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Weighted MeansWeighted Meansand RE modelsand RE models

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INFERENCE SPACEINFERENCE SPACE(Sanders)(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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Random Effects Random Effects should replace “unit of analysis”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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ACCOUNTING FOR ACCOUNTING FOR (explaining)(explaining)

UNEXPLAINED VARIABILITYUNEXPLAINED 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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TEACHER EXPECTANCYTEACHER EXPECTANCY(data are in “Datasets” )

Data are from a Raudenbush & Bryk meta-analysis of 19 studies (see Cooper and Hedges,1994)

Effect sizek = distance between treatment and control group means measured in population standard deviation units

SEk = the standard error of the effect size

Weeksk = estimated weeks of teacher-student contact prior to expectancy induction

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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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