This presentation provides you with the introduction and applications of meta analysis. Several case studies are also discussed with their findings.

2. Master Seminar-II
Meta-Analysis in Agriculture
Aman Vasisht
PGS20AGR8404
Dept. of Agricultural Statistics
UNIVERSITY OF AGRICULTURAL SCIENCES, DHARWAD
COLLEGE OF AGRICULTURE, DHARWAD

3. OUTLINE
META-ANALYSIS
FORMAT & ASSUMPTIONS OF META-ANALYSIS
CONCEPTS OF META-ANALYSIS
CASE STUDIES
CONCLUSION
REFERENCES

4. What is Meta-Analysis?
• Analysis of Analyses
• An objective and quantitative methodology for synthesizing
previous studies and research on a particular topic into an overall
finding.
• Meta-Analysis allows us to collect, code, compare or combine
results from different studies and interpret using statistical
methods facilitating statistically guided decisions about the
strength of observed effects and the reliability of results across a
range of studies.

5. Why Meta-Analysis?
• To provide a summary effect of all previous studies.
The appeal of Meta analysis is that, it leads to effect combines all
the research on one topic into one large study with many studies.
• Overall conclusion of various studies.
• Strength of relationship between studies.
• Relative impact of independent variables.
• Tool for theory development.

6. STEP
I
STEP
II
STEP
III
STEP
IV
STEP
V
STEP
VI
Selecting
area of
interest
and
selecting
variables
Systematic
literature
review
Compile
the results
of these
studies in
a format
Converting
all statistics
to effect
sizes
Meta-
analysis
using
software
Reporting
results

7. STEP
I
STEP
II
STEP
III
STEP
IV
STEP
V
STEP
VI
Selecting
area of
interest
and
selecting
variables

8. STEP
I
STEP
II
STEP
III
STEP
IV
STEP
V
STEP
VI
Systematic
literature
review

9. STEP
I
STEP
II
STEP
III
STEP
IV
STEP
V
STEP
VI
Compile
the results
of these
studies in
a format

10. STEP
I
STEP
II
STEP
III
STEP
IV
STEP
V
STEP
VI
Converting
all statistics
to effect
sizes

11. STEP
I
STEP
II
STEP
III
STEP
IV
STEP
V
STEP
VI
Meta-
analysis
using
software

12. STEP
I
STEP
II
STEP
III
STEP
IV
STEP
V
STEP
VI
Reporting
results

13. STEP
I
STEP
II
STEP
III
STEP
IV
STEP
V
STEP
VI
Selecting
area of
interest
and
selecting
variables
Systematic
literature
review
Compile
the results
of these
studies in
a format
Converting
all statistics
to effect
sizes
Meta-
analysis
using
software
Reporting
results

14. Sr. No. Study (Year) N r
1 ABC 2011 40 0.5
2 DEF 2012 90 0.6
3 GHI 2013 250 0.4
4 IJK 2014 400 -0.2
5 LMN 2015 60 -0.3
Sample Format
Sr. No. Study (Year) n1 n2 x1 x2 sd1 sd2
1 ABC 2011
2 DEF 2012
3 GHI 2013
4 IJK 2014
5 LMN 2015

15. Sr. No. Study (Year) N r
1 ABC 2011 40 0.2
2 DEF 2012 90 0.5
3 GHI 2013 25 0.4
4 IJK 2014 400 0.2
5 LMN 2014 60 0.7
6 OPQ 2015 50 0.45
Example:
Huh! Statistics is boring just with theoretical formulas! I know
you can feel this too! Let’s learn Meta-Analysis practically on
Excel.

16. Output: Forest Plot
Study weights Confidence Interval
Prediction Interval
Summary Effect

17. Study N r
ABC 1989 40 0.5
DEF 1990 90 0.6
GHI 1991 250 0.4
IJK 1992 400 0.48
LMN 1993 60 0.35
Study N r
ABC 1989 40 0.5
DEF 1990 90 0.6
GHI 1991 250 0.4
IJK 1992 400 -0.2
LMN 1993 60 -0.3

18. Concepts in Meta-Analysis

19. Concepts in Meta-Analysis
Summary Effect
1
Fixed Effect / Random Effect
2
Heterogeneity – Identification and Quantification
3
Confidence Intervals vs Prediction Intervals
4
Subgroup Analysis
5
Meta Regression
6

20. Assumptions
• An effect is precisely defined, i.e. an independent as well as a
dependent variable are defined, and all studies in the Meta - Analysis
are empirical studies of that effect.
• The type of unit or object in which this effect might occur is
specified e.g., persons, countries, teams specific types of
organizational units) and the domain for which the effect will be
meta-analyzed is clearly delimited.
• Effect size measures in these studies are comparable. Specifically,

21. • Usually the set of studies that are meta-analyzed are not complete
because some studies have not been published. This is a
problematic assumption..
• All studies are methodologically sound, i.e., data have been
collected from a complete probability sample of a defined
population, measurement has been valid and reliable, and the
statistical analysis has been adequate.
• Assuming that the researcher’s aim is to synthesize empirical
results about the effect in a domain, all empirical studies of the
effect in that domain should have been identified.
Assumptions

22. Types of Effects
Fixed Effect Random Effect
• Here we assume that there is one
true effect size (hence the term
fixed effect) which underlies all
the studies in the analysis, and
that all differences in observed
effects are due to sampling error.
• No Generalization
• Used rarely and not recommended.
• Here we allow that the true effect
could vary from study to study. If
it were possible to perform an
infinite number of studies, the true
effect sizes for these studies would
be distributed about some mean.
• Purpose is Generalization
• Used frequently and recommended.

23. Measures of Heterogeneity
• Q-statistic (also referred to as Cochrane’s Q)- It is only a measure of
variation around the average and is not yet a measure of heterogeneity.
• I2 - Proportion of observed variance that reflects real differences in effect
size-expressed as a percentage with a range from 0 to 100%.
• τ2 - Estimate of the variance of the true effect sizes-used to assign weights
to the studies assuming Random Effect.
• Tau (τ) - Estimate of the standard deviation of the distribution of true
effect sizes- used for computing the prediction interval.
Too many formulas.. Let’s go to excel to understand
heterogeneity better

24. Factors affecting Measures of Dispersions
Range of possible
values
Depends on number of
studies
Depends on scale
Q 1 ≤ Q 
p 0 ≤ p ≤ 1 
T2 0 ≤ T2 
T 0 ≤ T 
I2 0% ≤ I2 ≤ 100%

25. Confidence Interval vs Prediction Interval
• The confidence interval quantifies the accuracy of the mean, i.e. 95% of
cases the mean effect size falls inside the horizontal black lines.
• Prediction interval addresses the actual dispersion of effect sizes, i.e. 95%
of cases the true effect in a new study will fall inside the horizontal green
lines

26. Confidence Interval vs Prediction Interval
• The confidence interval quantifies the accuracy of the mean, i.e. 95% of
cases the mean effect size falls inside the horizontal black lines.
• Prediction interval addresses the actual dispersion of effect sizes, i.e. 95%
of cases the true effect in a new study will fall inside the horizontal green
lines

27. Confidence Interval vs Prediction Interval
• The confidence interval quantifies the accuracy of the mean, i.e. 95% of
cases the mean effect size falls inside the horizontal black lines.
• Prediction interval addresses the actual dispersion of effect sizes, i.e. 95%
of cases the true effect in a new study will fall inside the horizontal green
lines
Confidence Interval
Prediction Interval

28. Sub-Group Analysis (Non-Metric Moderation)
• When we are working with a single set of studies the effect analysis
assumes that all studies share a common effect size
• When we are working with subgroups, it assumes that all studies within a
subgroup share a common effect size.
• It is determined by I2

29. Sub-Group Analysis (Non-Metric Moderation)
• When we are working with a single set of studies the effect analysis assumes that all
studies share a common effect size
• When we are working with subgroups, it assumes that all studies within a subgroup
share a common effect size.
• It is determined by I2
Study N r
1. ABC 1989 40 0.5
2. DEF 1990 90 0.6
3. GHI 1991 250 0.4
4. IJK 1992 400 -0.2
5. LMN 1993 60 -0.3
Heterogeneity
Q 78.58
p 0.000
I2 94.91%
T2 0.24
T 0.49
Mod
A
A
A
B
B

30. A
B

31. Meta Regression (Metric Moderation)
• When we are working with a single set of studies the effect analysis assumes
that all studies share a common effect size.
• When we are working with meta-regression, it assumes that all studies
which have the same values on the covariates share a common effect
size.

32. Meta Regression (Metric Moderation)
Sr. No. Study r N Moderator
1 ABC 2007 0.5 40 25
2 DEF 2007 0.6 90 32
3 GHI 2009 0.4 25 28
4 IJK 2011 0.2 400 40
5 LMN 2012 -0.4 60 62
6 OPQ 2014 -0.45 50 73
7 RST 2015 -0.3 100 68
Heterogeneity
Q 92.05
p 0.000
I2 93.48%
T2 0.17
T 0.42
Combined effect size 0.09
R2 91.06%

33. Effect Size
• Discovering Statistics using SPSS by Andy Field (2013)
explains:
 Just because a test is significant does not mean that it is
important.
 When we measure the size of an effect it is known as
effect size.
 An effect size is simply an objective and (usually)
standardized measure of the magnitude of observed
effect.

34. Effect Size
• An effect size is a Quantitative measure of the magnitude of a
phenomenon.
• For most types of Effect size, a larger absolute value always indicated
stronger effect (Except odds ratio).
• Effect sizes complement statistical hypothesis testing and play an
important role in Power Analysis, Sample Size Planning and in Meta-
Analysis.

35. Types of Effect Size
1. Correlation
family
Correlation
coefficient
Coefficient of
determination (R2)
Eta-squared (ƞ2) Omega-squared
(ω2)
Cohen’s f2
Cohen’s q
Used in ANOVA
Effect sizes based
on “variance
explained”

36. 2. Difference
family
Cohen’s d Glass ∆ Hedge’s d 𝜓, root-
mean-square
standardized
effect
Other
metrics
Effect sizes based on
differences between
means

37. Categorical
family
Cohen’s w Odd ratio
Relative
risk
Cohen’s h
Risk
difference
Effect sizes for
associations among
categorical variables
Interpretation of Effect size:
According to Cohen (1992)
• r = 0.10 (small effect): In this case the effect explains 1% of the total variance.
• r = 0.30 (medium effect): The effect accounts for 9% of the total variance.
• r = 0.50 (large effect): The effect accounts for 25% of the variance.

38. Formula of Effect Size
Statistics Formula
Correlation r
Independent sample t-test
Paired t-test
Statistics: ANOVA Formula
Eta squared (ƞ2)
Omega squared (ω2)
Cohen’s f2
Again the same
thing…With formulas I
get confused. Show me
in excel with an
example
Effect Size

39. CASE STUDY-1:
Arbuscular mycorrhizal fungi and antioxidant enzymes
in ameliorating drought stress: a meta-analysis
Chandrasekaran M and Paramasivan M (2022)

40. Data Source
• Study period: Till 2022 year
• Source: Google Scholar and Web of Science.
• Methodology: Sub-group Meta-Analysis
• Sub-groups : SOD: Superoxide dismutase, CAT: Catalase, POD: Peroxidase,
PPO: Polyphenol peroxidase, APX: Ascorbate peroxidase, GR: Glutathione
reductase, H2O2: Hydrogen peroxide
• Sub-sub groups : Mild (60-80%), Moderate (40-60%) and Severe (0-40%)
based on field capacity.
• Effect size: Response ratio:
ln R = ln
𝑋𝑖
𝑋𝑐
Where, Xi : AMF (Arbuscular mycorrhizal fungi) inoculated plants
(Treatment)
Xj : Without AMF inoculation (control)

41. Studies identified:
700
Considered: 262
Study excluded:
202
Final studies for
Meta-Analysis: 60
with 505
observations
Results:
AMF inoculation increased
the drought stress alleviation
by 17% more than non-
AMF inoculations.
AMF inoculated plants
significantly reduced the
H2O2 by 20%.
No significant effect for GR
and PPO (11% & 13%,
respectively).
SOD enzyme activity increased
significantly by 32% for AMF
compared to non-AMF

42. • AMF inoc. increased H2O2 by 1% at mild, decreased by 24% & 25% at moderate and severe, respectively.
• It showed a linear relationship between drought stress and CAT activity in AMF inoculated plants.
• Similar increased linear relationship was seen in APX activity but decreasing linear relationship in POD
activity.

43. Conclusion of Case Study :
• The Meta-Analysis results showed noticeable up-regulation of the
antioxidant enzyme system (SOD, CAT, POD, and APX) in AMF-
inoculated plants.
• Thereby mediating alleviation of oxidative stress effects of drought stress
through the removal of H2O2.
• Therefore, the necessity to apply eco-friendly approaches, such as AMF-
based bio fertilization is of great importance for agriculture and the
environment.
• Based on enzymatic activities, the effects of drought stress alleviation were
varying with the intensity of drought stress, which were found to be much
more important in predicting plant responses to drought stress than other
variables.

44. CASE STUDY-2:
Realizing the potential of a low-cost technology to
enhance crop yields: evidence from a meta-analysis of
biofertilizers in India
Praveen K V and A Singh (2019)

45. Data Source
Studies
identified:
16700
Study titles
screened:
16700
Study
excluded:
16464
Study
abstracts
screened:
236
Final
studies for
Meta-
Analysis:
18
• Study period: 2000 to 2019 year.
• Source: Google Scholar and Consortium of E-Resources in Agriculture (CeRA).
• Methodology: Sub-group Meta-Analysis, Meta regression.
• Sub-groups: Nitrogen fixing biofertilizer, Phosphate solubilizing
biofertilizers, Combined, VAM, Others.
• Moderators: Organic Carbon (%), pH, Total N (kg/ha), Total P (kg/ha).

46. Forest plot for the effect of different biofertilizer categories on crop yield

51. Meta Regression

53. • The analysis suggests that biofertilizer use improves overall yield by 1.59
tonnes per ha.
• The biofertilizers perform better in soils with low pH values, high organic
carbon and low total nitrogen and phosphorus.
• The government must amend the regulatory system to improve the quality
of biofertilizers, and make it easier for farmers to benefit from government
support schemes.
• The government needs to encourage the sector to raise production and
make biofertilizers an integral part of agriculture practices because the
current production is insufficient, even though it has grown rapidly in
recent years.
Conclusion of Case Study :

54. CASE STUDY-3:
Comparing the Grain Yields of Direct-Seeded
and Transplanted Rice: A Meta-Analysis
Xu Le et al. (2020)

55. Data Source
• Study period: 1970 to 2017 year.
• Source: Google Scholar and Web of Science.
• Crops: Comparison of direct seeded rice (DSR) and transplanted rice (TPR)
• Methodology: Sub-group Meta-Analysis
• Sub-groups 1: Properties of soil, weed management, tillage and water
management practices.
• Study collected: 53
• Observations used: 440 paired observations
• Effect size: Response ratio:
ln R = ln
𝑋𝐷𝑆𝑅
𝑋𝑇𝑃𝑅
Where, XDSR is mean yield of DSR and XTPR is mean yield of TPR

56. Results:
DSR yield was 12% lower
than TPR yield on an
average. CI of 13% to 10%
DSR had 7% more panicle
per m2 compared to TPR
Non-significant results

57. Sub-groups

58. * Significant at 0.05, ** Significant at 0.01, *** Significant at 0.001

59. Conclusion of Case Study :
• The meta-analysis indicated that DSR yield was 12% lower than that of TPR
on an average.
• The lower yield of DSR might result from the reduction in spikelet per panicle
and grain weight.
• Weed management, climatic stress and seeding method were the major
contributing factors for the change in yield of DSR from TPR.
• To obtain a comparable yield with TPR, an integrated package of management
technologies should be applied to deal with the major constraints of DSR.
• These results suggest that DSR is a promising alternative planting system in
the face of looming global water scarcity and labour shortages, but more effort
should be made to implement appropriate management strategies and breeding
innovations.

60. • A Meta-Analysis uses a statistical approach to combine the results to
increase power (over individual studies), improve estimates of the size of the
effect and/or to resolve uncertainty when reports disagree.
• The most important part of Meta-Analysis is systematic review of literature
as publication bias also plays a major role.
• Now, Meta-Analysis is being considered as one of the solid statistical
methods in agriculture.
• Although in cross-sectional agricultural researches there are difficulties due
to different environmental conditions, yet Meta-Analysis has become an
inevitable method, as it can serve as a summary or base for data and results
that can help determine researcher’s path.
Conclusion: