Equating

Definition

Equating is the psychometric process that converts raw scores to scaled scores while adjusting for differences in test-form difficulty. The point is fairness: a student who happens to take a harder test form should not be penalized relative to a student who took an easier one.

Why equating exists

Standardized tests like the SHSAT are administered in different forms across different years (and sometimes different sessions within a year). Even when test designers try to create equivalent forms, small differences in difficulty are inevitable. Without equating:

• A student who got 45 of 47 correct on an easy form would be tied with a student who got 45 of 47 correct on a hard form, even though demonstrating the same raw score on a harder form represents more ability.
• Cutoff scores wouldn’t be comparable across years — a 510 in a year with an easier test would represent less ability than a 510 in a year with a harder test.

Equating adjusts the raw-to-scaled conversion so that, in theory, a given scaled score represents the same level of ability regardless of which form you took or what year you tested.

A concrete example

Suppose form A is slightly easier than form B. After analysis, psychometricians determine that:

• On form A, a raw score of 42 represents a particular ability level.
• On form B (harder), a raw score of 40 represents that same ability level.

The equating process sets both of these to the same scaled score — say 290. So a student with raw 42 on the easy form and a student with raw 40 on the hard form both receive scaled 290. Same demonstrated ability, same scaled score, despite different raw scores.

How equating works in practice

The NYC DOE uses anchor items — questions that appear on multiple test forms across years — to calibrate difficulty differences. By comparing how a known population of students performs on the anchor items across forms, psychometricians can estimate the difficulty differential and adjust the raw-to-scaled conversion accordingly.

This is why the raw-to-scaled conversion is slightly different each year. The conversion isn’t arbitrary; it’s the result of calibration designed to keep scaled scores comparable.

Equating is not the same as “curving”

Curving typically refers to adjusting scores based on how the current cohort of test-takers performed. If everyone did badly, the curve might give the top students an A, the middle students a B, and so on. The grade depends on relative performance.

Equating is different. The scaled score doesn’t depend on how your specific cohort performed. It depends on the test form’s difficulty, calibrated against the anchor items and prior administrations. In a year where every test-taker performs poorly, the cutoffs might rise or fall (because cutoffs depend on cohort scores), but the individual scaled scores reflect ability, not relative performance.

What changes with the CAT format

The new Computer Adaptive Test format uses Item Response Theory (IRT) parameters for each question rather than traditional equating. Each item has a calibrated difficulty, discrimination, and guessing parameter. Your final score reflects both your accuracy and the difficulty of the questions you correctly answered. The end result is similar — comparable scaled scores across years and administrations — but the underlying math is IRT-based rather than traditional equating.

Common misconceptions

“Equating means the test is curved.” No. The scaled score doesn’t depend on how your specific cohort performed; it depends on the test form’s calibrated difficulty.

“If everyone bombs the test, my score will be higher.” Sort of. Your scaled score won’t change — that reflects your demonstrated ability. But the cutoffs might be lower in such a year (because cutoffs depend on cohort scores), making admission easier even at the same scaled score.