PROBLEMMuch MMPI research has attempted t o determine exactly what the test I n attempting to answer this question, the method of factor analysis It has been applied t o M M P I subtest scores. This assumes that the subtest scores accurately measure or reflect the diagnostic names that were applied by the test-makers. This assumption has been challenged frequently because the scoring of the same item on more than one subtest poses serious problems in statistical handling of data. Factor analysis has also been applied t o MMPI test items. Constraints on the data processing capacity of computers have severely curtailed attempts in this direction. Conventional factor analytic methods are typically limited to a data matrix of approximately 150 items, thereby requiring the investigator t o select a reduced set of items for study. This selection process involves a gamble that the remaining items are inconsequential, either inherently or in relation to the 150 items selected for study.Horst (I4) addressed himself to the problem of statistical analysis of large numbers of variables. He provided a rationale and a mathematical proof for a factoranalytic procedure based on a reduced data matrix. The matrix of MMPI items may be reduced to the size that corresponds to the number of Ss employed. For example, the data matrix for the 373 item short form of the M M P I based on 100 Ss can be reduced to a data matrix (100 X 100). (Note that this size is well within computer capability.) Factor analysis is then applied to the reduced matrix, and the results are appropriately transformed back as though the full set of items were factor analyzed.Although this approach makes possible the computer processing of large data matrices, it suffers from one serious fault. The number of variables under study may far exceed the number of Ss and raise serious questions regarding the reliability of the findings. Perhaps the consequence of this state of affairs is best appreciated within the context of multiple regression. It is analogous to examining college Grade Point Average by means of a multiple regression equation derjved from 30 predictor variables based on an original sample of 10 people.Cattell (') proposed that the number of Ss for a factor analytic study be approximately 100 more than the number of variables. If this proposal were met in the case of the short form MMPI, the data matrix could not be reduced to be analyzed by Horst's procedure.Nunnally (I8) proposed the most stringent criterion for factor-analytic studies. He asserted that there should be 10 Ss for every variable-in the case of the short form MMPI, this means 3,730 Ss. measures. has been employed frequently and routinely applied in two ways:(1)(2)
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