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I have a test divided into two sections of 25 questions each. The two sections (A & B) use different likert scales: A - 0 to 6, and B - 1 to 5. I want to calculate the mean score (score / number of answers) for everybody on those scale for each section and for the test.

Since there are two Likert-type scales, can I calculate separate mean for each part and then transform them into z-scores and then add them together?

(Because after that I want to do a t-test to compare the two groups on that.)

gung - Reinstate Monica
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lili
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    Technically you should not be taking the mean of a likert scaled response since it is ordinal. Of course people routinely do this with 5 or 6 category response sets. You'd be adding another layer on this by converting the mean scores to z scores so now you're building in standard deviation into the scores as well (which is not appropriate for ordinal items such as yours). So can you do it? Yes. Should you? Maybe not. If I were a reviewer I would take issue. Isn't this something that could be better handled with item response theory or factor analysis of a polychoric correlation? – whauser Apr 18 '16 at 14:41
  • I edited my question and for the rest I will read on that because I never heard of those solution, thank – lili Apr 18 '16 at 15:55
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    As to the issue with the t-test, again that's a difference of means test, not really appropriate for ordinal data. If you want to compare one form of the test to the other (to examine the difficulty of it, for example) then I think this is something that IRT would do really well. If you have two groups that you want to compare (say men and women) then you could compare the individual items across sex using the wilcoxon rank-sum test also referred to as the mann-whitney u (a t-test for ordinal data). – whauser Apr 18 '16 at 17:11
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    See https://stats.stackexchange.com/questions/97/what-are-good-basic-statistics-to-use-for-ordinal-data – Tim Apr 18 '16 at 20:32

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