The concept of test and item reliability in relation to factor pattern |
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Authors: | Robert J Wherry Richard H Gaylord |
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Institution: | (1) University of North Carolina, USA |
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Abstract: | It is shown that approaches other than the internal consistency method of estimating test reliability are either less satisfactory or lead to the same general results. The commonly attendant assumption of a single factor throughout the test items is challenged, however. The consideration of a test made up ofK sub-tests each composed of a different orthogonal factor disclosed that the assumption of a single factor produced an erroneous estimate of reliability with a ratio of (n–K)/(n–1) to the correct estimate. Special difficulties arising from this error in application of current techniques to short tests or to test batteries are discussed. Application of this same multi-factor concept to item-analysis discloses similar difficulties in that field. The item-test coefficient approaches 1/K as an upper limit rather than 1.00 and approaches 1/n as a lower limit rather than .00. This latter finding accounts for an over-estimation error in the Kuder-Richardson formula (8). A new method of isolating sub-tests based upon the item-test coefficient is proposed and tentatively outlined. Either this new method or a complete factor analysis is regarded as the only proper approach to the problem of test reliability, and the item-sub-est coefficient is similarly recommended as the proper approach for item analysis. |
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