IQ Confidence Interval Calculator
An IQ score is an estimate, so psychologists report it with a confidence interval. Enter an observed score, the test reliability and the scale to get the standard error of measurement (SEM) and the 68%, 90% and 95% ranges. Example: a score of 110 with reliability 0.95 on SD 15 has SEM 3.35 and a 95% interval of about 103.4 to 116.6.
Full-scale IQ reliability is often reported near 0.95 to 0.98. Check the test manual.
Show steps
How to use the IQ Confidence Interval Calculator
- Enter the observed IQ score.
- Enter the reliability coefficient from the test manual (for example 0.95).
- Pick the scale (SD 15 for most tests).
- Press Calculate to see the SEM and the 68%, 90% and 95% intervals.
Formula and method
The standard error of measurement is SEM = SD x sqrt(1 - r), where r is the reliability. An interval is score +/- z x SEM, with z = 1.00 for 68%, 1.645 for 90% and 1.96 for 95%. The Kelley estimate of the true score is 100 + r x (score - 100) with standard error SD x sqrt(r(1 - r)).
What is a confidence interval for an IQ score?
No test measures ability perfectly. If the same person took parallel versions of a test, scores would vary a little. The confidence interval gives a range that is likely to contain the person’s underlying score. It is the reason a report might say 110 (95% CI 104-116) rather than just 110.
Reliability and SEM table (SD 15)
| Reliability | SEM | 95% margin |
|---|---|---|
| 0.90 | 4.74 | +/- 9.3 |
| 0.93 | 3.97 | +/- 7.8 |
| 0.95 | 3.35 | +/- 6.6 |
| 0.97 | 2.60 | +/- 5.1 |
| 0.98 | 2.12 | +/- 4.2 |
Why a single score is not a single number
Scores can differ across days, test versions and examiners. Short online tests have lower reliability, so their intervals are much wider than for a full-length individually administered battery. If a quiz has a reliability of 0.80, the SEM on SD 15 is 6.7 points and a 95% interval spans about 26 points.
Limits and responsible use
Important: this is a statistics tool, not an IQ test. It converts a score you already have into a percentile and a descriptive band using a normal (bell-curve) model. Clinical IQ scores come only from a standardized test given and interpreted by a qualified psychologist, and online quizzes give estimates at best.
Frequently asked questions
What is the standard error of measurement of IQ?
Typically around 2 to 4 points for full-scale scores on major tests, depending on reliability.
What is a 95% confidence interval for an IQ of 100?
With reliability 0.95 on SD 15, about 93.4 to 106.6.
Why does reliability matter?
The lower the reliability, the larger the error and the wider the interval.
What is the Kelley true score?
A regression-based estimate of true ability that shrinks the observed score toward the mean in proportion to unreliability.
Does the interval tell me my real IQ?
It tells you a likely range, not a guarantee. Roughly 5 percent of intervals miss the true value.
Can I use this for online tests?
Only if you know the test reliability, which most online quizzes do not publish.
Sources
- Standard error of measurement (Wikipedia)
- Reliability (psychometrics) (Wikipedia)
- Intelligence quotient (Wikipedia)
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