θ-hat is a statistic with a range from 0 to 1, which measures the degree to which a designated pattern successfully partitions a matrix of pre-and post-treatment ratings into regions typical of each of two treatments. A value of 1 is obtained when there is complete separation in the predicted direction; 0 is obtained when there is complete separation in the direction that is reverse to that predicted; and 1/2 is obtained when the pattern fails to differentiate between the treatments. In this paper, θ-hat is extended to multivariate and multigroup cases. The methods are illustrated with real data.
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