A comparison of fixed and random effect models by the number of research in the meta-analysis studies with and without an outlier

Abstract

The purpose of this research was to compare the performances of the Fixed Effect Model (FEM) and the Random Effects Model (REM) in the meta-analysis studies conducted through 5, 10, 20 and 40 studies with an outlier and 4, 9, 19 and 39 studies without an outlier in terms of estimated common effect size, confidence interval coverage rate and heterogeneity measures. In this descriptive study, real data set consisting of different studies examining teachers’ emotional burnout in terms of gender were used and a total of 72 meta-analyses were performed with R program. The results indicated that REM was more advantageous when compared to FEM for the meta-analysis of data sets with an outlier. On the other hand, without an outlier, it was determined that the common effect size was generally estimated to be similar for all methods. Moreover, the increase in the number of studies included in the meta-analysis reduced the effect of the outlier on the effect size estimation and decreased the heterogeneity. When the examination of the confidence interval coverage accuracy rates of the meta-analysis methods was examined, it was concluded that the confidence intervals included the estimated effect sizes in all data sets and all methods. The findings of the current study showed that the methods used in meta-analysis studies with 20 or more studies were less affected by the outlier runs in the estimated common effect size.