The Least Biased d to r_pb-r_pb to d Conversion Formula Combinations for the Meta-Analysis of Studies Using the Two...

In a meta-analysis of ds, the utility of converting d to a point-biserial correlation (r_pb), correcting r_pb for study artifacts, and then converting r_pb back to d depends on how accurately the d to r_pb-r_pb to d (dr-rd) method reproduces the original uncorrected ds. This study compared test ds (d_t) converted to dr-rd ds to control ds (d_c) to determine the dr-rd formula combinations with the least bias, defined as the difference between dr-rd ds and d_c. d_t were calculated with available conversion and r_pb correction formulas at various base rates and SD ratios, whereas d_c were calculated without conversion formulas at base rate .50 and SD ratio 1.00. Results showed that the lowest bias formula combinations reproduced d_c at SD ratio 1.00, bias increased as SD ratio decreased, and formula combinations that produced the lowest bias values were, on average, more accurate than formula combinations that produced the next to lowest bias values. Findings provide the lowest bias dr-rd formula combinations for artifact-corrected meta-analyses of studies using the two independent-groups design.