Free tool · Ranges
IQ confidence interval calculator
Updated
The short answer
A score's range is the score plus or minus a multiple of its standard error of measurement, SEM = 15 × √(1 − reliability). With the WAIS-IV's retest reliability of .96, the SEM is 3.0 points, so a 118 has a 95% range of about 112 to 124. The lower the reliability, the wider the range.
112 to 124
95% of sittings by someone whose true score is 118 would land in this range. WAIS-IV Full Scale IQ, 298 people retested after a mean of 22 days (r = .96).
- Standard error (SEM)
- 3.0 pointsSame as a reliability of .960 on the SD 15 scale.
- Labels in the range
- High Average to SuperiorThe range crosses a WAIS-IV label boundary.
- Two sittings
- Up to 8.3 points apart95% of the time, from measurement error alone (1.96 × SEM × √2), before any practice effect.
Our result comes with its own 95% range. 25 puzzles, about 12 minutes, no sign-up.
The published reliabilities, and what they do to a range
The presets in the calculator are the Full Scale IQ figures we could verify in published studies. Each row shows the SEM it implies and the 95% range around a score of 118.
| Score and study | r | SEM | 95% around 118 |
|---|---|---|---|
| WAIS-IV Full Scale IQ, internal consistency in the standardization sample (Collinson et al. 2016) | .98 | 2.1 | 114 to 122 |
| WAIS-5 Full Scale IQ, reliability averaged across ages (Winter et al. 2024) | .97 | 2.6 | 113 to 123 |
| WAIS-IV Full Scale IQ, 298 people retested after a mean of 22 days (Collinson et al. 2016) | .96 | 3.0 | 112 to 124 |
| WAIS-5 Full Scale IQ, 201 people retested after an average of 29 days (Winter et al. 2024) | .93 | 4.0 | 110 to 126 |
| WISC-V Full Scale IQ, clinic children retested after about 2.6 years (Watkins et al., 2022) | .86 | 5.6 | 107 to 129 |
The spread from the top row to the bottom is the point. Internal consistency answers “do the items agree with each other today”; retest reliability answers “would you get the same number next month”. The WISC-V row, children retested after about 2.6 years in a clinic sample, is lower again (Watkins et al., 2022). Pick the one that matches your question.
The method
Classical test theory treats an observed score as a true score plus error. The standard error of measurement is the standard deviation of that error: SEM = SD × √(1 − r), with SD 15 for a deviation IQ. A range that holds 68% of sittings is the score plus or minus 1 SEM; 90% is plus or minus 1.645 SEM; 95% is plus or minus 1.96 SEM. Two sittings each carry their own error, so the difference between them has a standard error of SEM × √2.
Test authors make the same point in words. Roid, who built the Stanford-Binet 5, cautions against describing a Full Scale IQ “as an errorless, fixed entity” (Roid, 2004). The figure below shows why: one person, one true score, and where single sittings land.
Interactive · measurement error
- SEM
- 6.1 ptsOne standard deviation of retest scatter.
- 68% of sittings
- 98 to 110About two times in three.
- 95% of sittings
- 92 to 116About 19 times in 20.
Each tick will be one simulated sitting by the same person.
True score 104. Standard error of measurement 6.1 points. Two sittings in three land between 98 and 110; 19 in 20 land between 92 and 116.
Our own range is computed differently: the scorer estimates ability with a Rasch model and reports the posterior standard error, which is smallest in the middle of the scale and grows toward the ends. The raw score to IQ table lists it for every number correct, and the methodology explains the model.
Need this on a course page? The calculator is free to embed.
Sources
- Wechsler, D. (2008). WAIS-IV Technical and Interpretive Manual. Pearson.
- Collinson, Evans, Wheeler et al., Confirmatory Factor Analysis of WAIS-IV in a Clinical Sample: Examining a Bi-Factor Model, Journal of Intelligence 5(1):2, 2016 doi.org/10.3390/jintelligence5010002
- Winter, Trudel, Kaufman, Bratsberg et al., Wait, Where's the Flynn Effect on the WAIS-5?, Journal of Intelligence 12(11):118, November 2024 doi.org/10.3390/jintelligence12110118
- Watkins, M. W., Canivez, G. L., Dombrowski, S. C., et al. (2022). Long-term stability of Wechsler Intelligence Scale for Children, Fifth Edition scores in a clinical sample. Applied Neuropsychology: Child, 11(3), 422-428. doi:10.1080/21622965.2021.1875827 pubmed.ncbi.nlm.nih.gov/33556254/
- Estevis, E., Basso, M. R., & Combs, D. (2012). Effects of practice on the Wechsler Adult Intelligence Scale-IV across 3- and 6-month intervals. The Clinical Neuropsychologist, 26(2), 239-254. doi:10.1080/13854046.2012.659219 pubmed.ncbi.nlm.nih.gov/22353021/
- Roid, G. H. (2004). Essentials of Stanford-Binet Intelligence Scales (SB5) Assessment. Wiley. Chapter 1, Overview of the SB5 and its history (publisher excerpt). catalogimages.wiley.com/images/db/pdf/0471224049.excerpt.pdf