Why Meta-Mar?

Meta-Mar is a free online meta-analysis service developed as an adjunctive tool for running a full meta-analysis (including meta-regression and subgroup analysis) or can be used as a calculator/convertor of effect sizes!

  • Possibility of choosing the Data entry methods between manual Data entry or .xlsx upload.
  • Calculation of effect sizes based on SMD , Correlation and Ratios models for every single study.
  • Calculation of the overall effect size of the analysis based on fixed and random effect models.
  • Calculation of Fail-N Safe based on fixed and random effect models.
  • Calculation of heterogeneity of the analysis (Q Cochrane, I2 and Tau2).
  • Possibility of meta regression and subgroup analysis.
  • Visualization of Forest Plot and Funnel Plot.
  • Possibility of exporting the results of the analysis via a .xlsx file.
  • Finally and regardless of your analysis, you may just want to use an Effect Size Calculator

Start Your Analysis!

Or take a look at a solved example by Meta-Mar:

Download the results as an Excel file

Table.1 summary of studies

Study N1 Mean1 Sd1 N2 Mean2 Sd2 Moderator subgroup Cohen's d CorrectionFactor Hedges'g (SMD) SEg 95%CI-Lower 95%CI-Upper weight(%)-fixed model weight(%)-random model %
1 A 23 30 2.50 23 32 3.3 24 subgroup1 0.683187 0.982857 0.671475 0.298164 0.087074 1.255876 3.063359 9.703777
2 B 47 33 3.34 47 35 3.1 22 subgroup1 0.620687 0.991826 0.615613 0.209466 0.205059 1.026168 6.206951 9.982981
3 C 44 39 2.30 44 41 4.1 33 subgroup1 0.601657 0.991254 0.596395 0.216064 0.172908 1.019881 5.833654 9.965102
4 D 78 47 4.10 78 55 2.5 40 subgroup2 2.356000 0.995122 2.344508 0.207386 1.938030 2.750985 6.332079 9.988515
5 E 311 26 1.40 311 33 6.1 51 subgroup2 1.581744 0.998790 1.579830 0.091769 1.399962 1.759698 32.337834 10.214405
6 F 144 75 2.60 144 80 4.2 41 subgroup3 1.431496 0.997375 1.427739 0.131738 1.169531 1.685946 15.692129 10.155089
7 G 79 55 2.20 79 66 4.3 31 subgroup1 3.220700 0.995185 3.205191 0.239966 2.734859 3.675524 4.729433 9.896295
8 H 59 26 6.60 59 34 2.1 29 subgroup1 1.633504 0.993521 1.622919 0.211237 1.208896 2.036943 6.103360 9.978232
9 I 214 98 1.80 214 110 2.5 38 subgroup1 5.508878 0.998238 5.499173 0.211284 5.085056 5.913291 6.100603 9.978104
10 J 110 72 5.10 110 77 5.6 42 subgroup2 0.933561 0.996556 0.930345 0.141506 0.652994 1.207697 13.600598 10.137501

Table.2 Summary of results - fixed and random effect models
Hedges'g (SMD)
SEg
95%CI
z score
p value
Heterogeneity
Fixed Effect Model
1.69
0.05
[1.59,1.79]
32.377
0.0
I2=98.1%, Chi2=472.78, df=9
Random Effect Model
1.85
0.395
[1.074,2.623]
4.677
3e-06
I2=98.0%, Tau2=1.52

Figure.1 Forestplot - fixed and random effect models

Figure.2 Funnel Plot - fixed and random effect models

Table.3 Fail-N Safe

Bias of the analysis regarding the file-drawer problem:

Fail-N Safe, the number of studies (or samples) with a null effect (g = 0)
needed to bring the calculated significance level of the pooled effect (p value < 0.0001) near the critical significance level (p value = 0.05),
is calculated as follows:

References:
* Rosenberg, M. S. (2005). The file‐drawer problem revisited: a general weighted method for calculating fail‐safe numbers in meta‐analysis. Evolution, 59(2), 464-468.
* Rosenthal, R. (1979). The file drawer problem and tolerance for null results. Psychological bulletin, 86(3), 638.
Rosenthal (1979)
tc(α = 0.05, df = 10) = 1.812
Rosenberg (2005)
Zc(α = 0.05) = 1.645
Fail-N Safe
3756.07
3181.01

Table.4 Results of Meta regression

OLS Regression Results
Dep. Variable: y R-squared: 0.050
Model: OLS Adj. R-squared: -0.069
Method: Least Squares F-statistic: 0.4228
Date: Thu, 19 May 2022 Prob (F-statistic): 0.534
Time: 20:50:35 Log-Likelihood: -17.649
No. Observations: 10 AIC: 39.30
Df Residuals: 8 BIC: 39.90
Df Model: 1
Covariance Type: nonrobust
coef std err t P>|t| [0.025 0.975]
const 0.5062 2.125 0.238 0.818 -4.395 5.407
Moderator 0.0383 0.059 0.650 0.534 -0.097 0.174
Omnibus: 9.889 Durbin-Watson: 2.280
Prob(Omnibus): 0.007 Jarque-Bera (JB): 4.420
Skew: 1.515 Prob(JB): 0.110
Kurtosis: 4.194 Cond. No. 154.


Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

Table.5 Results of Subgroup Analysis - fixed and random effect models

fixed model
k Hedges's g SEg 95%CI lower 95%CI upper z score p value Heterogeneity % df
subgroup1 6 2.121569 0.092199 1.940860 2.302279 23.010814 3.632910e-117 98.770556 5
subgroup2 3 1.503470 0.072181 1.361994 1.644945 20.829051 2.360932e-96 94.037451 2
subgroup3 1 1.427739 0.131738 1.169531 1.685946 10.837672 2.282038e-27 0.000000 0
total 10 1.689609 0.052186 1.587324 1.791893 32.376697 5.842358e-230 98.096375 9

random model

k Hedges's g SEg 95%CI lower 95%CI upper z score p value Heterogeneity % df
subgroup1 6 2.036985 0.835576 0.399257 3.674714 2.437822 1.477604e-02 98.770556 5
subgroup2 3 1.601711 0.331891 0.951204 2.252218 4.826013 1.392938e-06 94.037451 2
subgroup3 1 1.427739 0.131738 1.169531 1.685946 10.837672 2.282038e-27 0.000000 0
total 10 1.848747 0.395247 1.074064 2.623430 4.677453 2.904607e-06 98.096375 9

Results of ANOVA for subgroups

F value = 0.09313109449240511, p value = 0.9121839700696838

Figure.3 Intervals of effect sizes for subgroups - fixed and random effect models

fixed model

random model