What is important in using z-scores, is the ability to compare one individual's data from 2 different tests, regardless of the scale used. By converting the scores into z-scores, we can then determine in which tests the individual performed better compared to the rest of the people who took that test.
Imagine Rich has taken 2 agility tests (Illinois test and the shuttle test) and his following scores are: Illinois = 25 seconds; Shuttle = 42 seconds. He was part of a group of prospects and coaches are trying to determine who to recruit for their team.
Although it appears that the scores are almost identical and he might have performed better in the Illinois compared to the Shuttle, we need to be able to see if, in the grand scheme of things, it is actually true. In addition, we need to look at the group of people tested and how John did in comparison to the group.
Data needed:
Illinois Mean time for the group = 30 seconds; Standard deviation for the group = 3 seconds
Shuttle Mean time for the group = 40 seconds; Standard deviation for the group = 4 seconds
Determine if John is higher (+) or lower (-) on the Illinois test compared to the Shuttle test and by how many standard deviations. Your answer should be written using the following format: +2.10 (if Illinois is superior) or -0.45 (if Shuttle is superior) [those are just arbitrary numbers]. To get this, you will need to compute each z-score and then subtract them to see the difference.