1. EFFECTS AS CORRELATIONS
EPSY 642- LECTURE 6
Meta Analysis
FALL 2009
Victor L. Willson, Instructor

2. 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

3. 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

4. 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 2
0.70 33 55 88 3
0.75
0.90 22 45 67 4
0.88
111
222
0.67 5
0.85 34 68 6
0.78 92
N(r-rmean)
W(rdis-rdismean)
r(mean)=
rdis(mean)=
Var(rmean )=
s(rmean)=
s(emean)=
s(edismean)=
Q =
p(Q)=
E-05
9.31E-11

5. 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
0.70 33 55 88
0.75
0.90 22 45 67
0.88
111
222
0.67
0.85 34 68
0.78 92
disattenuated r
Ndisr
s(edis)
wdis
r*w
N(r-rmean)
W(rdis-rdismean)
r(mean)=
rdis(mean)=
Var(rmean )=
s(rmean)=
s(emean)=
s(edismean)=
Q =
p(Q)=
3.454E-05
9.31E-11
Qdis=
9.311E-11

6. Correcting correlations
r(corrected) = r*(1-r2)/(2N-2)
r(disattenuated) = r/sqrt(xy)
If only one reliability is reported, use that, assume other reliability is 1.0

7. Weight Functions For sample size correction, use N
For disattenuated correlations, use
w = (1/sr2)/xy
Where sr2 = (1-r2)/(N-1)

8. Mediator Analysis
Use SPSS Regression analysis as with effect size analysis, with WLS, put in appropriate weight function as N or w