The Least Biased d to r pb - r pb to d Conversion Formula Combinations for the Meta-Analysis of Studies Using the Two Independent-Groups Design

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