Comparing two populations: Mann-Whitney-U test

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En provenance du cours de University of Cape Town

Understanding Clinical Research: Behind the Statistics

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University of Cape Town

Understanding Clinical Research: Behind the Statistics

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If you’ve ever skipped over`the results section of a medical paper because terms like “confidence interval” or “p-value” go over your head, then you’re in the right place. You may be a clinical practitioner reading research articles to keep up-to-date with developments in your field or a medical student wondering how to approach your own research. Greater confidence in understanding statistical analysis and the results can benefit both working professionals and those undertaking research themselves. If you are simply interested in properly understanding the published literature or if you are embarking on conducting your own research, this course is your first step. It offers an easy entry into interpreting common statistical concepts without getting into nitty-gritty mathematical formulae. To be able to interpret and understand these concepts is the best way to start your journey into the world of clinical literature. That’s where this course comes in - so let’s get started! The course is free to enroll and take. You will be offered the option of purchasing a certificate of completion which you become eligible for, if you successfully complete the course requirements. This can be an excellent way of staying motivated! Financial Aid is also available.

À partir de la leçon

Which test should you use?

The most common statistical test that you might come across in the literature is the t-test. There are, in actual fact, a few t-tests, but the one most are familiar with, is of course, Student’s t-test and its ubiquitous p-value. Not everyone, though, knows that the name Student was actually a pseudonym, used by William Gosset (1876 - 1937). Parametric tests have very strict assumptions that must be met before their use is justified. In this lesson we take a closer look at these tests, but perhaps more importantly, their strict assumptions. Once you know these, you will be able to identify when these tests are used inappropriately.

Introduction to nonparametric tests3:18

Checking for normality5:07

Thinking nonparametrically2:27

Comparing paired observations: Signs2:42

Ordering values: Ranking2:33

Paired comparisons: Sign ranks2:22

Summation of ranks: Rank sums6:04

Comparing two populations: Mann-Whitney-U test4:07

More nonparametric tests5:09

Case study 313:40

Rencontrer les enseignants

Juan H Klopper
Dr
Department of Surgery

So, in this section let's do the Mann-Whitney-U test.

Now, this is the most common non-parametric test that you're going to

find out there in the literature.

Quite confusing though,

for the pure reason that there are so many names for it.

And that is really what happens when you attach people's names to tests.

So, you're going to see Mann-Whitney-U most commonly.

You're probably also going to see Mann-Whitney-Wilcoxon and

that makes it difficult because Wilcoxon on its own has a different type of test.

You're also going to see Wilcoxon-Mann-Whitney.

You're also going to see Wilcoxon rank-sum test.

At least that last name helps us out because we are going to use the rank-sums

method when this is done.

So look at an example, read the study by Craig and colleagues.

And they looked at the risk factors for overweight and

overfatness, two different things, in rural South African children.

That was published in the Journal of Public Health in 2015.

Now if you read the abstract method section there,

you'll see they say the use the Mann-Whitney-U test.

Now look at Table 1 specifically, some halfway down Table 1.

You'll see that they compare between the non-obese and

obese and non-overfat and overfat.

Let us compare the median distances to the schools.

So for each group, there's two little groups there,

two little groups there, two separate analysis, two groups in each.

And they just look at comparing the medians to the school, distance to

school for those childrens, that obviously be between their houses and their schools.

Now what they are doing what you use the Mann-Whitney-U for

is exactly the same as you would a normal t-test or student's t-test.

You are comparing two groups with each other.

Values in two groups.

Now, those values that we looking at, they've gotta be either numerical or

at least, if they are categorical, they've gotta be ordinal categorical.

In this instance, they we're using kilometers,

that's the distance to the schools.

So in case it is numerical then, as in this case, they are using the medians,

they are using nonparametric tests.

Because they found that those distances to school did not follow

a normal distribution pattern.

So, we are going to go for a nonparametric test.

Now, remember when we had the AB, AB, when we looked at rank sums,

that's exactly what is happening in the Mann-Whitney-U test.

So you could rank those distances to school for each group, and

they're gonna fall in sum rank.

You can follow either of the two methods which we discussed, either those tennis

playing matches or simply just summing up the rank values for each of those values.

Again, we're talking about the distribution of the ranks and

not the actual values,

because those actual values do not come from a normal distribution.

Now the null hypothesis for this Mann-Whitney-U test would just suggest

that there is no difference in the medians between the two groups and the alternative

hypothesis if it's two tailed, will just say that there is a difference.

And the one sided test with one group actually having a median more or

less than the other group.

And it's purely determined by the actual matter at hand, what you are researching

and should make logical sense why a two tailed test and one tailed test was used.

And as with all hypothesis testing, you really have to make that

judgement call between a one-tail and a two tail-test as far as the alternative

hypothesis is concerned, before any data acquisition or data analysis concerned.

Otherwise, it is purely unethical.

Now, whichever of the two rank sum methods that is used,

you then, calculate it with a computer, or just look it up in the table.

You'll get the statistic which you can convert to p-value.

So that is the Mann-Whitney-U test.

It's a non-parametric test comparing the medians of two groups.

Now in the next section, the last section on this lesson we're just going

to discuss a few other of the more commonly used nonparametric tests.

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