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Mann–Whitney U test is a method which is used for statistical analysis for the differences between two independent groups which is mostly applied when the data does not conform to the assumptions of a parametric test which. It is essential to remember that any test, however, must be interpreted correctly otherwise it can lead to erroneous results.
This test is not meant to be the means comparison statistical tools, but many researchers assume this that it does which adds to the common pitfalls of Mann-Whitney U Test. This however is not accurate as the tool seeks to establish whether the first group tends to have bigger or smaller figures compared to the second group which is not the intent of this test as it looks at the value of the distributions as opposed to the central tendency value like mean.
If we have two groups say A and B, one B tends to be symmetrical while A is skewed, then the test will not necessarily be accurate post the means comparison which in in our case is B, then the results will not be accurate, comparison of the two diverse shapes in terms of distributions will be more useful in drawing conclusions rather than measuring the means.
The Mann-Whitney U Test requires both distributions in the groups to have the same or evenly shape, if not identical. This requirement, if left unaccounted for, will cause the test to mislead inferences. For instance, if one pair of groups has a skewed and the other has not, the test will find a difference that does not reflect mean.
To circumvent this error, one should begin with visualizing the data with the aid of box plots or histograms in order to analyze the shape of the current distributions before executing the tests to analyze the differences. If the distribution shapes are circular or normal to each other, one can try different statistical approaches.
This investigation should not be conjointly applied on paired or dependent data which includes, but is not limited to, pre- and post-operative readings on the same set of individuals due to its underlying nature, which is to compare two independent group settings. Sub dual analysis performed in these instances would be severely flawed.
Instead of using the Mann-Whitney U Test, apply the Wilcoxon Signed Rank Test on the dependent sets of data due to its intrinsic nature of using the paired data sets.
Mann-Whitney U Test works under the assumption that no duplicate values exist in the given data. If there are tied values and they are not catered for, the conclusions reached might be flawed as a result of faulty calculations.
It is a standard feature for Statistical Package for the Social Scientist or even R to do this tie adjustment during finding of results. In any case, ensure the package or method you are using does have this adjustment as well.
During analysis of the Mann-Whitney U Test, a p value is reported and taken to be all that there is. Even though a significant p value denotes that there is an existing difference of some sort within the groups, it does p value for difference in size. Failing to account for the effect size may result in disproportionate attention being paid to statistically significant findings that are perhaps not relevant in practice.
Always include the p value for the effect size also. Very good approximations in measures such as rank-biserial correlation or Cliff’s delta can yield values to indicate of how significant the difference between the groups is and how relevant your research was.
Understand Your Data: Before you go ahead and apply the test, you need to evaluate whether it is well suited to your dataset. Assess under which assumptions it can be used, the shape of its distribution and whether the groups are independent.
Mann Whitney U is a powerful statistical analysis tool serving a myriad of functions. However, without careful application, the results may be subject to rendering ineffective results. Measuring and accounting for five of the most common problems with inferring outcomes such as employing assumptions, misreporting outliers, misunderstanding data types, and not taking into account effect sizes ensures correct usage.
You should always keep in mind that the strength of the mann whitney u test rests not only on its features and non-parametric data, but also on the quality of its implementation.
