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What is a z-score?

What is a z-score?

Lead consultant at Test Partnership, Ben Schwencke, explains what is a z-score.

grey clock icon 0:25 Quickly understand z-scores.

Z-scores are standardised scores which quantify the number of standard deviations a particular raw score (the raw number of correct answers) is above or below the mean. For example, a Z-score of +1 indicates that a particular score is exactly one standard deviation above the mean, whereas a Z-score of -1 indicated that a particular score is exactly one standard deviation below the mean.

By definition, a Z-score of 0 represents a score which is identical to the mean itself, equivalent to a percentile rank of 50. Z-scores are commonly used in psychometric testing, providing a benchmarked score against a particular norm group.

Z-scores are calculated using the following formula:

(Raw score – Mean) / Standard deviation

Here is a worked example:

Raw score: 20

Mean: 16

Standard deviation: 5

(20-16) / 5 = 0.8

In psychometric assessment, Z-scores are more useful than raw scores, as raw scores tell us nothing about how that score compares to any external benchmark.

For example, if a student scores 80/100 on an assessment, is that a high or low score? If the mean score is 50, then this likely represents a high score.

However, if the average score is 90, then this score is technically below average. A Z-score of 1.25 however, gives us everything we need to know about the student’s score in context, making it far more useful for decision making.

Z-scores are also the simplest form of standardised score to calculate, and thus many other standardised scores are derived from it. This includes Sten scores, T-scores, Stanine scores, and even IQ test scores.

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