I have a sample including all students within 52 schools which have been randomly assigned to be treatment or control (we have group randomized trial in which all students in each school is either assigned to treatment or to control ). I'd like to know whether there is any school clustering effect in this data. In other words, I'd like to compare the within-school variability of students to between school variability. One way to measure whether there is any school clustering effect is to use ICC (intra class correlation). The ICC for my data (with schools as clustering units) is 0.04. I'd like to have a statistical method helping me decide whether ICC of 0.04 is large enough to take the school clustering effect into account in my model. What would you recommend? Can F test on the ratio of the variability between schools over the variability with-in schools answer this question?
Thank you for helping me on this issue.