Say I have a test administered 5 times. The scores of each administration are reported as z scores. I need to aggregate the 5 scores and report a percentile. Take the average z and its associated percentile? The percentile of each test and average those? Since percentiles are not linear, I'd advocate for the first method, but want to hear arguments. (I realize there are concerns both ways.)
The first method is the percentile of average Z scores and the second method is the average percentile of the Z scores. What you do depends on what is meaningful. What is meaningful depends what your data is about. So if your data was exam results of 5 exams and you wanted to find who the top students were you would use method one. In this example I don't know what the second method would actually tell you. Now in some different circumstance (perhaps a very special circumstance) the second method may be more meaningful than the first.
On the whole I think the first method will be more informative in most circumstances.
Since percentiles are ordinal (rather than interval) measures it would not be appropriate to average them. You could take the median value of the percentiles. However if you are only deriving the percentiles from the z-score assuming a normal distribution then I would tend to aggregate on the z-scores and perform one conversion unless there was a strong reason for the other approach.
Thanks for this, Helen. Do you know of any spss syntax or excel formula to perform the z score conversion?
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