How to Understand Standard Scores

This short article aims to explain – in a non-technical way – what standard scores (Z-scores) are and also give you a few tips about how to interpret and use them.

So, what should you, as a novice EFL teacher, need to know and understand about standard scores? Here are just a few useful tips worth remembering.

A standard score is defined by the formula below: ‘X’ is the student’s actual score, ‘AV’ is the average class score, and ‘SD’ is the standard deviation of the class scores.

Z= (X-AV)/SD

To calculate the AV, add all the students’ scores together and divide this sum by the number of students. The calculation of the SD is beyond the scope of this article; however, you can easily do it on your calculator or on some on line sites: just feed in the students’ actual scores and relax! The SD is important because it gives you a measure of the spread of the Z-scores from the AV.

Here’s an example to show you one way Z-scores can be useful. A student scored 86 in grammar test-1 in which the AV was 75 and the SD was 10. In grammar test-2, in which the AV was 84 and the SD was 16, the student scored 90. In which test was the student’s relative standing higher?

The Z-score for test-1 was 1.1, and for test-2 it was 0.375; therefore, the student’s relative standing was better in test-1 because the Z-score was 1.1 SDs above the AV – whereas in test-2 it was only 0.375 SDs above the AV.

You can also use Z-scores for single tests: the Z-scores will then tell you exactly how well a particular student performed in terms of the distance of the student’s Z-score from the AV, e.g., a Z-score of –1.3 means that the student has scored below the AV: in fact, the Z-score is 1.3 SDs below the AV – not good!

Finally, here are a few useful tips:

1.) A Z-score of 0 means an actual score equal to the AV.
2.) Z-scores that are ±2 SD or more beyond AV are called outliers: very few students will get such Z-scores.
3.)Approximately 68% of the Z-scores should lie within ±1 SD of the AV.
4.) Z-values can be graphically represented by a bell curve.

Next time you set a test, try using Z-scores to analyze your class’s test scores – impress yourself!