# Minimal detectable change based on >2 measurements

by soschnei   Last Updated February 13, 2018 12:19 PM

I need to calculate the minimal detectable change (MDC) for my dataset and found the following formula in several publications:

$MDC = 1.96 * SD * \sqrt(1-ICC) * \sqrt2$

They argue $\sqrt2$ is used, because of the uncertainty of two measurement timepoints. However, in my dataset I don't have just test-retest measurement, but indeed 7 different measurement timepoints, based on which I need to calculate the MDC. Do I need to exchange $\sqrt2$ by $\sqrt7$?

Tags :

No, there is no need to change $\sqrt{2}$ to $\sqrt{7}$.
With more observations for a subject, it is easier to detect a change. Therefore $MDC_7 \le MDC_2$.
Recall that the $\sqrt{2}$ is an adjustment for a small number of observations. Therefore, we need to use $MDC = 1.96*SD*\sqrt{1-ICC}$.