1. A meta-analysis systematically combines data from multiple studies to identify patterns among study results, increase statistical power, and resolve uncertainties in areas where individual studies may be too narrow. 2. Key steps include defining the question, reviewing literature and extracting data, computing effect sizes, determining average effect sizes and confidence intervals, and looking for associations that may explain variability among studies. 3. Factors like study quality and publication bias must be considered, as missing or unpublished studies could change conclusions. Meta-analyses aim to synthesize evidence from diverse studies and elucidate general patterns.

1. SARVESH KUMAR V. ATAL
2016
Meta-analysis

2. “If only we knew what we know…”
-Caria O’ Dell and Jack Grayson
“Anything you can do, I can do meta“
“Meta-Analysis, Shmeta-Analysis.”
-Shapiro 1994
What is a meta-analysis?

3.  An analysis of analyses: A set of methods to systematically and
reproducibly search, sample and (statistically) synthesize evidence
from studies.
What is a meta-analysis?

4. “To do science is to search for repeated patterns, not simply to accumulate
facts.”
-Robert McAuthur
“Meta-analysis has become an important tool in ecology for generalizing
trends across studies and revealing overall patterns, even when single
studies are too small or cover too narrow a range of conditions to detect an
effect”
-Stein et al. 2014

5. Why should we do meta-analyses?
1. Repetition: Many studies address the same or very similar issues and some collect similar
data to look at different things.
• Meta-analyses can quantitatively combine information from many studies that examine
the same question
2. Meta-analyses increases statistical power and reduce the rates of type II errors (but could
potentially increase type I errors relative – publication bias)
3. Can elucidate general patterns and associations that are not readily visible from one study

6. The Transylvania Effect:
Some studies showed abnormal human behavior and
psychiatric hospital admissions increased during full
moons
Aspirin and heart attacks
• 1984, 1994, 2000
Stein et al. 2014
“Environmental heterogeneity as a universal driver
of species richness across taxa, biomes and spatial
scales”

7. How to conduct a meta-analysis:
1. Define the question
2. Review the literature and data extraction
3. Compute effect sizes
4. Determine the average effect size
5. Calculate confidence intervals and test hypothesis
6. Look for effect of study quality
7. Look for associations and general patterns

8. Typical questions that a meta-analysis can address:
1. How strong is the effect we are studying?
2. Does the collection of studies reject a null hypothesis?
3. How variable is the effect and what factors can explain this
variability?
4. Is there any bias resulting from the publication of some studies and
not others?
5. Are there enough unpublished studies to change our conclusions?

10. Size matters: How broad is your question?
• Homogeneous vs Heterogeneous studies/data sets?
-Specific tests exist to determine what data you have and which
model you should use (woolf test)
• Fixed vs Random effect models

11. How to conduct a meta-analysis:
1. Define the question
2. Review the literature and data extraction
3. Compute effect sizes
4. Determine the average effect size
5. Calculate confidence intervals and test hypothesis
6. Look for effect of study quality
7. Look for associations and general patterns

12. Include all relevant studies without bias.
 Most difficult part of a meta-analysis
• Data can be hard to obtain
• Leads to what is called publication bias a.k.a
the “file-drawer problem”
• Data inequality
• a priori standards
• Weighted studies
• Depends on question

13. How to conduct a meta-analysis:
1. Define the question
2. Review the literature and data extraction
3. Compute effect sizes
4. Determine the average effect size
5. Calculate confidence intervals and test hypothesis
6. Look for effect of study quality
7. Look for associations and general patterns

14. Effect Size
The effect size is a standardized measure of the magnitude of the relationship
between two variables (e.g. X & Y)
• Odds ratio: Mantel-Haenszel test
• Correlation coefficient ( r )
• Standardized mean difference (SMD)

15. How to conduct a meta-analysis:
1. Define the question
2. Review the literature and data extraction
3. Compute effect sizes
4. Determine the average effect size
5. Calculate confidence intervals and test hypothesis
6. Look for effect of study quality
7. Look for associations and general patterns

16. • Weigh studies by quality/sample size and
calculate the weighted average
• Calculate confidence intervals and test the
hypothesis for your models
• Depends on type of model and effect size
• It is crucial that these results are interpreted in
the context of the studies used to calculate
them

17. How to conduct a meta-analysis:
1. Define the question
2. Review the literature and data extraction
3. Compute effect sizes
4. Determine the average effect size
5. Calculate confidence intervals and test hypothesis
6. Look for effect of study quality
7. Look for associations and general patterns

18. • Funnel plots
• Rosenberg’s fail-safe number
• Assume missing studies
fail to reject the null
hypothesis
• Calculate number of
missing studies needed to
change the conclusion

19. How to conduct a meta-analysis:
1. Define the question
2. Review the literature and data extraction
3. Compute effect sizes
4. Determine the average effect size
5. Calculate confidence intervals and test hypothesis
6. Look for effect of study quality
7. Look for associations and general patterns

20. Look for moderator
variables— variables
that can explain some of
the variation in effect
size.

21. How to make your paper meta-accessible?
1. Always give estimates of the sizes of the effects and provide their
standard errors
2. Give the values of your test statistics and the number of degrees of
freedom
3. Make the data accessible
• Publish raw data in the paper, supplemental information, or on
an online archive such as datadryad.org

22. Thanks for listening!
Questions?

23. References
1. Stein, A., Gerstner, K., & Kreft, H. (2014). Environmental
heterogeneity as a universal driver of species richness across taxa,
biomes and spatial scales. Ecology letters, 17(7), 866-880.
2. Whitlock, M. C., & Schluter, D. (2009). The analysis of biological data
(p. 700). Greenwood Village, Colorado: Roberts and Company
Publishers.
3. https://www.zoology.ubc.ca/~bio501/R/lectures/