How GAI and Full Scale IQ are scored

The composites

GAI was added so a clinician could estimate general ability when working memory or processing speed distort the Full Scale (Saklofske et al., 2005; Wechsler manuals). We use the same idea, written as simple means, because we are not looking up Pearson conversion tables.

Official GAI is not a mean of index scores. On WISC-V it is five named subtests (Similarities, Vocabulary, Block Design, Matrix Reasoning, Figure Weights). Visual Puzzles is in VSI and not in GAI. On WAIS-IV, GAI was VCI + PRI. On WAIS-5, GAI is still “FSIQ without WMI/PSI,” and Visual Puzzles stays out of both FSIQ and GAI. Our analog averages the three reasoning domains so the gap is readable. It is not a Wechsler GAI. Official composites you already have: GAI vs IQ, GAI vs CPI, or the primary indexes.

Five domains, CHC names

WAIS-5 reports five primary indexes. Those line up with broad CHC abilities (Carroll, 1993; Schneider & McGrew, 2018).

Why each task exists

Each task is an original item set aimed at one published subtest construct. We do not use official items.

1. 1 · VCI · Gc · analog of Similarities

   Analogies

   Same-relation verbal pairs. The Wechsler analog is saying how two words are alike.

2. 2 · VCI · Gc · analog of Vocabulary

   Vocabulary (antonyms)

   Pick the opposite. Depth of word knowledge, not a definition list.

3. 3 · FRI · Gf · analog of Matrix Reasoning

   Matrix reasoning

   Induce the rule from a grid. The prompt does not name the rule.

4. 4 · FRI · Gf · analog of Figure Weights

   Figure weights

   Keep a quantitative rule and apply it to a new set of shapes. Not arithmetic achievement.

5. 5 · VSI · Gv · analog of Paper Folding / visual-spatial construction

   Paper folding

   A fold, a punch, then the opened sheet. Track where the hole lands.

6. 6 · VSI · Gv · analog of Visual Puzzles

   Visual puzzles

   Which parts make the target. Construction without motor blocks.

7. 7 · WMI · Gwm · analog of Letter–Number Sequencing / computation span

   Computation span

   Solve a short sum, then recall the left numbers. Memory under load.

8. 8 · WMI · Gwm · analog of Picture Span / visual working memory

   Visual reversal

   Watch shapes, tap them backwards. Visuospatial manipulation, not digits.

9. 9 · PSI · Gs · analog of Symbol Search

   Symbol search

   Are any targets in the row? Accuracy and speed both count.

How a raw score becomes 100 ± 15

Standard scores, mean 100, SD 15 — the Wechsler convention.

standard = clamp(100 + 15 × (raw − max × 0.58) / (max × 0.18), 55, 155), with slightly different mean/SD ratios for memory and speed tasks.

Without a standardization sample we cannot claim percentile ranks from real people. We place a moderate raw score near 100 so the two composites are on the same scale and can be compared to each other.

Reading the gap

On WAIS-IV, the revised Table C.2 critical values for FSIQ vs GAI are small (often about 3–4 points at p < .05 across ages) because the composites share subtests. A 5-point gap can already be a real difference, not noise.

Clinicians then ask how rare the gap is (base rate), not only whether it is significant. A difference of about 10 points is commonly treated as worth discussing. “Unusual” is often a base rate under 10%, and that threshold varies by ability level. We do not copy Pearson’s base-rate tables.

Our reading bands (under 5 / 5–14 / 15+) are for plain language, not clinical cutoffs. The calculator uses your official numbers. The test uses the same bands on an estimate.

What we do not claim

• This is not the WAIS, WISC, or any Pearson test. Items are original. We do not use official Wechsler items, norms, or conversion tables.
• The 9-task battery is a construct-aligned estimate. It is not age-normed on a census sample. Scores use a conventional IQ metric (mean 100, SD 15) from a provisional raw-to-standard conversion.
• The calculator does not re-score a Wechsler. It only subtracts the two composites you already have and names the gap.
• A gap can be statistically detectable on a Wechsler at only a few points because FSIQ and GAI share subtests. Whether a gap is unusual is a base-rate question, not a p-value. We do not reprint Pearson’s tables.
• Nothing here diagnoses ADHD, a learning disability, giftedness, or anything else. It is for personal understanding.
• If a sitting is mostly the same option, or finished faster than the items can be read, we mark it as thin. That is a check on the session, not a clinical validity scale.

Sources

The same reading note is also on a few public records. Those copies do not replace this method page.

1. Wechsler, D. (2008). WAIS-IV Technical and Interpretive Manual. Pearson.FSIQ vs GAI as two composites; discrepancy tables; GAI from VCI + PRI (the four-index edition).
2. Pearson. WAIS-IV Technical and Interpretive Manual update, Table C.2.Critical values for FSIQ–GAI must account for shared subtests. Statistical significance is often only a few points.
3. Wechsler, D. (2024). Wechsler Adult Intelligence Scale, Fifth Edition. Pearson.Five primary indexes: VCI, VSI, FRI, WMI, PSI. GAI remains an ancillary composite that drops WMI and PSI.
4. Wechsler, D. (2014). WISC-V Administration and Scoring Manual. Pearson.GAI from Similarities, Vocabulary, Block Design, Matrix Reasoning, and Figure Weights. Visual Puzzles is not in GAI.
5. Saklofske, D. H., Prifitera, A., Weiss, L. G., Rolfhus, E., & Zhu, J. (2005). Clinical interpretation of the WISC-IV GAI.Why GAI exists: a general-ability estimate less pulled by working memory and speed.
6. Carroll, J. B. (1993). Human Cognitive Abilities. Cambridge University Press.Three-stratum model behind later CHC work.
7. Schneider, W. J., & McGrew, K. S. (2018). The Cattell–Horn–Carroll theory of cognitive abilities.Gc, Gf, Gv, Gwm, Gs as the broad abilities our five domains map onto.