I meant that if you use median as descriptive statistic and M-W test for comparison groups by categorical data with such small amount of values, you will often have situation in which medians are equal and the test shows statistical significance.
I don't think there's anything wrong with including the median in that case, necessarily. You're illustrating a measure of central tendency. I think including a histogram of the observed values may be best since the median, range, and shape can be seen, perhaps with an inset feature. Generalized distributional differences is likely what the MWW would be detecting, since, after all, it isn't a necessarily a test for medians.
It is very tempting to try to treat an ordinal variable like you treat the categorical variable, as in both cases you have categories. I can think about the following example from a continuous variable, which is similar to the ordinal variable to explain why it isn't correct.
group a: 55, 66, 77, 77, 88, 92. 92, 93
group b: 57, 64, 76, 77, 89, 93,93, 93
Value count A count B
55: 1 0
57: 0 1
64: 0 1
66: 1 0
76: 0 1
77: 2 1
Now you tried to compare how many times value 77 appears in group A (2) to group B (1)
on the other hand, you can compare a sample of a distribution to the model distribution using Chi-square goodness of fit (for example check if sample distribute normally by dividing the data to groups and comparing the groups' count as if it was distributed normally)
Karabiner isn't it similar to what Greg tried to do? comparing the "distribution of answers" / like comparing entire distribution, not only the central value?
like two population may have the same mean and variance but different distribution?
The texts describe a place. The survey takers read one of the texts, then rate their interest in the place. The questions mostly relate to the place, not the text itself. (Like, "Do you have a positive impression of this place after reading the text?")
So I'm looking for significant difference between the two groups' impression of the place, which will indicate the effect of text A vs. text B on their impression.
Can you explain why you recommend chi-square over t-test for this, and clarify what you mean about the occurrence?
occurrence - just count / frequency . count of occurrences per each category (only example http://www.statskingdom.com/310GoodnessChi.html)
But the recommendation is to use Mann-whitney u test, related to the general impression
this is the common practice for ordinal variables.
But I also raise a question to Karabiner about the point of looking on each ordinal category by itself as you asked ("I am definitely interested " ...)
chi-square test combines all the differences in category level.
For example, if in one group all people answer only the edges: "I am definitely interested" and "I am definitely uinterested"
and second group only the middle values ("I am somewhat interested" ..."I am somewhat uninterested")
Mann-whitney u test may result in a no significant difference between the 2 groups. but clearly, there is?
While chi-square will find a significant difference. (or Fisher exact test, as some frequencies are less than 5)
What was interesting to me about the data was the bigger differences at the edges, actually. In the middle rankings, there was less obvious difference.
I didn't show all of the questions to you, but generally Group A had a lot more "strong" confidence or "definite" agreement rankings compared to Group B, whereas Group B often showed slightly stronger "somewhat" or indifferent rankings. Rankings of very weak confidence ("definitely not", etc.) was also stronger for Group A. Group B was more "meh" about it, as it were.
If I could use a test that would capture this, it would be nice. But basically I just want to use an appropriate test.