Each patient got 2 treatments randomized to either left or right leg, we wish to compare 3 months follow up expressed as -1, 0 , or 1 (worse, the same, improved).
With Likert scale data, the best measure to use is the mode, or the most frequent
response. This makes the survey results much easier for the analyst (not to mention the audience for your presentation or report) to interpret. You also can display the distribution of responses (percentages that are worse, the same, etc.) in a graphic, such as a bar chart, with one bar for each response category.
After descriptive methods, any good statistical analysis proceeds next to inferential techniques, which test hypotheses posed by researchers. There are many approaches available, and the best one depends on the nature of your study and the questions you are trying to answer. A popular approach is to analyze responses using analysis of variance techniques, such as the Mann Whitney or Kruskal Wallis test.
Emir,
You can use the Gamma (G) statistic or Spearman's Rho as well. Both statistics are easy to calculate and interpret and can help you understand the relationship between your treatment (which I am not sure why you say it is random) and your patients' perceptions.
These are survey responses from a rather small number of patients where you are trying to identify nonrandom associations, so descriptive statistics and measures of association are appropriate. I do not see how you can use inferential statistics with this nonrandom group of patients.
Emir, you have a problem, and not a small one...
Actually, your design has two factors (time x treatment) and the best way to analyse it would be a two-way ANOVA, with repeated measures. HOWEVER, once you used a Likert scale, this approach is not possible...
Traditional non-parametric inferential tests, as Kruskall-Walis and Friedman, are not able to analyse two simultaneos factors (there is no two-way Friedman...) . Even a common (and wrong) approach, as performing PRE x POST comparisons independently into each treatment and then comparing results will be misleading, because you have just a three points scales and the potencial number of ties is very large and your results will not be trustful..
There is some transformations that you can try to save your data, but it will suffer anyway...
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