*26*

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

where:

- 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.