5 - Forming composites and other redescriptions of variables

Summary

Forming composites

Suppose that our judges have rated the nonverbal behavior of a set of psychotherapists on three dimensions: warmth, empathy, and positiveness of regard. Suppose further that the retest reliabilities and the internal consistency reliabilities of all three variables are .75 and that each of our three variables is also correlated with the others .75. Under these conditions, when our variables are so highly correlated with each other, as highly correlated as they are with themselves, we may find no advantage to analyzing all our data separately for the three variables.

For most purposes we might well prefer to form a composite variable of all three. We might, therefore, standard score (z-score) each of the three variables we plan to combine and replace each therapist's three ratings by the mean of the three z scores the therapist earned from the judges. A mean z score of zero means the therapist scores as average on our new composite variable; a large positive mean z score means the therapist scores as very high on our new composite variable; and a large negative mean z score means the therapist scores as very low on our new composite variable of warmth, empathy, and positiveness of regard.