Measuring effect sizes using manifest versus latent variables: consequences and implications for research

Abstract

Reporting of effect sizes allows the description of mean differences independently of sample size. In current research, these statistical values are usually calculated at the manifest level. Calculating effect sizes at the latent level within a structural equation model can, however, result in more valid, different and potentially higher estimates. Therefore, the manifest and latent estimation of different types of effect sizes in a large rehabilitation research data set were compared. The impact of the different methods for estimating effect sizes in subgroups generated by indication, sex and age was demonstrated. Calculations were conducted using data from a meta-analysis (N=5809) in which the subjective health status of patients in orthopedic (N=2386), cardiological (N=1976) and psychosomatic rehabilitation (N=1447) was measured. The results were standardized effect sizes between 0.03 and 1.44 and standardized response means between 0.05 and 1.31 for manifest variables and standardized effect sizes between 0.04 and 1.58 and standardized response means between 0.07 and 1.45 for latent variables. Thus, latent effect sizes were generally higher, although no specific factor for transforming manifest into latent effect sizes seems to exist. Although the computation of latent effect sizes does not necessarily yield higher estimates, it should nonetheless be carried out as a matter of routine.