# Impacts of Land-Use Change from Primary Forest to Farmland on the Storage of Soil Organic Carbon
## 2 Materials and Methods
### Meta Analysis  
In this study, weighted mean difference (\(MD\)) and response ratio (\(RR\)) were selected as the dependent variables of meta-analysis, and the calculation formula was as follows:  
\[MD=\mu_{e}-\mu_{c} \tag{3}\]  
\[RR=\frac{\mu_{e}}{\mu_{c}} \tag{4}\]  
In the formula, \(\mu_{c}\) and \(\mu_{e}\) represent the average SOC storage before and after LUC. The random effect model (REM) of the single-arm meta-analysis method module of Stata software (version 17.0) was used to achieve a series of operations such as effect size merging, drawing the funnel plot, and linear testing of the symmetry of the funnel plot, and the forest plot was drawn by Origin2022 software. REM was based on the NNHM framework: it was assumed that the meta-analysis included \(k\) = 1,\(\cdots\), \(N\) independent studies, where \(\theta_{k}\) is the true value of each independent study, \(y_{k}\), \(S_{k}\), and \(\tau^{2}\) are the estimated value, the standard deviation of the estimated value (\({S_{k}}^{2}\) was the variation of the true effect within the study), and the variation of the true effect between studies, and the total combined effect is \(\mu\). The model is divided into two layers. The first layer is the sampling model \(y_{k}\)-\(N\) (\(\theta_{k}\), \({S_{k}}^{2}\)), which assumes that \(y_{k}\) obeys the normal distribution of the unknown mean value \(\theta_{k}\) and the known standard deviation \(S_{k}\); the second layer is the parameter model \(\theta_{k}\)-\(N\) (\(\mu\), \(\tau^{2}\)), which assumes that \(\theta_{k}\) obeys the normal distribution of the mean value \(\mu\) and the standard deviation \(\tau\), where \(\mu\) is the main parameter of interest and the parameter to be estimated,and the heterogeneous parameter \(\tau\) is considered as the annoying parameter. Based on the frequency framework, the parameter \(\mu\) is estimated by the constrained maximum likelihood estimation parameter estimation method. For this study, \(MD\) and \(RR\) were the parameters to be estimated. It should be noted that \(RR\) should be logarithmized before merging, that is, the logarithm of \(RR\) ln(\(RR\)) = ln(\(\mu_{e}\)) - ln(\(\mu_{c}\)), in order to make it statistically significant. Assuming that \(\mu_{e}\) and \(\mu_{c}\) both approximately follow the normal distribution, and both are positive numbers, then the logarithm of the quotient approximately follows the normal distribution, and its mean value is the same as the true mean value of \(RR\). The specific calculation steps of the effect size in this study are as follows:  
1. Calculate the absolute change of SOC in each sample of a single study as follows: \[MD_{mi}=\mu_{e,mi}-\mu_{e,mi}\] (5) where \(m\) represents the \(i\)-th sample of the \(m\)-th study. 2. Calculate the mean of the absolute change in SOC of a single study as follows: \[MD_{m}=\sum\limits_{i=1}^{n}\frac{MD_{mi}}{n}\] (6) where \(n\) is the sample size of each study. 3. Calculate the variance of the absolute change in SOC of a single study (intra-study variance) as follows: \[SD_{m,within}^{2}=\sum\limits_{i=1}^{n}\frac{(MD_{mi}-MD_{m})^{2}}{n-1}\] (7) (iv) Calculate the standard error of the absolute change in SOC in a single study as follows: \[SE_{m,within}=\frac{SD_{m,within}}{\sqrt{n_{m}}}\] (8) (v) Estimate the variance between studies as follows: \[SD_{between}^{2}=\left(\frac{1}{k-1}\right)\sum\limits_{m=1}^{k}\left(MD_{m}- \overline{MD}\right)^{2}-\frac{1}{k}\sum\limits_{m=1}^{k}\frac{SD_{m,within }}{n_{m}}\] (9) where \(k\) is the number of included studies. 4.