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Educational and Psychological Measurement
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A Four-Dimensional Sphere? a Paradox in AVA's Vector Model and Profile Analysis Method

Ann Howard

American Telephone and Telegraph Company, New York, N.Y.

Robert M. Carroll

U. S. Army Research Institute for the Behavioral and Social Sciences

A mathematical analysis is made of the geometric vector model and profile comparison method developed for the Activity Vector Analysis (AVA), a personality measure widely used in industry. The profile comparison formula is shown to be equal to a Pearson r but less parsimonious than the usual formulas. A contradiction is discovered in that the geometric model is presented in three-dimensional space as a sphere or spheroid, whereas the profile comparison formula mathematically requires four-dimensional space to reflect distances between profiles within the sphere. Some recommendations are made regarding resolution of the theoretical incongruency and revision of the measure based on empirical findings.

Educational and Psychological Measurement, Vol. 37, No. 1, 67-79 (1977)
DOI: 10.1177/001316447703700108
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