Is it possible to compute a mean/median score for a Mann Witney test/chi square test?

#1
There are two groups in my study (experimental N=19 and control N =14), and I want to see if there are any differences between the groups, so I made a survey. The survey has 15 different questions, all 5-point Likert items. However, I want to combine those items into 3 different categories, because I have 5 questions for each category. Would it be ok if I computed a mean/median score over those questions for a Mann Witney U test/chi square test (depending on if my data is normally distributed or not)? If so, which one would be better, mean or median?

Another question: what measure of central tendency should I use to see if there are differences between the two groups? I believe for a Mann Witney U test it’s very common to use the median, however won’t you have problems with ties if you do this for Likert items?
 

Karabiner

TS Contributor
#2
A sum score from 5 Likert items would usually be considered as interval scaled.
Therefore, you could consider using a Welch t-test, The t-test /
Welch t-test assumes normally distributed variables in each separate population, but
with n > 30 it is usually considered robust against violation of that assumption.

Or maybe you would like to treat your data as ordinal, and perform a U-test, or a median
test (the latter compares medians).

I would not recommend to use Chi², since it is for categorical variables.

With kind regards

Karabiner
 
#3
Thank you for your answer Karabiner. If I did use a U-test, would it still be valid if I use the average score of 5 likert scale items to compare the two groups?
 

Karabiner

TS Contributor
#4
The U-test (or Wilcoxon rank sum test, which produces exactely the same result) does not
compare means, and does not compare medians. Therefore, your descriptive statistics and your
inferential statistics will to slightly different things. You could maybe display means and medians
and add a comment about that discrepancy.

With kind regards

Karabiner
 
#5
Would it be better if I used a t-test here?
I forgot to mention the full context: I am doing research at a school. I want to see what effects a certain teaching method has on the students. For this I have one class which is the control group and another class in which I am applying the teaching method. At the end of the experiment I want to take surveys in both classes and compare them to each other, to see if the teaching method has had any effects on the class. The survey I have made is a 1-5 likert scale. I have 5 questions for each effect. There are 3 effects (motivation, discipline and ambience in class), so 15 questions in total. This means that I want to compare the average scores from both classes for each effect. Should I use mean or median for this? Do you think the u-test would work better here or the t-test?