How this IQ test is scored

1. The instrument: built on ICAR

The test is built on David Condon and William Revelle’s International Cognitive Ability Resource (ICAR), an open cognitive-ability item bank developed at Northwestern University and published in Intelligence (2014). Its 33 questions cover matrix reasoning (3×3 pattern completion), letter and number series, and verbal reasoning, plus a short numerical section. ICAR was created so that anyone could give a defensible reasoning test without licensing a proprietary instrument, and that is what we use it for.

The 33 were chosen for (a) coverage of the four reasoning kinds, (b) a difficulty curve that ramps from a five-item warm-up into harder matrix puzzles, and (c) a sitting most people finish in about nine minutes.

Source: icar-project.com · Condon, D. M., & Revelle, W. (2014). Intelligence, 43, 52–64.

2. The 33 items, by domain

Item IDs are stable: each question has a fixed identifier in our scoring data so the same item always scores the same way. Spatial reasoning is intentionally over-represented because matrix reasoning is the single best-validated proxy for fluid intelligence (g_f).

A five-item warm-up (iq-mx-01, iq-mx-02, iq-ar-04, iq-mx-03, iq-ar-08) is presented first to ease test-takers in before harder spatial items are introduced.

3. How we score

Scoring runs in your browser the moment you finish. Three steps:

1. Domain raw counts. For each of the four domains, count the number of correct answers. Maximums are 6 (Abstract), 4 (Verbal), 3 (Numerical), and 20 (Spatial), summing to 33.
2. Composite raw → IQ scale. The composite is the sum of domain raw scores. We map this composite onto a normative IQ scale with mean = 100 and standard deviation = 15, clamped to a 55–155 display range.
3. Percentile & band. We convert IQ to a percentile using the standard normal CDF (Abramowitz & Stegun rational approximation), then label one of six bands (Significantly Below Average through Very Superior) for plain-English context.

The display formula is fixed and deterministic. You can reproduce it from these constants:

// apps/myiqtested/packages/scoring/src/iq-norm.ts
const IQ_REFERENCE_MEAN_TOTAL = 16.5;
const IQ_REFERENCE_SD_TOTAL   = 5;
const IQ_MIN = 55;
const IQ_MAX = 155;

function totalCorrectToNormativeIq(totalCorrect) {
  const z  = (totalCorrect - IQ_REFERENCE_MEAN_TOTAL) / IQ_REFERENCE_SD_TOTAL;
  const iq = Math.round(100 + 15 * z);
  return Math.max(IQ_MIN, Math.min(IQ_MAX, iq));
}

Result pages show a ±5 IQ confidence band (the “display SE”). This reflects the typical day-to-day fluctuation an online test taker can expect from session-level noise (fatigue, distraction, screen size). It is not a clinical confidence interval.

4. Reliability & validity: what we can and cannot say

ICAR’s published validation (Condon & Revelle, 2014) found its total score correlated r = .81 with the Shipley Institute of Living Scale, with internal consistency of α = .81–.93 across its subtests, and its items correlate r = .60–.80 with established measures such as Raven’s Progressive Matrices and WAIS subtests. On top of that, here is what we measure on this test, on our own takers:

• Retest movement. Of 894,632 people who took the test twice, 35.1% changed by ten points or more, and very high first scores usually came down. A calm first attempt is the fairer read.
• Time on task. In our US data, people who finished in under two minutes averaged about 30 points lower than people who took ten to fifteen. Rushing costs more than most people expect.
• Internal consistency. The split-half figure on the adult country sample, and how it changes as the sample is narrowed, is reported with the country dataset, where the method and its weak points are set out in full.

What we have not done is validate this test against a clinical instrument such as the WAIS-IV, and we make no claim that its scores agree with one. Online, unsupervised scores on this test run higher than supervised scores, and the results page says so.

5. Known limitations

We publish these so you can decide for yourself how much weight to put on the result.

• Item exposure. The 33 items are currently fixed. A motivated test-taker who has seen the answers elsewhere can inflate their score. We have a planned expansion to a larger item pool with per-session randomisation.
• Internet sample bias. Online IQ test takers skew younger, more educated, and more curious about cognitive science than the general population. Norms derived from internet samples may shift the distribution slightly versus census-representative samples.
• Flynn drift. Population IQ has historically risen by about 3 points per decade. Our display norms (mean=100, SD=15) follow the WAIS-IV convention but do not auto-recalibrate for current cohort drift.
• No working memory or processing speed subtests. This is a reasoning-only test. Two of the four CHC broad abilities (Gwm, Gs) are not measured here.
• Not a clinical assessment. A full clinical IQ evaluation requires a licensed psychologist, controlled conditions, and a comprehensive battery (WAIS-IV, Stanford-Binet). Online tests can shift by 5–10 points based on session conditions alone.

6. Changelog