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
Informed by visual-reasoning research
Matrix-reasoning and general-intelligence research inform the design. These references describe its background; they are not studies validating BrainRank's own measurement accuracy.
A non-verbal figure format
The questions ask you to find rules in figures rather than answer factual questions. This reduces reliance on language knowledge, but does not remove the effects of education, culture, or familiarity with the format.
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)
An IRT model allows for chance success on six-choice questions, then applies a response-time adjustment and converts ability θ using IQ=100+15θ. Item difficulty and conversion include model assumptions; the result is not equivalent to a standardized assessment.
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.