The Concept of Test and Item Reliability in Relation to Factor Pattern

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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 of K 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.