Short answer
A percentile describes relative position in a specified reference distribution. The 84th percentile means approximately 84% of that reference distribution falls below the score, subject to the publisher's handling of ties. It does not mean 84% correct or 84% more ability.
A worked mathematical example
For an ideal normal distribution with mean 100 and standard deviation 15, calculate z = (score − 100) / 15, then use the standard normal cumulative distribution function Φ(z). The modeled percentile is 100 × Φ(z).
| Score | z | Modeled percentile |
|---|---|---|
| 100 | 0 | 50.00 |
| 105 | 0.333 | 63.06 |
| 130 | 2 | 97.72 |
| 135 | 2.333 | 99.02 |
Why equal score gaps do not mean equal percentile gaps
The change from 100 to 105 is about 13.06 percentile points. The change from 130 to 135 is about 1.29 percentile points. Equal point increases produce smaller absolute percentile jumps near the tails, where the curve contains less probability mass. Tail rarity can still change substantially in relative terms. These are different comparisons.
These values are calculations from an assumed distribution, not observed population frequencies or evidence of a test's precision. Actual norm tables can differ, and scores near an instrument's limits require particular care.
Does this convert my AurorIQ result?
No. AurorIQ now reports a proprietary 20–80 reasoning index from a bounded internal model, with no representative population norm sample. Converting that index to a percentile would turn a product scale into an unsupported population ranking. The site therefore reports observed answers, model-based domain evidence and explicit limitations instead.
How to read a real norm-referenced report
Identify the test, reference population, version and intended use. Follow its published guidance on measurement uncertainty and appropriate interpretation. A small movement in rank is not automatically a meaningful change in the person.
Read AurorIQ's norming status and the IQ explanation.
References
- AERA, APA & NCME (2014). Standards for Educational and Psychological Testing. American Educational Research Association.
These sources support the specific research statements linked above. They do not establish reliability, norms or validity for AurorIQ.