There are two types of intraclass correlation coefficients (ICCs): ICC1 & ICC 2. We calculate the ICC(1) to know at how much of the variance in the variables is due to group membership and calculate the ICC(2) to know the reliability of group means. 

Both forms of the ICC can calculate from a one-way random-effects ANOVA. 

ICC(1) = MSB - MSW / MSB + [(k-1) * MSW]

where

MSB is the between-group mean square

MSW is the within-group mean square

k is the group size

ICC(2) = k(ICC(1))/1+(k-1)ICC(1)