This study investigates the estimation of mediated effects through statistical simulations. The authors compared various approximate solutions for the point and variance estimators of the mediated effect, the ratio of the mediated to the direct effect, and the proportion of the total effect that is mediated. The simulations involved 500 replications of three normally distributed variables for eight sample sizes (10, 25, 50, 100, 500, 1000, and 5000) and 64 parameter value combinations. The results showed that the point estimates of the mediated effect had minimal bias for all sample sizes, while the estimates of the ratio and proportion were less accurate, especially for small sample sizes. The standard error estimators for the mediated effect were generally similar across sample sizes, except for the binary independent variable case, where one estimator was significantly larger than the true standard error. The ratio and proportion point estimates did not stabilize until sample sizes of at least 500 and 5000, respectively. The study also found that the second-order Taylor series solutions performed better than first-order approximations, and that the standard errors of the proportion mediated were more stable than those of the ratio. The findings have implications for the estimation of mediated effects in both experimental and non-experimental studies.This study investigates the estimation of mediated effects through statistical simulations. The authors compared various approximate solutions for the point and variance estimators of the mediated effect, the ratio of the mediated to the direct effect, and the proportion of the total effect that is mediated. The simulations involved 500 replications of three normally distributed variables for eight sample sizes (10, 25, 50, 100, 500, 1000, and 5000) and 64 parameter value combinations. The results showed that the point estimates of the mediated effect had minimal bias for all sample sizes, while the estimates of the ratio and proportion were less accurate, especially for small sample sizes. The standard error estimators for the mediated effect were generally similar across sample sizes, except for the binary independent variable case, where one estimator was significantly larger than the true standard error. The ratio and proportion point estimates did not stabilize until sample sizes of at least 500 and 5000, respectively. The study also found that the second-order Taylor series solutions performed better than first-order approximations, and that the standard errors of the proportion mediated were more stable than those of the ratio. The findings have implications for the estimation of mediated effects in both experimental and non-experimental studies.