- inducers There are many “units” and so in effect no single set of units Random Effects induce unexplained (co)variance Some of the unexplained may be explicable by including additional covariates MLMs are one way to induce a structure and estimate the REs

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Term 3, 2008Bio753 Advanced Methods III11 ACCOUNTING FOR (explaining) UNEXPLAINED VARIABILITY Including regressors can explain (account for) some of unexplained variability Doing so is always a trade-off in that you need to use degrees of freedom to do the explaining Going too far--adding too many regressors-- inflates residual variability In MLMs there is variance at various levels that can potentially be taken into account

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Term 3, 2008Bio753 Advanced Methods III12 TEACHER EXPECTANCY TEACHER EXPECTANCY (data are in “Datasets” ) Data are from a Raudenbush & Bryk meta-analysis of 19 studies (see Cooper and Hedges,1994) Effect size k = distance between treatment and control group means measured in population standard deviation units SE k = the standard error of the effect size Weeks k = estimated weeks of teacher-student contact prior to expectancy induction

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Term 3, 2008Bio753 Advanced Methods III13 TEACHER EXPECTANCY TEACHER EXPECTANCY (continued) Each study consisted of either telling teachers that a student had great potential or not All students received a pre-test and a post-test Teachers evaluated progress A positive effect size indicates that the teachers rated students who were “likely to improve” as having improved more than the control group A negative slope on “Weeks” indicates that the more a teacher got to know a student before the experiment,the less the influence of the expectancy intervention

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