# 3 values ordinal variable: Mann-Whitney or Chi-squared?

#### estrucida

##### New Member
Hello,

I have an ordinal variable which assumes only 3 values. I need to do a comparison between 2 treatments.

I used Mann-Whitney test, since is an ordinal. My "p-value" is quite high (0.9388) which is strange because the values distribution is quite different for each group.

Then I perform a Fisher a chi-squared test and my "p-value" decreased to 0.0885, which I believe, reflects a little bit better the behavior of the sample.

What should I do? Stick to Mann-Whitney, go to chi-squared or do another type of evaluation?

Thank you very much

#### PeterFlom

##### New Member
It would help if you could post your results (the 3x2 table) but it sounds like there may be a non-linear relationship, or you may have coded something incorrectly

#### estrucida

##### New Member
Thank you for answering so quickly.

Here goes my data:

A B
(bad) 1 2 (6.7%) 6 (21.4%)
(ok) 2 15 (50%) 7 (25%)
(great) 3 13 (43.3%) 15 (53.6%)

I also applied a Fisher Exact. I got a "p-value" of 0.0965

#### PeterFlom

##### New Member
Thanks. The relationship is not ordinal, so the ordinal test shows a high p value.

#### estrucida

##### New Member
I'm sorry if this a dummy question, but what is the difference between a ordinal variable (bad,ok,great) and a ordinal relationship between 2 subgroups (A and B)?

#### PeterFlom

##### New Member
The variable is ordinal because it is "bad", "OK", "great" - they are in order but not equally spaced.

The relationship is not ordinal because the ratio of A to B is 0.31 for bad, 2.00 for OK and 0.86 for great. The ratio goes up and then down. So, you can't say which is "better" only that they are different.

#### estrucida

##### New Member
So, imagine that instead of "bad", "ok" and "great" I am working with classes of ages: [18,39] years, [40,59] years and [60,80] years
So, even if my variable is based on a quantitative, since the ratio is not constant I can't work it as an ordinal. I will have to treat the age classes as nominal?

#### PeterFlom

##### New Member
No. Ordinal does NOT require equal spacing. That would be interval. Your variable is ordinal but it has a non-monotonic relationship with your groups.

#### hlsmith

##### Less is more. Stay pure. Stay poor.
Was treatment randomized or do you have baseline data to show groups were equal (comparable) to start with?

#### estrucida

##### New Member
It was a randomized treatment with a similar baseline. Right now I'm evaluating pain which is measured in a scale between 1 to 5. My values decreased from 4 and 5 to 1 2 3, but the distribution is not identical any more, therefore, there is a difference in the treatments during follow-up. My sample size is very small, however it is important for us to have an idea of this behavior is affecting both groups.

I didn't calculated the ratio of the categories between groups because I wanted a statistics on the overall behavior. Since I am not used to work with ordinal variables my first choice was the Mann-Whitney. However, the "p-value" indicated a similarity which I don't think it reflects the reality.

Since the variable is a qualitative I applied a fisher and a chi-squared test just to have another overview about the categories distribution. Both these tests indicate gave me a calculated probability closer to my opinion of existing differences. Therefore, I need an alternative test for Mann-Whitney since I want to keep on treating the variable as a ordinal.

Peter, I'm sorry if I wasn't understanding your answers but now I understand what you where trying to say. However, my goal since the beginning is to evaluate difference in the behavior and not correlation between variables. Do you think that I can not compare the differences between the two groups? For me, in a clinical point of view, having only 6.7% of subjects with pain against 21.4% is quite significant.