Questions: Score Linking and Test Equating Methods

Question 1

A university converts SAT and ACT scores to a common 1600-point scale using a published concordance table. An admissions officer says 'a 1200 on our scale means the same thing whether it came from SAT or ACT.' Is this defensible?

• A. Yes — the concordance was derived from a large sample of students who took both tests, making the scores equivalent
• B. No — SAT and ACT measure overlapping but non-identical constructs with different reliabilities, so the conversion is a concordance, not an equating; the scores are not fully interchangeable
• C. Yes — both tests are normed to the same college-bound population, which makes their scales equivalent
• D. No — common-item equating was not used, so no valid comparison is possible

Answer: (B)

True equating requires that both forms measure the same construct with equal reliability. SAT and ACT overlap substantially but differ in construct coverage (e.g., ACT includes a science reasoning section; the SAT emphasizes evidence-based reading differently). A concordance table translates scores statistically but does not make them fully interchangeable — it documents a predictive relationship, not construct equivalence. Claiming the scores 'mean the same thing' overstates what concordance can support.

Question 2

Two forms of a reading test are built to identical blueprints, but Form B turns out slightly harder. Student X scores 68 on the harder Form B; Student Y scores 68 on the easier Form A. Without equating, what is the correct interpretation of their scores?

• A. Both students have equivalent ability — they answered the same number of items correctly
• B. Student X demonstrated more ability — achieving the same raw score on a harder form indicates higher proficiency
• C. Student Y demonstrated more ability — Form A's lower difficulty means Y answered easier items correctly
• D. No comparison is possible without knowing each student's raw score percentile

Answer: (B)

The same raw score on a harder form represents greater demonstrated ability than on an easier form. This is precisely the problem equating solves: it maps raw scores to a common scale so that equivalent scaled scores represent equivalent ability, regardless of which form was taken. Without equating, identical raw scores on forms of different difficulty are not comparable — the student who took the harder form is systematically underrepresented.

Question 3

Equipercentile equating maps a score on Form A to the score on Form B that corresponds to the same percentile rank in the equating sample.

• T. True
• F. False

Answer: True

This is the defining logic of equipercentile equating. If the 80th percentile on Form A is a raw score of 64, and the 80th percentile on Form B is a raw score of 61, then Form A raw 64 equates to Form B raw 61. The method requires no assumption about the shape of the score distributions and adjusts for differences in both central tendency and spread, making it more flexible than linear equating when score distributions are asymmetric or differently shaped.

Question 4

Any two tests that measure related psychological constructs and are administered to similar populations can be equated to make their scores fully interchangeable.

• T. True
• F. False

Answer: False

Equating requires that both forms measure the same construct with equal reliability and equal construct representation. When this assumption fails — because the tests differ in what they measure — only concordance or linking is appropriate. Concordance establishes a statistical translation between the scales but does not make scores interchangeable. Treating a concordance as an equating implies a level of comparability the data do not support, and can lead to consequential errors in selection and comparison decisions.

Question 5

Explain the difference between test equating and concordance, and why conflating the two is a practical problem in educational or clinical settings.

Model answer: Equating adjusts scores on different forms of the same test to a common scale, making identical scaled scores truly interchangeable — a student who took Form A and one who took Form B with the same scaled score demonstrated the same ability. Concordance statistically relates scores from different tests measuring overlapping but non-identical constructs; the resulting translations are predictive, not equivalent. Conflating the two is a problem because decision-makers may treat concordanced scores as if they were equated — for example, using an SAT-to-ACT conversion to claim a student meets a cutoff they would not have met if they'd actually taken the other test. This overclaims comparability and can disadvantage test-takers.

The conceptual crux is that equating preserves construct identity across forms, while concordance only preserves statistical prediction. The distinction matters most in high-stakes contexts: admissions cutoffs, clinical diagnostics, and credentialing.