Question

Explain how standard scores are relative vs absolute and give your own example of the difference between the two. Discuss when relative scores as opposed to absolute scores are important?

Answer 1

Standard scores are nothing but normalised scores for the set of values.

The formula of a standard score is given by

Where, x is the absolute score, ie. the original observation; mean and s are respectively the mean and standard deviations of the distributions.

So, the original score was x, whereas the standard score was

For example, a student gets 75 in a test, where the mean score is 79, and the standard deviation is 4.

So, the z-score or standardised score is

So, here the original absolute score was 75, but the z-score or the standard score is -1.

Relative scores are important, when comparing two different scores from two different populations.

For example, in section A a student scores 80, and in section B, a student scores 82 in the same subject.

But, we cannot compare these scores directly, for they come from different populations.

Let, section A has mean score 76 and standard deviation 4; section B has mean score 85 and standard deviation 3.

So, we note that the z-score of the first student is +1, whereas that of the second student is -1.

So, now these two can be compared as they are both standardised.

So, we can say that though the second student has more absolute marks, his z-score is actually less, and thereby the first student has done better.