Why a CogAT 132 and an NNAT 132 Are Not the Same Score

A gifted-screening report comes home with a number on it, and the number looks like an IQ. A CogAT composite of 132. An NNAT index of 132. Parents compare them across schools, across siblings and against a district cutoff, and treat them as the same measurement. They are not. The two tests print their results on scales that differ by one point of standard deviation, and that single difference moves the same printed number by most of a percentile point at exactly the level where gifted cutoffs get drawn.

Neither test is an IQ test, and neither publisher says it is

The Cognitive Abilities Test (CogAT) and the Naglieri Nonverbal Ability Test (NNAT) are the two instruments most often used to screen for gifted programmes in American schools. Both are group-administered, both finish inside a morning, and neither is an individually administered intelligence test. Their publishers describe them as measures of reasoning ability — the CogAT from Riverside Insights, the NNAT from Pearson.

The distinction is not a technicality. An individually administered test is given one-to-one by a qualified examiner who can see when a child is guessing, tired, unwell or misreading the instructions, and who records that in the report. A screener given to thirty children at once cannot see any of it. What comes back is a mark on an answer sheet and no information about how it got there.

That does not make screeners worthless. It makes them screeners: a first pass designed to find the children worth looking at more closely, at a cost per child low enough that a district can test everybody rather than only the children somebody thought to nominate. Read as what they are, they do real work. Read as an IQ, they mislead — and the misreading starts with the fact that both print a number near 100.

What a CogAT report actually contains

The CogAT runs three batteries and reports each separately as well as combined: Verbal, Quantitative and Nonverbal. A child can be strong on one and unremarkable on another, and that profile is the part of the report a teacher can act on. The headline figures are these:

• Standard Age Score (SAS) — a normalised standard score with an average of 100 and a standard deviation of 16. The standard deviation is the unit the whole scale is built from: it describes how far apart children's results typically fall.
• Age Percentile Rank — the percentage of children in the same age band in the reference sample who scored at or below this result.
• Grade Percentile Rank — the same comparison against children in the same grade rather than the same age. For a child who is young or old for their grade these two are materially different numbers.
• Age and Grade Stanines — the percentile compressed onto a 1-to-9 band with an average of 5 and a standard deviation of 2. Districts often set cutoffs in stanines precisely because a stanine is honest about how coarse the underlying measurement is.

The composite SAS is the figure most likely to be mistaken for an IQ, because it is a mean-100 standard score and it lands in the same range as one. Everything below follows from the fact that it is not measured in the same units.

What an NNAT report actually contains

The NNAT is a single battery of matrix-style items with no words in them at all. A child sees a pattern with a piece missing and picks the piece that completes it. Because there is no reading and very little instruction-dependent content, it is used where language would otherwise get in the way: English learners, children with a speech or language difficulty, and districts trying to widen the pool their gifted programme draws from. The item format is the one Raven's Progressive Matrices made standard, and it inherits the same caveat: a matrix item is only ever as good as the norm table sitting behind it.

It reports the Naglieri Ability Index (NAI) — a normalised standard score with an average of 100 and a standard deviation of 15 — alongside a percentile rank and a stanine. One battery, one composite, one scale, and a scale that is one point narrower than the CogAT's.

The arithmetic that pulls 132 away from 132

Both scales put the average at 100. They disagree about how wide a single step away from average is. Sixteen points is one standard deviation on the CogAT; fifteen points is one standard deviation on the NNAT. Convert each printed score into the position it describes and the two 132s come apart:

• CogAT SAS 132 — 32 points above 100, divided by a standard deviation of 16, is exactly 2.00 standard deviations. That is the 97.7th percentile. Roughly one child in 44 scores at or above it.
• NNAT NAI 132 — 32 points divided by 15 is about 2.13 standard deviations, or roughly the 98.4th percentile. About one child in 61.
• Translated onto each other's scales, a CogAT 132 is about an NNAT 130, and an NNAT 132 is about a CogAT 134.

Two points of printed score, and a qualifying pool about a third smaller. At the level where gifted cutoffs are typically drawn that is not a rounding difference; it is the difference between a child clearing a threshold and not clearing it. Our note on what changes when the standard deviation changes runs the same arithmetic through the adult scales, where the identical trap catches everyone quoting a Mensa figure without naming the test.

Why there are two conventions at all

The split is historical rather than principled. Before deviation scoring, an IQ was a ratio: a child's assessed mental age divided by their actual age, multiplied by 100. That formula has no standard deviation at all, which is one reason it was abandoned — the same printed number meant a different rarity at every age. When deviation scoring replaced it, the score became a position in a reference sample, and the spread of that sample had to be fixed by convention. The Wechsler scales fixed it at 15 points, and they are common enough that 15 became the default assumption.

Some Stanford-Binet forms and a number of group-administered instruments settled on 16 instead, and the CogAT sits in that family. Neither figure is more correct than the other. A standard deviation of 15 or 16 is a unit of measurement chosen by a publisher, in the same way a temperature can be reported in Celsius or Fahrenheit without either scale being the true one. The error is never the choice of unit. It is quoting a number without saying which unit it is in.

The percentile is the part that transfers

This is why any district cutoff worth defending is written as a percentile rather than a score. A percentile is a position in a reference sample, and positions compare across instruments. A standard score is that position printed on one test's scale, and printed scores do not compare. A programme that admits at the 97th percentile keeps the same rule when it changes vendor. A programme that admits at 130 quietly becomes a different programme the day the paperwork changes, and nobody has to approve the change because nobody notices it.

If you are holding a score and want its rank rather than its label, our IQ percentile calculator takes a score together with the standard deviation it was measured on, and the score converter moves a figure between the SD-15 and SD-16 scales — which is precisely the CogAT-to-NNAT translation set out above. Doing it by hand is two operations, and doing it by hand is also where the rounding creeps in. If you want to see what a deviation score looks like when it is reported properly before arguing about a screener's, our own assessment returns the scale, the percentile and the confidence range together.

What one screening score does not settle

• It is one administration on one morning. Every result carries a standard error of measurement — a published figure describing how far a score moves between sittings for the same child. A 129 and a 133 from the same child on the same instrument are not reliably different results.
• It was group-administered. Nobody was watching whether one particular child lost their place on the answer sheet in section three.
• Nonverbal does not mean culture-neutral. Removing language removes one source of unfairness. It does not remove familiarity with pencil-and-paper matrix puzzles, which is itself something children meet unevenly.
• A composite hides its parts. Two children with an identical CogAT composite can have opposite profiles across the three batteries, and the profile is the actionable half of the report.
• Neither result diagnoses anything. Gifted identification is a placement decision made by a district under its own written policy, not a clinical finding about a child.

The practical move when a score lands near a cutoff is to ask for the confidence interval rather than to argue about the point estimate. Our piece on the margin of error on an IQ score explains what that band is and why every serious report prints one. Most districts already have a second-look procedure for scores inside the band, for the straightforward reason that the people who wrote the policy know how wide it is.

None of this is an argument against screening. It is an argument for reading the report the test actually produced. A screener answers one narrow question — is this child worth a closer look — and it answers it with a position in a reference sample, printed on a scale that is a publisher's convention. When someone quotes a cutoff, ask which scale it is on and which norm it is against. If they cannot say, the number is not yet meaningful. It is the same habit that stops achievement results and ability results being read as though they measured the same thing, and it costs about thirty seconds to apply.

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