Transforming intraclass correlation coefficients with the Spearman–Brown formula

Objectives De Vet, Mokkink, Mosmuller, and Terwee (2017) discovered that the Spearman–Brown formula (SB formula) can be used to transform certain intraclass correlation coefficients (ICCs) for single measurements into the corresponding ICCs for average measurements, without knowledge of the variance components. Results A formal proof of the discovery by De Vet et al. is presented. It is also proved that, vice versa, the SB formula can be used to transform certain ICCs for average measurements into the corresponding ICCs for single measurements. Furthermore, it is specified to which type of ICC the transformations can be applied. Finally, several illustrations of the transformations are presented. Conclusion The discovery by De Vet et al. is quite remarkable because ICCs and the SB formula come from quite different scientific disciplines.