Question

Imagine you are in charge of a program in which members are evaluated on five different tests at the end of the program. Why doesn't it make sense to simply compute the average of the five scores as a measure of performance rather than compute a z score for each test for each individual and average those?

Answer 1

Here, it is given that the members are evaluated on five different tests. When tests are different, we cannot say for certain that the difficulty level of all tests are the same. All tests may have different difficulty levels and scoring criteria. The test scores can have varying mean and standard deviation values. So, the raw scores of different tests cannot be directly compared. When we convert a value to z score, what we are doing is standardizing the raw score to a known distribution. All scores, when converted to z score, is a standardized score on a distribution with mean 0 and standard deviation 1.

Once standardized, the values will on come on a common scale and the problem of scores being on different scale no longer exists, making the scores comparable. Now if average is taken to assess the performance, it will account for the variation between the original distributions and will give a more sensible or meaningful average score.