Hello
I have 2 groups with different sample sizes of (experts: 5 to 8) and (Users: 28 to 35) answering 21 questions on a 7 points Likert scale about the importance of some dimensions for different products.
I want to compare the means of these groups for each question. I have first tested for normality of both data sets per question.
For datasets whose skewness and kurtosis were between -/+ 2 and others with a p-value above 0.05 in the Kolmogorov-Smirnov test, I have considered them normal and performed Independent T-test. For the rest of the datasets that were not normal, I performed the Mann-Whitney U test.
1- Have I done the correct procedure on the data?
2- What should I do for groups that have a variance of zero in the Mann-Whitney u test? is the result of those groups correct? (The means of the level of importance rated by both groups are not that much different but the variance of zero resulted in the rejection of the null hypothesis)
3- How can I interpret the results of the Mann-Whitney U test? since it does not compare means anymore! what does it actually compare?
Thank you for your help
There is a considerable difference between a single Likert-scored variable (which is ordinal) and a Likert-scale composed of multiple Likert-scored variables (which may be considered interval if the appropriate conditions are met). If you are working with a single Likert-scored variable, then you should definitely use the Mann-Whitney.
If you run 21 tests on the same groups, you should maybe correct for multiple testing, e.g. with a Bonferroni correction. Maybe you could run a principal components analysis on the 21 questions in order to be able to calculate subscales. These might very well have a more normal distribution.
Additionally to the previous answer you can look up this article that may provide a help for decision making:
Article Wilcoxon–Mann–Whitney or t-test? On assumptions for hypothes...
Jos Feys Yes, I will run 21 tests on the same groups, however, their answer on each question is independent of the others. Should I still go for correction for multiple testing?
You are absolutely wright that the individual t-tests between Treatment and Control groups are independent. But by running 21 such tests on the answers upon the questions, you treat these as independent, as if you know 'a priori' that they measure different 'dimensions for different products '. If there are no correlations at all between these 21 questions, then you are wright. I would suggest you run a Cronbach alpha for internal consistency of the questionnaire.
This will indicate if there are undelying 'factors' or components. If the alpha is acceptable (.70 or higher) this means there are correlations. This would imply the t-ttest are not really independent; that you should use 'a posteriori' tests. As I suggested earlier, you could run a principal components analysis and or a factor analysis for calculating factor scores. See, e.g.
https://www.statsdirect.com/help/regression_and_correlation/pca.htm
I do not believe that the tests are independent because they use the same independent variable in each one. And besides that, how would you interpret the overall outcome for this approach?
Rather than running 21 tests, I would recommend that you first do an Exploratory Factor Analysis (with Principal Factors extraction and oblique rotation) to determine how many separate scales you have. Then you can examine coefficient alpha for each of your proposed scales to determine its reliability. This procedure will allow you to use a t-Test for each of your scaled variables, which can be treated as interval.
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