5.2 – Standardizing Scores

As we have seen thus far, the z-score can simply be used to describe where an individual’s score lies within a distribution, using the scale of a standard deviation. However, the z-score has other important uses as well. For one, it can be used to compare an individual’s scores on two different measures that have different scales (different means and standard deviations). Secondly, it can be used to compare two different individuals’ scores to each other, even if they are on different scales.

To make comparisons between scores on different scales, it is necessary to standardize the scores. A standardized scale is a scale that has a “standard” or set scale, meaning that the mean and the standard deviation are pre-determined. For example, all intelligence tests have a standardized scale where the mean is μ = 100, and the standard deviation is σ = 15. If someone were to create a new intelligence test, or IQ test, they would need to translate the results so that the average score was μ = 100, with a standard deviation of σ =  15 (we’ll discuss how to do that later in this chapter).

z-scores as a Standardized Scale

If you think about it, z-scores are actually already on a standardized scale. All z-scores have a mean of μ = 0, and a standard deviation of σ = 1. Scores that are right at the mean on the original scale will become a z-score of 0, while scores that are one standard deviation above the mean on the original scale will become a z-score of +1.0. And so on.

Thus, when we convert scores from any particular scale to z-scores, we have actually “standardized” the scores because we have translated them to a standardized scale. It is through this standardization that we can then make comparisons between scores that come from drastically different scales.