EFFECTS AS CORRELATIONS EPSY 642- LECTURE 6 Meta Analysis FALL 2009 Victor L. Willson, Instructor
Computing Correlation Effect Sizes Reported Pearson correlation- use that Regression b-weight: use t-statistic reported, e = t*(1/NE + 1/NC )½ t-statistics: r = [ t2 / (t2 + dferror) ] ½ Sums of Squares from ANOVA or ANCOVA: r = (R2partial) ½ R2partial = SSTreatment/Sstotal Note: Partial ANOVA or ANCOVA results should be noted as such and compared with unadjusted effects
Computing Correlation Effect Sizes To compute correlation-based effects, you can use the excel program “Outcomes Computation correlations” The next slide gives an example. Emphasis is on disaggregating effects of unreliability and sample-based attenuation, and correcting sample-specific bias in correlation estimation For more information, see Hunter and Schmidt (2004): Methods of Meta-Analysis. Sage. Correlational meta-analyses have focused more on validity issues for particular tests vs. treatment or status effects using means
Computing Correlation Effects Example STUDY# OUTCOME# x alpha y alpha Ne Nc N r r corrected s(r ) Nr N*(r-rmean) reliabiltiy 1 0.80 0.77 47 76 123 0.352646 0.351381 0.079277 43.21983 -5.1631 2 0.70 33 55 88 0.323444 0.32178 0.095995 28.31665 -6.26369 3 0.75 0.90 22 45 67 0.190571 0.18918 0.118621 12.67504 -13.6715 4 0.88 111 222 0.67 0.669165 0.037071 148.5545 61.13375 5 0.85 34 68 0.169989 0.168757 0.118639 11.47548 -15.2751 6 0.78 92 0.177133 0.17619 0.101539 16.20946 -20.0091 N(r-rmean) W(rdis-rdismean) 0.229994041 3.358562 r(mean)= 0.394623 0.466932722 2.484647 rdis(mean)= 0.634424 2.827858564 7.770396 Var(rmean )= 0.001138 16.73286084 21.54429 s(rmean)= 0.033739 3.469040187 8.371607 4.389591025 12.18353 s(emean)= 0.080498 s(edismean)= Q = 28.11627737 55.71303 p(Q)= 3.45424E-05 9.31E-11
Computing Correlation Effects Example STUDY# OUTCOME# 1 2 3 4 5 6 x alpha y alpha Ne Nc N r reliabiltiy 0.80 0.77 47 76 123 0.352646 0.70 33 55 88 0.323444 0.75 0.90 22 45 67 0.190571 0.88 111 222 0.67 0.85 34 68 0.169989 0.78 92 0.177133 disattenuated r Ndisr s(edis) wdis r*w 0.449313 55.26549 0.101008 98.01415 44.03903 0.432221 38.03544 0.128279 60.76996 26.26604 0.231956 15.54103 0.144381 47.97109 11.12716 0.853659 189.5123 0.047233 448.2416 382.6455 0.210119 14.28811 0.146647 46.50003 9.770554 0.211412 19.44991 0.12119 68.08759 14.39454 N(r-rmean) W(rdis-rdismean) 0.229994 3.358562 r(mean)= 0.394623 0.4669327 2.484647 rdis(mean)= 0.634424 2.8278586 7.770396 Var(rmean )= 0.001138 16.732861 21.54429 s(rmean)= 0.033739 3.4690402 8.371607 4.389591 12.18353 s(emean)= 0.080498 s(edismean)= Q = 28.116277 55.71303 p(Q)= 3.454E-05 9.31E-11 Qdis= 55.713032 9.311E-11
Correcting correlations r(corrected) = r*(1-r2)/(2N-2) r(disattenuated) = r/sqrt(xy) If only one reliability is reported, use that, assume other reliability is 1.0
Weight Functions For sample size correction, use N For disattenuated correlations, use w = (1/sr2)/xy Where sr2 = (1-r2)/(N-1)
Mediator Analysis Use SPSS Regression analysis as with effect size analysis, with WLS, put in appropriate weight function as N or w