I have survey results from one question about the respondent's group's performance with a 4-point Likert-like scale (strongly disagree, disagree, agree, strongly agree).
People from multiple groups answer the survey about their own group. The number of respondents corresponding to each group can vary from 20 to 200.
E.g. The statement could be "My group is effective" and the respondents indicate their agreement.
The task is to rank the best-performing groups.
One method is to code each possible answer (strongly agree=4, agree=3, etc.), work out a mean "score" per group, and rank them by highest to lowest mean. However, that relies upon making certain assumptions in order to convert the ordinal data to interval data, which I don't want to do. We know the distributions of the data within each group varies greatly, and is generally quite skewed.
What I think is best is to use a mean rank for each group; that is, rank all responses in order (strongly agrees, then agrees, etc.), assign a sequential rank to each response and break the ties by assigning the mean of the rank sum of that group (the "fractional rank"?). Then, for each group, calculate the mean of the fractional ranks to work out the order of best performance.
E.g.
Group | Result | Fractional Rank
--------------------------------
A | 4 | 1.5 (average of 1,2)
B | 4 | 1.5
A | 3 | 4 (average of 3,4,5)
B | 3 | 4
B | 3 | 4
A | 2 | ...
Then calculate the mean of the fractional ranks for each group.
My main question(s): Is this a commonly-used / acceptable / conventional ranking method? Are there any credible online references I can refer to?
I see this is the method used to rank in non-parametric statistical tests like the Mann-Whitney U Test, etc., but I can't find references similar to the application that I am interested in, so perhaps they don't exist...But it could also be that they I am not searching for the right terms.
The survey was not designed by me...