Z scores and sten scores are both standardized scores used to compare data points from different distributions. While they share similarities, they differ in their scales and interpretation.
Z Scores
A Z score represents how many standard deviations a data point is away from the mean of its distribution. It is calculated by subtracting the mean from the data point and dividing by the standard deviation.
- Formula: Z = (X - μ) / σ
- Where:
- X = Data point
- μ = Mean of the distribution
- σ = Standard deviation of the distribution
- Interpretation:
- A Z score of 0 indicates the data point is equal to the mean.
- A positive Z score indicates the data point is above the mean.
- A negative Z score indicates the data point is below the mean.
Sten Scores
A sten score is a standardized score that falls on a scale of 1 to 10, with a mean of 5.5 and a standard deviation of 2. Sten scores are commonly used in psychology and education.
- Scale: 1 to 10
- Mean: 5.5
- Standard Deviation: 2
- Interpretation:
- Sten scores are used to compare individuals within a group on a specific trait.
- A sten score of 5.5 represents the average score.
- Scores above 5.5 indicate above-average performance, while scores below 5.5 indicate below-average performance.
Key Differences
- Scale: Z scores have an infinite scale, while sten scores have a finite scale of 1 to 10.
- Mean: Z scores have a mean of 0, while sten scores have a mean of 5.5.
- Standard Deviation: Z scores have a standard deviation of 1, while sten scores have a standard deviation of 2.
- Interpretation: Z scores indicate the distance from the mean in standard deviations, while sten scores provide a relative ranking within a group.
Examples
- Z Score: If a student scores 80 on a test with a mean of 70 and a standard deviation of 10, their Z score would be 1. This means their score is one standard deviation above the mean.
- Sten Score: If a student's sten score on an intelligence test is 7, it indicates they are above average in intelligence compared to others in their group.
In summary, Z scores and sten scores are both standardized scores used to compare data points, but they differ in their scales, means, and interpretations. Z scores provide a precise measure of distance from the mean in standard deviations, while sten scores offer a relative ranking within a group.
