EPSY 642- LECTURE 6Meta Analysis

FALL 2009Victor L. Willson, Instructor

Computing Correlation Effect SizesReported Pearson correlation- use thatRegression 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 SizesTo 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 reliabiltiy                1 1 0.80 0.77 47 76 123 0.352646 0.351381 0.079277 43.21983 -5.16312 1 0.70 0.80 33 55 88 0.323444 0.32178 0.095995 28.31665 -6.263693 1 0.75 0.90 22 45 67 0.190571 0.18918 0.118621 12.67504 -13.67154 1 0.88 0.70 111 111 222 0.67 0.669165 0.037071 148.5545 61.133755 1 0.77 0.85 34 34 68 0.169989 0.168757 0.118639 11.47548 -15.27516 1 0.90 0.78 47 45 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 12 13 14 15 16 1

x alpha y alpha Ne Nc N r

reliabiltiyreliabiltiy        

0.80 0.77 47 76 123 0.3526460.70 0.80 33 55 88 0.3234440.75 0.90 22 45 67 0.1905710.88 0.70 111 111 222 0.670.77 0.85 34 34 68 0.1699890.90 0.78 47 45 92 0.177133

disattenuated r Ndisr s(edis) wdis

      r*w0.449313 55.26549 0.101008 98.01415 44.039030.432221 38.03544 0.128279 60.76996 26.266040.231956 15.54103 0.144381 47.97109 11.127160.853659 189.5123 0.047233 448.2416 382.64550.210119 14.28811 0.146647 46.50003 9.7705540.211412 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

p(Q)= 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 FunctionsFor sample size correction, use N

For disattenuated correlations, usew = (1/sr

2)/xy

Where sr2 = (1-r2)/(N-1)

Mediator AnalysisUse SPSS Regression analysis as with effect

size analysis, with WLS, put in appropriate weight function as N or w