I'm trying to analyse a questionnaire with responses to questions ordered on a Likert Scale ( 1= Disagree strongly to 5 = Agree strongly).

We are comparing question responses between two groups of students, one group (n-25) who saw a video, one group (n=35) who were given a practical demonstration.

I have summarised the response score for each question by taking the median and used the Mann Whitney U test to test for statistically significant differences in response score between groups.

In addition one of my supervisors suggested adding the standard error of the median to the tables. So I've bootstrapped the samples to get a standard error and bias.

Now, here comes the question.

Because there are only 5 possible responses (1-5) some of the medians are the same, while the Mann Whitney U test says that there are stat sig. differences between the groups. I guess this is because the scores are different but the median is not sensitive enough to show this (because there are a lot of tied scores in the middle)

To bring out the differences in the discussion, can I add the bias to the sample median?

Here's an example from question 7 "The video/presentation was audible and understandable":

Raw Data

Group 1 - shown video

3 3 4 2 4 4 3 4 2 3 4 3 4 4 2 3 4 3 4 4 4 3 4 4 3

Group 2 - given presentation

4 4 3 5 4 4 4 4 4 5 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 4 4 4 4 5 5 5 5 5 4

Just scanning the data seems to show that the presentation did better than the video. The Mann Whitney confirms this with p < 0.0001.

The problem is that median is 4 for both, so it's hard to show in the discussion in which direction the preference was, or what the magnitude of the preference is.

Sample median, bias (from bootstrapping), standard error of median (from bootstrapping) and sample mean for groups 1 and 2 are given below:

Group 1

4, -0.42, 0.49, 4.2

Group 2

4, 0, 0.03, 3.4

So, in the discussion should I write (a) or (b)

(a) The presentation was considered more understandable than the video (mean 4.2 versus 3.4, P<0.0001) [but this confuses the parametric and non parametric statistics]

or can I say

(b) The presentation was considered more understandable than the video (median + bias, 4.03 versus 3.58 p<0.0001)

Which of the two is preferable?

Many thanks for your help with this!

Simon