Transcript META-ANALYSIS OF RESEARCH

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
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excel program “Outcomes Computation correlations”
The next slide gives an example.
Emphasis is on disaggregating effects of unreliability
and sample-based attenuation, and correcting samplespecific 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
reliabiltiy
Ne
Nc
N
r
r corrected
s(r )
Nr
N*(r-rmean)
reliabiltiy
1
1
0.80
0.77
47
76
123
0.352646
0.351381
0.079277
43.21983
-5.1631
2
1
0.70
0.80
33
55
88
0.323444
0.32178
0.095995
28.31665
-6.26369
3
1
0.75
0.90
22
45
67
0.190571
0.18918
0.118621
12.67504
-13.6715
4
1
0.88
0.70
111
111
222
0.67
0.669165
0.037071
148.5545
61.13375
5
1
0.77
0.85
34
34
68
0.169989
0.168757
0.118639
11.47548
-15.2751
6
1
0.90
0.78
47
45
92
0.177133
0.17619
0.101539
16.20946
-20.0091
N(r-rmean)
W(rdisrdismean)
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# x alpha
1
2
3
4
5
6
y alpha
Ne
Nc
reliabilti
reliabiltiy y
1
0.80
0.77 47 76
1
0.70
0.80 33 55
1
0.75
0.90 22 45
1
0.88
0.70 111 111
0.77
0.85 34 34
1
0.90
0.78 47 45
1
W(rdisN(r-rmean) rdismean)
0.229994 3.358562
0.4669327 2.484647
2.8278586
16.732861
3.4690402
4.389591
7.770396
21.54429
8.371607
12.18353
Q=
28.116277 55.71303
p(Q)=
3.454E-05 9.31E-11
Qdis=
55.713032
p(Q)=
9.311E-11
N
disattenuate
dr
Ndisr
r
123
88
67
222
68
92
r(mean)=
rdis(mean)=
Var(rmean
)=
s(rmean)=
0.352646
0.323444
0.190571
0.67
0.169989
0.177133
0.394623
0.634424
0.001138
0.033739
s(emean)=
0.080498
s(edismean)
=
0.449313
0.432221
0.231956
0.853659
0.210119
0.211412
55.26549
38.03544
15.54103
189.5123
14.28811
19.44991
s(edis)
0.101008
0.128279
0.144381
0.047233
0.146647
0.12119
wdis
98.01415
60.76996
47.97109
448.2416
46.50003
68.08759
r*w
44.03903
26.26604
11.12716
382.6455
9.770554
14.39454
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
Weight Functions
 For sample size correction, use N
 For disattenuated correlations, use
 w = (1/sr2)/xy
 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