A test of Frederic Lord's premise relative to formula scoring

Abstract

Although formula scoring has been used since the early 1900s, it was not until 1975 that Frederic Lord offered the following potential psychometric justification for its use: If under formula-scoring directions an examinee omits only those items which would result in completely random guesses under number-right scoring directions, then the formula score will be a more efficient estimator of the examinee's standing on the trait measured. Whenever the number of omissions is greater than zero, the formula score will be more reliable than the number-right score.

The purpose of this study was to test the premise that examinees omit only those items for which they have no knowledge when taking a test under formula-scoring directions. Several studies had been carried out previously to test this premise, and the design used in this study was a synthesis of the previous designs.

Included in this study was an investigation of examinees' responses, under formula-scoring directions, to items that were constructed to be obscure. Also examinees responded to questions about their attitudes towards formula-scored tests and their strategies when taking formula-scored tests.

Because of the results of the test of Lord's premise, also included in this study was a further investigation of omissiveness, the tendency to omit items under formula-scoring directions. Item difficulty and item omissions were examined relative to Lord's premise. A variable, called L for convenience, was computed for each item in order to find to what extent responses to test items support Lord's premise. Finally, the possibility of misinformation producing a counter effect to inappropriate omissions relative to Lord's premise was investigated.