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Why Meta-Analysis?
Mata Hari, notMeta-Analysis
Slide 15.1
1. When Narrative Literature Reviewers Have Drawn Conflicting Conclusions
2.When There are Many Studies
3.When It Is Desired to Synthesize Study Results Across Different Samples and Materials.
Meta-Analysis Purposes
Slide 15.2
1. Summarizing available data.
2. Explaining the variability among different studies.
Steps in Completing a Meta-Analysis
Slide 15.3A
Sampling Quantitative
Studies
Steps in Completing a Meta-Analysis
Code EssentialStudy Differences
in Studies and ComputeEffect Sizes
from Studies
Slide 15.3B
Sampling Quantitative
Studies
Steps in Completing a Meta-Analysis
Code EssentialStudy Differences
in Studies and ComputeEffect Sizes
from Studies
If fail-safe number < 5NL + 10, collect additional studies
Slide 15.3C
ComputeFail-Safe Number
Sampling Quantitative
Studies
Steps in Completing a Meta-Analysis
Code EssentialStudy Differences
in Studies and ComputeEffect Sizes
from Studies
If fail-safe number < 5NL + 10, collect additional studies
ComputeMean Effect
Size
Slide 15.3D
ComputeFail-Safe Number
Sampling Quantitative
Studies
Steps in Completing a Meta-Analysis
Code EssentialStudy Differences
in Studies and ComputeEffect Sizes
from Studies
If fail-safe number < 5NL + 10, collect additional studies
ComputeMean Effect
Size
ComputeDiffuse
Comparison
Slide 15.3E
ComputeFail-Safe Number
Sampling Quantitative
Studies
Steps in Completing a Meta-Analysis
Code EssentialStudy Differences
in Studies and ComputeEffect Sizes
from Studies
If fail-safe number < 5NL + 10, collect additional studies
ComputeMean Effect
Size
ComputeDiffuse
Comparison
Slide 15.3F
Compute (additional)Focused
Comparisons
ComputeFail-Safe Number
Sampling Quantitative
Studies
If diffuse comparison statistically significant
Steps in Completing a Meta-Analysis
Code EssentialStudy Differences
in Studies and ComputeEffect Sizes
from Studies
If fail-safe number < 5NL + 10, collect additional studies
ComputeMean Effect
Size
ComputeDiffuse
Comparison If diffuse comparison statistically significant
Conclude If diffuse comparison not statistically significant
Slide 15.3
Compute (additional)Focused
Comparisons
ComputeFail-Safe Number
Sampling Quantitative
Studies
Criteria for Including Studies
• Make sure the studies meet the assumptions underlying the use of meta-analysis:– Empirical studies only– Studies must include clear information about:
» final sample sizes» actual effect sizes—or there must be access to all the
coefficients necessary to compute the effect sizes» reliability for measured variables.
• The number of studies drawn from a single article or research report should not be too great. Usually no more than two or three studies from the same research article or report.
• Studies should be excluded if they are radically different from others.
Slide 15.4
Transforming a Fisher’s Z Back into a Correlations
• To transform a ZFisher back to an untransformed correlation, the following formula is used:
Slide 15.6A
1
12
2
FisherZ
FisherZ
e
er
The Diffuse Test
Slide 15.7A
jFisherZ
FisherZ
is the is the Fisher Z for the effect from study j,
is the mean Fisher Z score, andk is the number of effects analyzed.
Applying the data from the study, the following computation is revealed:
221 *3 FisherjFisherjk ZZn , where
n is the number of events in study j,
Focused Comparison 1:The Number of Variables in the Study
Slide 15.10A
3
2
j
j
Fisherj
n
ZZ j
Computing a “Fail-Safe” Number
Slide 15.14A
Lp
j Nz
ZX
2
2
Computing a “Fail-Safe” Number
Slide 15.14B
, where
• Zj is (Zrj * ) [the Fisher’s Z transformation of correlations (r) for each (j) study included in the meta-analysis multiplied by , where Nj is the sample size of each (j) study];
L
p
j Nz
ZX
2
2
3-N j
3-N j
Computing a “Fail-Safe” Number
Slide 15.14C
, where
• Zj is (Zrj * ) [the Fisher’s Z transformation of correlations (r) for each (j) study included in the meta-analysis multiplied by , where Nj is the sample size of each (j) study];• is the square of the z value the corresponds to the one- tailed probability level of the significance tests. Since p is commonly .05, the one-tailed z score including all but the last 5% of the area under the standard normal curve is 1.645
L
p
j Nz
ZX
2
2
3-N j
3-N j
2pz
Computing a “Fail-Safe” Number
Slide 15.14
, where
• Zj is (Zrj * ) [the Fisher’s Z transformation of correlations (r) for each (j) study included in the meta-analysis multiplied by , where Nj is the sample size of each (j) study];• is the square of the z value the corresponds to the one- tailed probability level of the significance tests. Since p is commonly .05, the one-tailed z score including all but the last 5% of the area under the standard normal curve is 1.645 • NL is the number of studies located for use in the meta- analysis.
L
p
j Nz
ZX
2
2
3-N j
3-N j
2pz
