A stanine score, short for “standard nine” score, is a way to scale test scores on a nine-point standard scale.
Using this method, we can convert every test score from the original score (i.e. 0 to 100) to a number between 1 and 9.
We use a simple two-step process to scale test scores to stanine scores:
1. Rank each test score from lowest to highest.
2. Give the lowest 4% of scores a stanine score of 1, the next lowest 7% of scores a stanine score of 2, and so on according to the following table:
In general, we regard test scores as follows:
- Stanines 1, 2, 3: Below average
- Stanines 4, 5, 6: Average
- Stanines 7, 8, 9: Above average
It turns out that a stanine scale has a mean of five and a standard deviation of two.
Pros & Cons of Stanine Scores
Stanine scores offer the follow pros and cons:
Pro: Stanine scores allow us to gain a quick understanding of where a given test score lies relative to all other test scores.
For example, we know that a student who receives a test score in stanine 5 belongs to the middle 20% of all test scores. And we know that a student who falls in stanine 9 received a test score in the top 4% of all scores.
Con: The drawback of using stanines is that each stanine is not equally sized and a test score in a given stanine could be closer to scores in the next stanine compared to scores within its own stanine.
For example, students who receive a score in the 40th through 60th percentile are all grouped together in stanine 5. However, a student whose test score falls in the 58th percentile would be closer to the scores received in stanine 6 compared to most of the scores received in stanine 5.
Alternatives to Stanine Scores
Two alternatives to stanine scores are percentiles and z-scores.
1. A percentile tells us the percentage of all scores that a given test score lies above.
For example, a test score at the 90th percentile is higher than 90% of all test scores. A test score that falls at the 50th percentile is exactly in the middle of all test scores.
2. A z-score tells us how many standard deviations a given score is from the mean. It is calculated as:
z = (X – μ) / σ
- X is a single raw data value
- μ is the mean of the dataset
- σ is the standard deviation of the dataset
We interpret z-scores as follows:
- A positive z-score indicates that a test score is above the mean
- A negative z-score indicates that a test score is below the mean
- A z-score equal to zero indicates a test score that is exactly equal to the mean
The further away a z-score is from zero, the further a given test score is from the mean.
Both z-scores and percentiles give us a more precise idea of where certain test scores rank compared to stanine scores.