Box 1.

Attenuation of observed group differences in different scenarios.

${\delta }_{\text{observed}}={\delta }_{\text{true}}\sqrt{ICC}$	Continuous outcome measured with reliability ICC; classification is error-free.
${\delta }_{\text{observed}}={\delta }_{\text{true}}\sqrt{ICC·sin\left(\frac{\pi }{2}\kappa \right)}$	Continuous outcome measured with reliability ICC while classification reliability is κ.
${\delta }_{\text{observed}}={\delta }_{\text{true}}\sqrt{\frac{2IC{C}_{1}IC{C}_2}{IC{C}_1+IC{C}_2}}$	Continuous outcome with group-specific reliabilities ICC1 and ICC2; classification is error-free.
${\delta }_{\text{observed}}={\delta }_{\text{true}}\sqrt{\frac{2IC{C}_{1}IC{C}_2}{IC{C}_1+IC{C}_2}sin\left(\frac{\pi }{2}\kappa \right)}$	Continuous outcome measured with group-specific reliabilities ICC1 and ICC2 while classificaiton reliability is κ.
${\delta }_{\text{observed}}={\delta }_{\text{true}}\sqrt{\frac{{\sigma }_{b,1}^2+{\sigma }_{b,2}^2}{{\sigma }_{b,1}^2/IC{C}_1+{\sigma }_{b,2}^2/IC{C}_2}}$	Continuous outcome with group-specific variances ${\sigma }_{b,1}^2$, ${\sigma }_{b,2}^2$ and reliabilities ICC1, ICC2; classification is error-free.
${\delta }_{\text{observed}}={\delta }_{\text{true}}\sqrt{\frac{{\sigma }_{b,1}^2+{\sigma }_{b,2}^2}{{\sigma }_{b,1}^2/IC{C}_1+{\sigma }_{b,2}^2/IC{C}_2}sin\left(\frac{\pi }{2}\kappa \right)}$	Continuous outcome measures with with group-specific variances ${\sigma }_{b,1}^2$, ${\sigma }_{b,2}^2$ and reliabilities ICC1, ICC2, while classification reliability is κ.