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Principal components and other standard factor analyses can yield misleading results if an assumed subsidiary condition is untrue or if data are missing. This is illustrated by absurd results obtained from a problem with known answers. Even when test data are complete (e.g., 70 data on seven properties, dependent on both radii and heights of ten cylinders), principal components followed by varimax or other standard rotations gives incorrect rank orders for factors (factor scores for radilus and height for each of the ten cylinders) and sensitivities (factor loadings for each of the seven properties). When no data are missing, a transformation incorporating valid subsidiary conditions can be used instead of such rotations to obtain correct factors and sensitivities, although no such transformations have been used in any previously published work. However, when a moderate number (e.g., 20, or 29%) of the possible data are missing (randomly deleted), factors and sensitivities can have wrong rank orders and therefore be misleading even with this transformation. When data are missing, standard factor analysis is evidently unreliable and should be replaced by another method, such as that in the preceding paper.

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