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# Percentages, percentiles, and stanines

It is important to know the different ways different tools measure student achievement, and what that might mean for your analysis.

## Percentage

A percentage is the number out of every hundred with a particular attribute. For example, if 120 of 150 candidates pass an assessment, the percentage pass rate is 80% (80 out of every hundred).

## Percentile

A percentile is a position in a rank ordering expressed as the percentage who are lower in the rank order. For example, a student at the 70^{th} percentile performed better than 70% of other candidates.

## Stanine

Stanine(STAndard NINE) is a method of scaling test scores on a nine-point standard scale with a mean of five (5) and a standard deviation of two (2).

Test scores are scaled to stanine scores using the following algorithm:

- Rank results from lowest to highest
- Give the lowest 4% a stanine of 1, the next 7% a stanine of 2, etc., according to the following table:

Calculating Stanines |
|||||||||
---|---|---|---|---|---|---|---|---|---|

Result Ranking
| 4% | 7% | 12% | 17% | 20% | 17% | 12% | 7% | 4% |

Stanine
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

The underlying basis for obtaining stanines is that a normal distribution is divided into nine intervals, each of which has a width of 0.5 standard deviations excluding the first and last. The mean lies at the centre of the fifth interval.

Stanines can be used to convert any test score into a single-digit number. However, because all stanines are whole numbers, two scores in a single stanine are sometimes further apart than two scores in adjacent stanines. For example, students with scores represented at the top of stanine four are closer to those students at the bottom of stanine five than those at the bottom of stanine four, but both are represented as just stanine four. This reduces their value.

# Percentiles and stanines – interactive illlustration

The following interactive illustration shows how different test scores for students can be compared in terms of percentiles and stanines. Click on the buttons for the five different students to see how their marks compare to the rest of the class.

## Percentiles of Students

This test was marked out of 50. The mean is % and the standard deviation is %.

*This score is ?/50 (?%) and it is in the ? percentile. This means that the student performed better than ?% of the other students. This student is in the ? stanine.*