# Mann-Whitney U Test: Ordinal data with few categories

#### jwoo94

##### New Member
Hello,

I am trying to use the Mann-Whitney U Test to compare ordinal data between 2 groups, but the problem is that there are only 3 categories for my ordinal data. I have never seen the Mann-Whitney U Test be used on ordinal data with fewer than 5 categories. So I was wondering, what is the minimum number of categories in order for Mann-Whitney U Test to be used?

Any input would be much appreciated. Thank you!!

#### Disvengeance

##### New Member
What exactly do you mean by "only 3 categories"? Can you elaborate a little more on what you goal/hypothesis is?

#### hlsmith

##### Less is more. Stay pure. Stay poor.
Yes, describe these data in more detail. Could you conduct a Fisher's Exact, chi square, or a trend test.

#### jwoo94

##### New Member
Sorry for the confusion! I am trying to compare quiz scores between controls and patients, in order to determine if one group performed worse on the quiz than the other. The possible scores are 0, 1, and 2 - which is what I meant by 3 "categories."

I was also thinking of doing Fisher's exact test or Chi squared test, but I was wondering if they would be applicable since they are usually used for nominal data (i.e. they don't take into consideration the "order" of data, which would take away the ordinal nature of scores). I have never heard of a trend test and found multiple different versions when I Googled it, so if you could clarify what it is that would be great.

Would Mann-Whitney U Test be used for a situation like this?

Thank you so much for all your help!

#### hlsmith

##### Less is more. Stay pure. Stay poor.
Can they really only score 0, 1, 2? Where there only 3 questions? Also, how many people took the quiz?

#### jwoo94

##### New Member
We are actually looking at 2 questions out of the whole quiz, which is why they could only score 0, 1, or 2 (since each question was out of 1). There were about 50 controls and 80 patients who took the quiz.

#### Disvengeance

##### New Member
I would suggest you define your hypothesis; how do you want to determine whether one group performed better than another? You could use chi-squared or Cochran-Armitage test for trend to see if the proportion of scores is different between groups. The Mann-Whitney test is usually used to compare the medians between groups.

#### jwoo94

##### New Member
Ideally we would like to compare the medians between groups (so our null hypothesis would be that controls and patients had the same median score on the quiz). But I wasn't sure if the Mann-Whitney Test can be used in this case, since there are only 3 possible scores.

#### hlsmith

##### Less is more. Stay pure. Stay poor.
Well you do kind of have nominal data if you think about the number with 0% correct, 50%, or 100%.

#### Disvengeance

##### New Member
Since the data is ordinal, you could calculate the mean score of each group for descriptive statistics. Since there are only three possible scores I think the median of each group will not be very informative. Instead, why not first construct a table of the score (0, 1, or 2) by each group, and then just look at the numbers and percentages. Then, if you want a formal significance test you could use chi-square, Fishers, Cochran-Armitage, etc. But it's generally a good idea just to look at the table of your data first.

#### hlsmith

##### Less is more. Stay pure. Stay poor.
Not sure what the minimum range needed would be for the Wicoxon? Do you have persons in all of the mentioned categories? I do not know off hand why you could not use it, besides issues with the very small range. It is a sign ranking style test. I know some use it for Likert data with as low as 4 groups (some have issues with this based on how they define Likert data).

#### jwoo94

##### New Member
Great, thank you so much!! I think I will try constructing a contingency table first and see how it goes.

#### Disvengeance

##### New Member
I couldn't find any reference describing a minimum range for the Wilcoxon test, but I think I was wrong to assume that the test won't work on data with a range of 2. I ran a simple simulation and performed the test on some data with 2 groups and a variable with values of 1, 2, or 3 and it is possible to get a significant result.