Aurelian Skills Academy · Cognitive Assessment

Measure how you reason.

Choose an assessment. Find a quiet place, use a laptop or phone, and complete it in one sitting without calculators or outside help.

Indicative

Standard IQ Test

The classic online IQ format: matrices, number series, analogies and shape rotation.

30 questions
20 minutes
Estimated IQ score

Disclaimer: This test scores against assumed, not measured, population norms. Results are indicative only and less reliable than the CRI. It is not a clinical or diagnostic IQ assessment.

Research-based · Recommended

Cognitive Reasoning Index

Four timed subtests built on the Cattell-Horn-Carroll model of intelligence, scored with Item Response Theory.

40 questions
28 minutes
Percentile & 95% confidence band

Reliability is measured live from real responses. Norm sample building · 0 / 300

The Science Behind These Tests

This page explains what each assessment measures, how it is scored, how reliable it is, and where its limits lie. We publish this so that anyone, including qualified psychologists, can check our reasoning.

1. What intelligence tests measure

Modern intelligence research is built on the Cattell-Horn-Carroll (CHC) theory, which organises cognitive ability into a general factor (g) and a set of broad abilities. These include fluid reasoning (Gf), crystallised knowledge (Gc), quantitative reasoning (Gq) and visual processing (Gv). CHC is the framework behind most major professional tests, including the WAIS-IV and the Woodcock-Johnson IV. Scores on different reasoning tasks correlate positively with one another, the so-called "positive manifold". This is why a short battery of varied tasks can estimate general reasoning ability.

2. How the two tests differ

	Standard IQ Test	Cognitive Reasoning Index (CRI)
Purpose	Familiar online IQ format	Research-grade estimate of reasoning ability
Items	Fixed set of 30 mixed items	40 items, randomly drawn from a 120-item bank, 10 per CHC ability
Difficulty values	Assumed (expert-set), never updated	Recalibrated from real response data
Norms	Assumed general population (mean 100, SD 15)	Measured from the Aurelian norm sample once n ≥ 300
Uncertainty reported	Yes (95% range)	Yes (95% confidence interval) plus live reliability
Best used for	Curiosity, engagement, workshops	Developmental feedback and comparison within the Aurelian population

3. Item design

Matrix reasoning (Gf). 3×3 grids governed by the rule types Carpenter, Just & Shell (1990) identified in Raven-style problems: constant, progression, distribution-of-three and addition. Difficulty rises with the number of rules operating at once. This relationship was demonstrated by Embretson (1998), whose cognitive-design approach underpins automatic item generation. Each wrong option breaks exactly one rule, so errors are informative rather than random.
Series reasoning (Gf/Gq). Number and letter series of the kind used in the public-domain ICAR project (Condon & Revelle, 2014). They range from constant steps to second-order and alternating rules. Wrong options include the answer a person would reach with a common faulty rule.
Verbal reasoning (Gc). Analogies, vocabulary and deductive logic, including syllogisms and contrapositives, which test reasoning rather than general knowledge.
Spatial rotation (Gv). A two-dimensional adaptation of the mental rotation paradigm (Shepard & Metzler, 1971). Every wrong option is a mirror image of the target, which no rotation can produce. The test therefore isolates mental rotation rather than shape matching.

All items are original. No items are copied from Raven's Progressive Matrices, the WAIS or any other copyrighted test. Generated items are deterministic: an item ID always produces the identical item, so statistics collected on an item stay valid over time.

4. Scoring: Item Response Theory

Both tests use Item Response Theory (IRT) rather than simply counting correct answers. Each item has a difficulty value b. The probability of a correct answer for a person of ability θ is:

P(correct) = c + (1 − c) / (1 + e^{−(θ − b)})

Here c is the chance of guessing correctly (1 ÷ number of options). Ability is estimated with the Expected A Posteriori (EAP) method (Bock & Mislevy, 1982). EAP gives a stable estimate even for very high or very low scorers. It also produces a standard error, which we use to report a 95% confidence interval. No test score is exact, and we show the range rather than hide it.

Scores are expressed on the conventional scale: mean 100, standard deviation 15. Descriptive bands follow the terminology of current Wechsler scales: Extremely Low (<70) through Extremely High (130+).

5. How the CRI earns its reliability

Stratified random forms. Each person receives 3 easy, 4 moderate and 3 hard items per subtest. Forms are parallel, and memorising answers is ineffective.
Calibration. Once an item has 50 or more responses, its difficulty is re-estimated from real performance. This happens automatically every 25 valid completions.
Measured norms. Until 300 valid completions exist, CRI scores are labelled provisional. After that, percentiles come directly from the Aurelian norm sample rather than from assumptions.
Reliability, published live. Because forms are randomised, we report IRT marginal reliability, the IRT counterpart of Cronbach's α (Green et al., 1984). Current CRI reliability: not yet available (needs at least 10 valid completions). Values of 0.80 or above are generally considered good for group-level and developmental use. Clinical and high-stakes decisions require 0.90 or above.
Item quality monitoring. Each item's discrimination (point-biserial correlation with overall ability) is tracked. Items below 0.15 are flagged for review.

6. Integrity checks

Online tests are unproctored, so each result records tab switching, completion speed and unanswered items. Results that trigger these checks are excluded from the norm sample until reviewed. This follows professional guidance on unproctored internet testing (Tippins et al., 2006).

7. Honest limitations

Not a clinical IQ test. Neither test replaces an individually administered assessment by a qualified psychologist (for example, WAIS-IV or Stanford-Binet 5). Neither should be used for diagnosis.
Norm group. CRI norms describe the people who take the CRI, not the general population. A percentile shows where you stand relative to that group.
Language. The verbal subtest assumes working fluency in English. Non-native speakers may score lower on Gc for language reasons rather than reasoning ones.
Flynn effect. Population performance on reasoning tests rose substantially during the 20th century (Flynn, 1987). Norms therefore age and must be refreshed, which is why CRI norms recalibrate continuously.
Employment use. General mental ability predicts job performance, but more modestly than older estimates suggested (Sackett et al., 2022, corrected r ≈ 0.31). Neither test has been validated for selection. They should not be the sole basis for hiring or screening decisions.
Short subtests. Ten items per ability give a useful profile, but subtest scores are less reliable than the overall score. Interpret differences between subtests cautiously.

8. Data and privacy

Your name, email, optional mobile number and responses are stored only with your consent, for assessment and research purposes, in line with India's Digital Personal Data Protection Act, 2023. To request access to or deletion of your data, contact [email protected].

References

Bock, R. D., & Mislevy, R. J. (1982). Adaptive EAP estimation of ability in a microcomputer environment. Applied Psychological Measurement, 6(4), 431–444.
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. Psychological Review, 97(3), 404–431.
Carroll, J. B. (1993). Human cognitive abilities: A survey of factor-analytic studies. Cambridge University Press.
Condon, D. M., & Revelle, W. (2014). The International Cognitive Ability Resource: Development and initial validation of a public-domain measure. Intelligence, 43, 52–64.
Embretson, S. E. (1998). A cognitive design system approach to generating valid tests: Application to abstract reasoning. Psychological Methods, 3(3), 380–396.
Embretson, S. E., & Reise, S. P. (2000). Item response theory for psychologists. Lawrence Erlbaum.
Flynn, J. R. (1987). Massive IQ gains in 14 nations: What IQ tests really measure. Psychological Bulletin, 101(2), 171–191.
Green, B. F., Bock, R. D., Humphreys, L. G., Linn, R. L., & Reckase, M. D. (1984). Technical guidelines for assessing computerized adaptive tests. Journal of Educational Measurement, 21(4), 347–360.
McGrew, K. S. (2009). CHC theory and the human cognitive abilities project: Standing on the shoulders of the giants of psychometric intelligence research. Intelligence, 37(1), 1–10.
Sackett, P. R., Zhang, C., Berry, C. M., & Lievens, F. (2022). Revisiting meta-analytic estimates of validity in personnel selection. Journal of Applied Psychology, 107(11), 2040–2068.
Shepard, R. N., & Metzler, J. (1971). Mental rotation of three-dimensional objects. Science, 171(3972), 701–703.
Tippins, N. T., et al. (2006). Unproctored internet testing in employment settings. Personnel Psychology, 59(1), 189–225.

IQ & Cognitive Reasoning Tests

Measure how you reason.

Standard IQ Test

Cognitive Reasoning Index