There is a population of teeth nested in a population of mouths.

Each tooth has a tooth health status value that differs from the whole population (mouths & teeth) mean. This is called (tooth) “RESIDUAL” or also “ERROR” in statistics.

Each mouth has a mean tooth health status value that differs from the whole population (mouths & teeth) mean. This is also called (mouth) “RESIDUAL” or also “ERROR” in statistics.

You can se (the red arrows) that all teeth within a mouth have a common (mouth) difference from the whole population (mouths & teeth) mean.

All teeth within a mouth have basal health status that is determined by the mouth they are located.

VARIANCE in statistics is a summary measure of the overall differences.