A university uses a concordance table to treat concorded ACT and SAT scores as fully interchangeable for admissions — accepting a 28 ACT as identical to a 1300 SAT. A psychometrician objects. What is the most defensible reason for the objection?
AThe concordance table was likely built from an unrepresentative sample, making percentile matching unreliable
BConcorded scores reflect equivalent percentile ranks but not interchangeable constructs — the tests differ enough that treating them as identical overstates precision
CEquipercentile linking systematically underestimates ACT scores relative to SAT scores at the high end
DRegression-based linking would have produced a more accurate concordance than equipercentile methods
The key distinction is equating versus concordance. Equated scores (parallel forms of the same test) are interchangeable. Concorded scores are comparable estimates — the SAT and ACT measure overlapping but non-identical constructs (the ACT includes a science section; formats and timing differ). Matching percentile distributions says nothing about construct identity. The admission office is treating a concordance as if it were an equating, ignoring the additional uncertainty that imperfect construct overlap introduces.
Question 2 Multiple Choice
A researcher pools data from two studies that used different depression screening instruments by regressing Instrument B scores onto Instrument A scores. What limitation should she specifically flag in her methods section?
ARegression-based linking will exaggerate extreme scores on Instrument B, inflating apparent severity
BRegression-based linking will compress predicted scores — extreme Instrument A scorers will have less extreme predicted Instrument B scores than their actual scores would be
CRegression-based linking cannot be applied unless both instruments use identical response formats
DRegression-based linking assumes the instruments measure completely unrelated constructs
Regression to the mean is the critical limitation. Predicted values from a regression are always more compressed (closer to the mean) than the observed distribution. Someone in the extreme 95th percentile on Instrument A will be predicted at a less extreme percentile on Instrument B. Concordance tables using equipercentile methods avoid this compression by directly matching observed score distributions rather than predicting through a regression line — making them preferable when preserving the full score range matters.
Question 3 True / False
A concorded score is an estimate of the score range a test-taker would likely achieve on the other instrument — not a precise equivalent that can be treated as interchangeable with the original score.
TTrue
FFalse
Answer: True
This is the defining distinction between equating and concordance. Equated scores from parallel test forms are interchangeable — admission officers can treat them identically. Concorded scores carry inherent uncertainty due to imperfect construct overlap between the instruments. They are useful for rough comparisons and population-level interpretations, but should not be used to make high-stakes individual decisions that hinge on precise cutpoints.
Question 4 True / False
Because equipercentile linking matches the full score distributions of two tests, it guarantees that scores mapped to the same percentile rank are measuring the same underlying construct.
TTrue
FFalse
Answer: False
Equipercentile linking is a distributional alignment procedure — it identifies scores where equal proportions of test-takers fall below. This says nothing about what the tests measure. Two tests with completely different content would produce a concordance table just the same. Construct validity — whether two scores reflect the same underlying trait — requires separate evidence from the statistical linking procedure. Matching percentile ranks establishes comparability in rank, not equivalence in meaning.
Question 5 Short Answer
Explain the key difference between equating and concordance, and give a concrete example of when treating a concorded score as equated would lead to a problematic decision.
Think about your answer, then reveal below.
Model answer: Equated scores come from parallel forms of the same test measuring the identical construct at equivalent difficulty — they are interchangeable. Concorded scores link different instruments measuring related but non-identical constructs — they are comparable estimates carrying additional uncertainty from imperfect construct overlap. Example of a problematic decision: using an SAT-ACT concordance to deny admission to a student whose concorded score falls exactly at the cutoff, when the uncertainty in the concordance could easily span several points in either direction. Or translating a clinical depression cutoff from one screening instrument to another via concordance and treating the translated cutoff as precise, when construct differences mean the threshold may not carry over.