Meta-analytic structural equation modeling with group data Navigating the maze of d-to-r conversions

The central question of this dissertation was whether and how group data from two groups can be included in meta-analytic structural equation modeling (MASEM). Substantive researchers have raised this issue, and the aim of this dissertation was to address this methodological challenge and provide advice and support to those researchers. Including data from two groups in MASEM poses challenges because the primary studies that investigate such data typically report standardized mean differences (e.g., Cohen's d or Hedges' g), while MASEM generally uses correlations as input. This challenge can be solved by converting standardized mean differences into correlations. However, one can convert to different kinds of correlation coefficients (i.e., biserial or point-biserial correlation) and can apply different conversion formulas. In this dissertation, I outline the decisions a meta-analyst needs to make when incorporating data from two groups into MASEM, specifically regarding which conversion to apply for converting a standardized mean difference to either a point-biserial or biserial correlation. I showed that if one wants to include a dichotomized variable in MASEM and one converts the standardized mean difference to a biserial correlation, this yields unbiased MASEM parameters. On the other hand, if one wants to include a dichotomous variable in MASEM, one should convert the standardized mean difference to a point-biserial correlation. In this dissertation, I demonstrated that which conversion to use depends on the aim of the meta-analyst. Moreover, whether all relationships in the MASEM model are estimated accurately also depends on the research designs of the primary studies, as an additional adjustment to the relationships between continuous variables in the MASEM model is required in some scenarios. To assist meta-analysts in applying the various conversion formulas I recommend in this dissertation, I developed a freely available web application entitled the Effect Size Calculator and Converter (ESCACO; hdejonge.shinyapps.io/ESCACO).