Methodology & Scientific Basis
BrainRank uses the Raven's Progressive Matrices format to measure nonverbal fluid intelligence (Gf). It is a global-standard method that does not depend on language, culture, or education and strongly reflects general intelligence g.
Why abstract figures can measure IQ
Strongly reflects the g factor
Raven's matrix reasoning is considered one of the tasks that best reflects the general intelligence g (Spearman 1904) common to many cognitive challenges, and it is known to have a high g loading.
Independent of language and culture
Because it uses only abstract figures, it is largely unaffected by language ability, educational background, or cultural knowledge, allowing fluid reasoning (Gf) to be measured in a pure form (CHC theory; McGrew 2009).
Rules are theoretically defined
Items are automatically generated based on the rules Carpenter et al. (1990) identified in the RPM (rotation, quantitative progression, addition and subtraction of figures, and distribution of three values). Each answer is uniquely determined.
Scored with item response theory (IRT)
Rather than counting correct answers, ability θ is estimated with an IRT model that adds a guessing floor c=1/6 for the 6-choice items (so lucky guesses are not mistaken for ability), so correctly answering harder items is weighted more heavily. The estimate is calibrated to a population of θ~N(0,1) and converted to IQ=100+15θ (deviation IQ, SD 15).
Test structure (4 domains · Carpenter et al. 1990 rules)
20 questions, 6 choices each. The rules of Raven's matrices are mapped to four categories and presented in random order.
Mental rotation and spatial transformation (fluid reasoning, Gf)
Induction of series and rules (quantitative progression)
Deduction by superimposing figures (addition and exclusion)
Distribution and classification of attributes (three-value rule)
Scoring (item response theory, IRT)
Rather than counting correct answers, we estimate each test taker's ability θ with the Rasch (1PL) model. Each item has a difficulty b, and correctly answering harder items is weighted more heavily.
P(correct | θ, b) = c + (1 − c) / (1 + exp(−(θ − b))), c = 1/6
Since each item has 6 choices, we add a guessing floor c = 1/6 (a 3PL-style lower asymptote) so that lucky guesses are not mistaken for ability — without it, scores inflate by ~7 IQ points. The 20-item MAP estimate is then calibrated to the population scale (Monte-Carlo tuned) so that θ ~ N(0,1) and IQ = 100 + 15θ (Wechsler-style deviation IQ, SD 15), deviation score = 50 + 10θ, top % = 1 − Φ(θ), and national rank = top % × a 1,000,000-person test-taker reference base.
References
- Spearman, C. (1904). “General Intelligence,” Objectively Determined and Measured (the discovery of general intelligence g) The American Journal of Psychology, 15(2), 201–293.
- Raven, J. C. (1938). Raven's Progressive Matrices (the standard measure of nonverbal, fluid intelligence) London: H. K. Lewis.
- Carpenter, P. A., Just, M. A., & Shell, P. (1990). What one intelligence test measures: A theoretical account of the processing in the Raven Progressive Matrices Test (decomposing RPM into five rule types) Psychological Review, 97(3), 404–431.
- Rasch, G. (1960). Probabilistic Models for Some Intelligence and Attainment Tests (IRT / the Rasch model) Danish Institute for Educational Research.
- McGrew, K. S. (2009). CHC theory and the human cognitive abilities project (CHC theory) Intelligence, 37(1), 1–10.
Try it yourself
Take the free IQ test* This service is not intended for medical or psychological diagnosis. The b parameters and population distribution are to be recalibrated once real data accumulates, and the displayed IQ is an estimate.