# Questions tagged [wilcoxon-mann-whitney-test]

The Wilcoxon rank sum test, also known as Mann-Whitney U test, is a non-parametric rank test to assess whether one of two samples has larger values than the other.

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### How to choose between t-test or non-parametric test e.g. Wilcoxon in small samples

Certain hypotheses can be tested using Student's t-test (maybe using Welch's correction for unequal variances in the two-sample case), or by a non-parametric test like the Wilcoxon paired signed rank ...
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### What exactly does a non-parametric test accomplish & What do you do with the results?

I have a feeling this may have been asked elsewhere, but not really with the type of basic description I need. I know non-parametric relies on the median instead of the mean to compare... something. ...
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### Post-hoc tests after Kruskal-Wallis: Dunn's test or Bonferroni corrected Mann-Whitney tests?

I have some non-Gaussian distributed variable and I need to check if there are significant differences between the values of this variable in 5 different groups. I have performed Kruskal-Wallis one-...
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### When to use the Wilcoxon rank-sum test instead of the unpaired t-test?

This is a followup question to what Frank Harrell wrote here: In my experience the required sample size for the t distribution to be accurate is often larger than the sample size at hand. The ...
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### Why is the Mann–Whitney U test significant when the medians are equal?

I've received a results from a Mann-Whitney rank test that I don't understand. The median of the 2 populations is identical (6.9). The uppper and lower quantiles of each population are: 6.64 & 7....
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### Why is the asymptotic relative efficiency of the Wilcoxon test $3/\pi$ compared to Student's t-test for normally distributed data?

It is well-known that the asymptotic relative efficiency (ARE) of the Wilcoxon signed rank test is $\frac{3}{\pi} \approx 0.955$ compared to Student's t-test, if the data are drawn from a normally ...
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### Is the W statistic output by wilcox.test() in R the same as the U statistic?

I've recently been reading about the Mann-Whitney U test. It turns out that to carry out this test in R you actually need to run a Wilcoxon test! My question: is the W statistic of ...
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### Power of a Mann Whitney test compared to a t test

So a Mann Whitney U test is supposedly about 95% as powerful as a t-test when t-test assumptions of normality and homogeneous variance are satisfied. I also know that a Mann Whitney U test is more ...
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### Mann-Whitney U test and K-S test with unequal sample sizes

I want to compare two distributions, to see if they are significantly different. They represent task time completions (so they range from 1 to around 1000 seconds) in two different months. They are ...
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### Which statistical analysis should I perform if the data sets are not normally distributed?

I am doing an experiment where there are two independent groups; one is the group of "infected" patients another is the group of "sepsis" patients. I am comparing "platelet monocyte aggregates(PMA)" ...
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### How to test for differences between two group means when the data is not normally distributed?

I'll eliminate all the biological details and experiments and quote just the problem at hand and what I have done statistically. I would like to know if its right, and if not, how to proceed. If the ...
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### Minimum sample size for unpaired t-test

Is there a "rule" to determine the minimum sample size required for a t-test to be valid? For example, a comparison needs to be performed between the means of 2 populations. There are 7 data points ...
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### Mann-Whitney null hypothesis under unequal variance

I'm just curious about the null hypothesis of a Mann-Whitney U test. I often see it stated that the null hypothesis is that two populations have equal distributions. But I'm thinking - if I had two ...
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### Always use Welch-t test (unequal variances t-test) instead of Student-t or Mann-Whitney test?

I want to do an AB test to check if one version does significantly increase revenue. Generically speaking I want to test whether the central tendency (mean) of 2 groups are different from each other ...
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### Reporting Results of Mann-Whitney U Test - Means vs Medians

I had a question yesterday that I got a bunch of great responses on. I have, hopefully, a quicker question here. There is a debate in the literature regarding reporting means vs medians in a ...
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### Wilcoxon rank sum test in R

I have results from the same test applied to two independent samples: ...
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### Mann-Whitney U test with unequal sample sizes

I have two unequal groups (94 and 52) and want to run a Mann-Whitney U-test to see whether their scores on a measured variable differ. I see that it is OK to do with Kruskall-Wallis, does the same ...
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### Relationship between AUC and U Mann-Whitney statistic

Recently I learned about the relationship between Area Under (ROC) Curve and $U$ statistic of the Wilcoxon-Mann-Whitney test. It is supposed to follow the following rule (got it from this nice post on ...
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### Can Mann-Whitney test be used for post-hoc comparisons after Kruskal-Wallis?

I have a simulation where an animal is placed in a hostile environment and timed to see how long it can survive using some approach to survival. There are three approaches it can use to survive. I ran ...
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### Mann Whitney test with unequal variances [duplicate]

I am confused on what I have read about the Mann whitney test. We are testing whether our actual data is the same as our projected data. We had been using the t-test until we realized the data might ...
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### Mann Whitney or two tailed t-test

I am new to statistics and am in need of some help. I am running a study where I am providing two groups with surveys to test for their perceptions using a Likert Scale. One group I'm testing prior to ...
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### Non-parametric test if two samples are drawn from the same distribution

I would like to test the hypothesis that two samples are drawn from the same population, without making any assumptions about the distributions of the samples or the population. How should I do this? ...
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### What is the difference between the Wilcoxon Rank Sum Test and the Wilcoxon Signed Rank Test?

What is the difference between the Wilcoxon Rank-Sum Test and the Wilcoxon Signed-Rank Test using paired observations? I know that the Rank-Sum test allows for a different number of observations in ...
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### Mann Whitney Test: Clearing Up Confusion

I have been reading many statistical websites stating that the Mann Whitney test is a test of medians. However, I believe that this is not really true? It is a test of the difference in the ranks. The ...
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### Assumptions of Mann-Whitney test for at least ordinal data

I am reading article by Divine et al. about using Mann-Whitney test for data that is at least ordinal (i.e. it may be discrete with many ties). It says the following (in section 2.3): That is, it (...
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### How to determine the effect size of a Wilcoxon rank-sum test in R?

I want to determine if there's a difference in mean p-values between two groups. In order to do this I perform a Wilcoxon's rank-sum test (the data is not normally distributed). So far, so good. ...
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### How to compare two non-normally distributed samples with very different sizes? (Mann-Whitney vs Randomization/Bootstrap)

Perhaps this is a very basic question, but I didn't find yet a simple solution for this simple problem: I want to compare two samples (say X and Y) for a continuous variable which is non-normally ...
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### Difference of 'centers' of 2 non-normal samples with Mann-Whitney test

I have 2 non-normally distributed samples of different sizes (N1~=N2). To evaluate whether there is a significant difference between these samples, I used the Mann Whitney U test (...
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### Can the Wilcoxon rank sum test give a different result to the Kolmogorov-Smirnov test result?

Let's say I have two data sets (in R, say); $x_1, x_2,..., x_n$ and $y_1, y_2,..., y_n$. The Wilcoxon rank sum test rejects, indicating that the "X" population distribution differs from that for "Y". ...
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### How to interpret Mann-Whitney's statistical significance if median is equal?

Testing the difference between the observations of two groups by using Mann-Whitney Test has given the following output (from minitab): ...
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### Testing for significance between means, having one normal distributed sample and one non normal distributed

I have following problem: Within an independent groups 1-factor design I have two independent groups, with a sample size of 20 each. The data of the treatment group is not normally distributed, ...
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### Reporting Mann-Whitney U-Test without homogenity of variance

The Mann-Whitney test requires homogeneity of variance if a median difference is suppossed to be statistically significant. In case homogenity of variance is not met, but the test is significant: ...
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### Mann-Whitney U Statistic seems very large - is something wrong?

I compared two unequal sized samples, N1 = 230 and N2 = 120 using a Mann-Whitney U test. The U is shown to be large such as 2829. The p value is non-significant but I want to know if such large ...
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### Wilcoxon-Mann-Whitney test giving surprising results

I'm comparing two datasets and want to test the null hypothesis on them. Both datasets contain a lot of meaningful zeros (around 50% of the values are 0). One of them, "test", has more zeros than the ...
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### How to find the difference between two set of scores of a single participant?

What I am trying to do? I have a data set which consists of only one undergraduate student's all courses scores. Let's assume, he has completed about 70 courses where 40 courses are related to ...
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### mann whitney assumption

By testing i found my data is non-normal so i can't apply t-test moving toward non-parametric test(mann whitney -U) the assumption that both distribution have same shape is violated although it is non ...
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### Which result to choose when Kruskal-Wallis and Mann-Whitney seem to return contradicting results?

I have these groups where the values are responses to a 10-point Likert item: g1 <- c(10,9,10,9,10,8,9) g2 <- c(4,9,4,9,8,8,8) g3 <- c(9,7,9,4,8,9,10) ...
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### How do I interpret the Mann-Whitney U when using R's formula interface

Say we have the following data: ...
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I have encountered two forms for calculating the two-sample Mann-Whitney U test statistic, which are: $$U_1 = R_1 - \frac{n_1(n_1 + 1)}{2}$$ and $$U_1 = n_1n_2 + \frac{n_1(n_1+1)}{2} - R_1$$ where ...