. Author manuscript; available in PMC: 2013 Feb 1.

Published in final edited form as: J Exp Child Psychol. 2011 Sep 25;111(2):212–229. doi: 10.1016/j.jecp.2011.08.012

Table 2.

Ratio of between by within mean sums of squares for determining the optimal number of clusters, segregated by grade.

Solution	Fourth Grade	Fifth Grade
Two clusters	111.436	64.558
Three clusters	138.049	40.893
Four clusters	142.734^*	48.069
Five clusters	141.352	54.821
Six clusters	134.708	59.797
Seven clusters	135.542	78.032^*
Eight clusters	139.718	70.790

Indicator values based on Calinski & Harabasz (1974). Asterisk indicates the optimal indicator value, which is the point where the ratio is maximized.