How the interval is worked out

No test is perfectly reliable. Every score contains some error from fatigue, distraction and the luck of which items were easy. The standard error of measurement (SEM) puts a size on it: SEM = SD × √(1 − reliability). The 95% interval is the score ± 1.96 × SEM.

Worked example: a score of 125 with reliability 0.95. SEM = 15 × √0.05 = 3.35. The interval is 125 ± 6.6, which rounds to 118 to 132. That runs from the 88.5th to the 98.4th percentile, and crosses from high average to very superior on the IQ chart.

Which reliability should you pick?

Use the figure published in the test's manual if you have it. The WAIS-IV manual reports a full-scale reliability of 0.98 (see Canivez, 2010, below). For a test with no published figure, the lower options are assumptions. They show how quickly the interval widens as reliability falls, and they are not measured values for any online test, ours included.

The interval covers random error only. It does not fix a test normed on the wrong group, or norms that have aged. To read the score itself, use the IQ percentile calculator, or put two scores side by side with the IQ comparison tool. For index, scaled or T-scores on a report, the standard score to percentile calculator converts each one. A score that will be used for a decision needs a psychologist, not an online estimate.

Frequently asked questions

What is a confidence interval for an IQ score?

A range built around an obtained score that is likely to contain the person's true score. A 95% interval means that if the same person were tested many times under the same conditions, about 95% of such intervals would contain the true value. It does not say how good any one test is, only how much error to allow for.

What is the standard error of measurement (SEM)?

The typical size of the error in a score. SEM = SD × √(1 − reliability). On the WAIS-IV full scale, reliability is 0.98 and the SEM is about 2.1 points. At a reliability of 0.90 it is about 4.7.

Why do different IQ tests have different reliability?

Reliability depends on the number and quality of items, testing conditions and how the test was normed. A long clinical battery given by a trained examiner is more reliable than a short test taken at home. The lower values in this calculator are assumptions, not measurements of any named test.

How wide is the interval for a typical IQ test?

About ±6.6 points at a reliability of 0.95 and ±9.3 at 0.90, for a 95% interval. So a score of 125 on a test of reliability 0.90 is better read as 116 to 134.

IQ chart: levels and score rangesEvery level from extremely low to very superior, with its score range and the share of people in it.
IQ bell curve and standard deviationThe shape of the distribution, and how many people fall within each standard deviation.
IQ percentile calculatorTurns an IQ score into an exact percentile and z-score.
Percentile to IQ converterWorks backwards: the IQ score that sits at a given percentile, such as the 99th.
How rare is my IQYour score as 1 in N, and how many people that is in a group of any size.
Compare two IQ scoresThe gap between two scores in points, standard deviations and percentiles.
IQ classifications explainedWhat labels such as superior, gifted and borderline mean, and who uses them.

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Sources

Canivez, G. L. (2010). Review of the Wechsler Adult Intelligence Test, Fourth Edition. In Mental Measurements Yearbook, Buros Institute (reports WAIS-IV full-scale reliability of .98).
Wikipedia, Standard error of measurement.