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Score Linking and Concordance Tables

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Test Equating and Score Linking MethodsLevels of MeasurementScore Linking and Test Equating Methods
linking concordance scale-translation equating score-conversion

Core Idea

Score linking creates empirical relationships between scales measuring related constructs (e.g., old and new versions of a test, or different tests of similar constructs), enabling researchers to translate scores from one test to another. Concordance tables or regression equations allow comparison of scores and facilitate interpretation when multiple measures exist. Linking assumes the constructs are sufficiently similar and requires sufficient overlap data.

Explainer

From your study of test equating and linking, you know that equating refers to the strict case of creating interchangeable scores across parallel forms of the same test — forms designed to measure the identical construct at the same difficulty level with the same scaling. Score linking is the broader family of methods that includes equating but extends to situations where tests are similar but not identical, and where the goal is translation rather than strict interchangeability.

The most common application is the concordance table — an empirically derived lookup table that maps scores from one test to scores on another. A familiar example is the SAT-ACT concordance: because millions of students take one or both, researchers can identify the ACT composite score that corresponds to each SAT total score by finding the scores at equivalent percentile ranks in the overlap sample. If 70% of students who score a 28 on the ACT score below a 1300 on the SAT, and 70% of students who score 1300 on the SAT score below a 1300, then 28 ACT ≈ 1300 SAT by equipercentile linking. This approach requires no strong parametric assumptions — it simply matches the percentile distributions.

The critical distinction you must hold onto is between equating and concordance, and the difference lies in what you can claim afterward. Equated scores are interchangeable — a 500 on Form A means the same thing as a 500 on Form B, and admission officers can treat them identically. Concorded scores are merely *comparable* — a concorded ACT score is an estimate of the score range a student would likely achieve on the SAT, but it carries more uncertainty and should not be treated as exact. The reason is construct overlap: the SAT and ACT measure overlapping but non-identical constructs (the ACT has a science section; the two differ in timing and format). When construct overlap is imperfect, equipercentile correspondence does not imply score exchangeability.

Regression-based linking is an alternative approach, particularly useful in research contexts. If you have a sample that completed both instruments, you can regress scores on one test onto the other and use the regression equation to predict one from the other. This is simpler but inherits a limitation: regression to the mean means predicted scores will be more compressed than actual scores — extreme scorers on one test will be predicted as less extreme on the other. Concordance tables using equipercentile methods avoid this compression. Understanding these trade-offs matters whenever you need to pool data from studies using different instruments, translate clinical cutoffs from one screening tool to another, or interpret scores when a test is revised and the new version cannot be directly equated to the old.

Practice Questions 5 questions

Prerequisite Chain

Understanding ZeroThe Number ZeroCounting to FiveCounting to 10Counting to 20Counting a Set of Objects Up to 20Cardinality: The Last Number CountedMatching Numerals to QuantitiesSubitizing Small QuantitiesAddition Within 10Number Bonds to 10Addition Within 20Doubles and Near DoublesDoubles Facts Within 10Near Doubles Facts Within 20Mental Math Strategies for AdditionMental Math: Adding and Subtracting TensAddition Within 100Repeated Addition as MultiplicationMultiplication as Equal GroupsMultiplication: ArraysBasic Multiplication Facts (0s, 1s, 2s, 5s, 10s)Multiplication Facts Within 100Division as Equal SharingDivision as Grouping (Measurement Division)Division: Grouping (Repeated Subtraction) ModelDivision: Fair Sharing ModelDivision as Equal SharingDivision as GroupingBasic Division FactsDivision Facts Within 100Multiplication and Division Fact FamiliesRelationship Between Multiplication and DivisionDivision Facts as Inverse of MultiplicationRemainders and Quotients in DivisionDivision Word ProblemsMulti-Step Word ProblemsSolving Multi-Step Word ProblemsMultiplication Word ProblemsDivision Word ProblemsIntroduction to Long DivisionFactors and MultiplesPrime and Composite NumbersEquivalent FractionsRelating Fractions and DecimalsDecimal Place ValueIntegers and the Number LineComparing and Ordering IntegersAbsolute ValueAdding IntegersSubtracting IntegersMultiplying IntegersDividing IntegersUnit RatesProportionsPercent ConceptConverting Between Fractions, Decimals, and PercentsOperations with Rational NumbersTwo-Step EquationsSolving Multi-Step EquationsEquations with Variables on Both SidesAngle Pairs: Complementary, Supplementary, and VerticalParallel Lines and TransversalsCorresponding AnglesAlternate Interior AnglesTriangle Angle Sum TheoremExterior Angle TheoremTriangle Inequality TheoremSimilar Triangles: AA SimilaritySimilar Triangles: SSS and SAS SimilarityProportions in Similar TrianglesRight Triangle Trigonometry IntroductionSine, Cosine, and Tangent RatiosTrigonometric Ratios ReviewRadian MeasureConverting Between Degrees and RadiansThe Unit CircleGraphing Sine and CosineGraphing Tangent and Reciprocal Trigonometric FunctionsDerivatives of Trigonometric FunctionsAntiderivativesIndefinite IntegralsBasic Integration RulesRiemann SumsDefinite Integral DefinitionProbability Density Functions and Continuous DistributionsCumulative Distribution FunctionsContinuous Random VariablesProbability Density FunctionsExpected ValueWeak Law of Large NumbersProbability Axioms and RulesConditional ProbabilityIndependence of EventsSampling DistributionsStandard Error of EstimatorsHypothesis Testing: Framework and LogicClassical Test Theory FoundationsItem Response Functions and Item Characteristic CurvesTest Equating and Score Linking MethodsScore Linking and Concordance Tables

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