Lord’s Equity Theorem Revisited

Wim J. van der Linden*

*Corresponding author for this work

    Research output: Contribution to journalArticleAcademicpeer-review

    2 Citations (Scopus)


    Lord’s (1980) equity theorem claims observed-score equating to be possible only when two test forms are perfectly reliable or strictly parallel. An analysis of its proof reveals use of an incorrect statistical assumption. The assumption does not invalidate the theorem itself though, which can be shown to follow directly from the discrete nature of the equating problem it addresses. But, surprisingly, an obvious relaxation of the problem is enough to obtain exactly the opposite result: As long as two test forms measure the same ability, they can always be equated, no matter their reliability, degree of parallelness, or even difference in length. Also, in spite of its lack of validity, the original proof of Lord’s theorem has an important interim result directly applicable to the problem of assembling a new test form pre-equated to an old form.

    Original languageEnglish
    Pages (from-to)415-430
    Number of pages16
    JournalJournal of educational and behavioral statistics
    Issue number4
    Early online date24 Mar 2019
    Publication statusPublished - 1 Aug 2019


    • UT-Hybrid-D
    • Equity
    • Local equating
    • Observed-score equating
    • Q-Q transformation
    • Compound binomial distribution
    • n/a OA procedure


    Dive into the research topics of 'Lord’s Equity Theorem Revisited'. Together they form a unique fingerprint.

    Cite this