What is Stanine?
Also called Standard nine
A stanine is a standardised score on a nine-point scale with a mean of 5 and a standard deviation of 2. The name contracts 'standard nine'. Each stanine covers a fixed slice of the normal distribution, so it reports a person's position deliberately coarsely — in nine bands rather than a hundred percentile points.
The fixed slices
Stanine 1 covers the bottom 4% of the distribution, then 7%, 12%, 17%, 20% for stanine 5 in the middle, then 17%, 12%, 7%, and 4% for stanine 9 at the top. The scale was developed by United States Army Air Forces psychologists during the Second World War, where a single-digit score was a practical advantage.
The coarseness is the design, not a limitation. Nine bands are close to what a typical instrument's measurement error can actually support, and reporting in stanines makes it awkward to claim a distinction between two candidates that the test cannot sustain.
Where it misleads
The bands are unequal in width, so a one-stanine difference means different things in different parts of the scale, and the boundaries are hard: a person a fraction of a point below a boundary is reported a whole stanine lower than someone a fraction above.
Report the underlying standard score alongside the stanine wherever a decision sits near a boundary, and never compute an average of stanines across scales.
How wide the band around a stanine actually is
The claim that nine bands are about as fine as measurement error will support is checkable rather than rhetorical. Because the stanine scale is defined with a standard deviation of 2, the standard error of measurement in stanine units is 2 × √(1 − reliability) — the general formula given in NCME’s instructional module on the topic as SEM = Sx√(1 − rxx′), where Sx is the standard deviation of the scores and rxx′ the reliability coefficient.
At a reliability of 0.85 that is 0.8 stanines, so a 95% confidence band around a reported stanine is roughly ±1.5 stanines — about three of the nine bands wide. A one-stanine gap between two candidates therefore sits well inside the error of either score, and reading it as a difference is reading noise.
Harvill states the reporting consequence plainly: "Score bands or confidence bands are the best way to report test scores to examinees or other interested persons." A stanine is already a coarse band; what it usually is not is a band whose width has been stated. Print the reliability next to it and the reader can work the width out in one line.
Stanine to z-score, and the error band around it
- z = (stanine − 5) ÷ 2
- Stanine 7 → z = (7 − 5) ÷ 2 = +1.0, roughly the 84th percentile
- Stanine 3 → z = (3 − 5) ÷ 2 = −1.0, roughly the 16th percentile
- SEM in stanine units = 2 × √(1 − reliability)
- Reliability 0.90 → 2 × √0.10 = 0.63 stanines; 95% band ≈ ±1.2, about 2.5 bands wide
- Reliability 0.85 → 2 × √0.15 = 0.77 stanines; 95% band ≈ ±1.5, about 3 bands wide
- Reliability 0.75 → 2 × √0.25 = 1.00 stanine; 95% band ≈ ±2.0, about 4 bands wide
Run the last three lines against whatever reliability the manual actually reports. Below about 0.85 the 95% band is wider than three of the nine bands, which means the scale is reporting a position to a precision it cannot defend.
Not the same as sten score
A sten is a ten-point scale with a mean of 5.5 and a standard deviation of 2, common in personality questionnaires. A stanine has nine points and a mean of 5. The names are one letter apart and the scales are not interchangeable.
Sources
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