41  ICC Visualization

The intraclass correlation (ICC) is the ratio of the level 2 variance to the total variance. It is a measure of between group differences, as it answers the question, “what proportion of total variance is accounted for by the level 2 units?” It is simultaneously a measure of within group similarity, answering the question, “what is the expected correlation in the outcome between pairs of observations drawn from the same cluster?” The ICC is also closely related to reliability in measurement, with a high ICC indicating more reliable measures (e.g., student test scores, inter-rater reliability, etc.)

The shiny app below allows you to set the number of level 1 units, level 2 units, and the ICC, using students in schools as the context. To build your intuitions, make a prediction for what the graph will look like with an ICC of 0, and an ICC of 1, then test them out by manipulating the ICC slider.