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.
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!