Some Vicissitudes of Chain P-Factor Analysis: Criterion of Meaningfulness

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Abstract
In a Chain P-factor analysis the elimination of the between person variance reduces the contribution of “true score” variance to the true score-total score variance ratio based on the reduced scores. Factors which emerge in such an analysis may unduly reflect the influence of error variance and demand caution in their interpretation. An expanded criterion of meaningfulness was proposed which contrasted an obtained solution with a randomly generated solution under the null hypothesis that independent judges could not do better than chance in distinguishing the real factors from the random ones. A Chain P-analysis of real data gathered from 45 female patients, tested after each of 10 successive psychotherapy sessions, was contrasted with a parallel analysis of Monte-Carlo data. Four judges significantly discriminated the real factors from the random factors in a paired comparison task. The results strengthened the credibility of the Chain P-analysis and established the usefulness of an expanded criterion of meaningfulness.

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