# Mann-Whitney test interpretation

I would be grateful for any help. I am using a Mann Whitney test to determine whether there are differences between two groups (adopters and non-adopters) on 15 explanatory variables that are scaled along a Likert scale (1=strongly disagree to 6=strongly agree).

I performed a Mann-Whitney for each of the 15 explanatory variables.

I am very confused about how to write-up the interpretation. For example, here is the output from one of the Mann-Whitney test:

ranksum Challreclackskills, by(Anyreg)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

Anyreg~l       obs    rank sum        expected

No            67           5417.5         4891
Yes            78          5167.5         5694

combined       145            10585       10585

Ho: Challr~s(Anyreg~l==No) = Challr~s(Anyreg~l==Yes)
z =   2.133
Prob > z =   0.0329


Firstly, what does the rank sum tell me? Is it something I would report as part of the interpretation? If so, how would I interpret this?

Using this output, it looks like there is no significant difference between adopters and non-adopters on perceptions about challenges related to lack of skills. However, when I run the summary statistics on these two variables, I see that the median value for Challreclackskills among adopters is 3.5 for the while the median for non-adopters is 4. So, would the correct interpretation be that while a higher proportion of non-adopters are more likely to agree that there are challenges, the differences between these groups are significant?

Firstly, what does the rank sum tell me?

The hypotheses you are testing under the Wilcoxon Rank-Sum test are:

$$H_0$$: The two population distributions are identical

versus

$$H_1$$: The distribution of population A is shifted to the right of the distribution of population B.

Is it something I would report as part of the interpretation?

You should make it clear, when writing your results, which population you are considering your "Population A" and which is "B." You must also make it clear that you are performing a Wilcoxon Rank-Sum test. Since this is a very common statistical test, I don't think you need to provide any additional information besides your sample sizes from Population A, and B, the p-value, and your test-statistic. It's also usually a good idea to simply provide some descriptive statistics such as the mean, median, and standard deviation of you samples. You will also want to supply the mean ranks and their standard deviations. A good guideline for reporting results is given here.

If so, how would I interpret this?

Assuming you are using a 95% confidence interval, you could simply say, that you have sufficient statistical evidence to believe that the distribution of non-adapters is shifted to the right of adapters. This is because your P-value is listed as $$z = 0.0329$$.

Keep in mind that the $$n=78$$ adapters had an rank sum of 5167.5 5694 while the $$n=67$$ non-adapters had a rank sum of 5417.5. So this tells you the direction in which the distribution are "shifted."

• Wonderful - thank you so much. So does "shifted to the right" mean that the 1-6 Likert scale (1-strongly disagree, 2-disagree, 3-slightly disagree, 4-slightly agree, 5-agree, 6-strongly agree) mean that it is shifted towards the "agree" side of the scale? – user3424836 Feb 19 at 21:03
• @user3424836, higher values on the scale indicate greater "agreement," so these values would receive higher ranks. So shifted to the right would imply there is greater agreement. – StatsStudent Feb 19 at 21:05
• Thank you - I'm sorry one last question. You mentioned that I should report Means. But I've read that means are essentially meaningless in Likert scaled data. Why would it be important to show the mean if it doesn't tell you anything? – user3424836 Feb 19 at 21:06
• It's a matter of preference, really. I always report measures of central tendency when you are comparing two distributions. The means do, in fact, tell you something -- the raw means are simply just not being used in the statistical test. What you certainly must provide is the value of the statistic, the sample sizes, and the $p$-values. Other values are optional, but I think more info is better than less. It helps readers get a feel for your data. Also: You should check with any publication you intend to publish to. They sometimes have reporting standards. – StatsStudent Feb 19 at 21:11
• Great, thank you so much! I was very stuck. I greatly appreciate it. – user3424836 Feb 19 at 21:14