Solved – Non-normally distributed data — what can I do with the z-scores

z-score

layman here…

I have some sets of several hundred scores that are not distributed normally. I want to normalize these scores onto a percentile scale.

The mean-median-mode for these look like this:

3-2-0,
1-1-0,
9-3-0,
1-5-5,

I have calculated the variance/std dev and z scores for these, but now I'm not sure what to do with this info. What good are z scores when the distribution isn't normal? What's the best way to get a normalized percentile score for these?

Best Answer

You can get percentiles from any distribution, normal or not. The percentile just says what percent of people did worse than the person. In fact, any reasonable transformation of the scores will leave the percentiles unchanged, because it will leave the order the same.

I am not sure I understand your mean, median, mode.

Were your scores all integers? Even if they were, the mean will be very unlikely to be an integer.

Why do you want to normalize the scores? What will you do with them once normalized?

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