Transforming intraclass correlation coefficients with the Spearman-Brown formula.
OBJECTIVE
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.


CONCLUSIONS
The discovery by De Vet et al. is quite remarkable because ICCs and the SB formula come from quite different scientific disciplines.
GION Education/Research, University of Groningen, Grote Rozenstraat 3, 9712 TG, Groningen, The Netherlands. Electronic address: m.j.warrens@rug.nl.
Matthijs J
MJ
Warrens
D035843:Biomedical Research / Q000706:statistics & numerical data*; D006801:Humans; D015233:Models, Statistical; D011594:Psychometrics; D015203:Reproducibility of Results; D012107:Research Design
Agreement; Average measurements; Consistency; Intraclass correlation coefficients; Single measurements; Spearman–Brown formula