Mann Whitney U Test - with Python Solution for Small Sample

In this part, I am going to show a demo on the Mann-Whitney U Test Python script which is able to perform test on both small and large sample size.

Mann-Whitney U test is very useful in small data sample cases, such as clinical dataset (many clinical trials only have very few samples). However, in many modern statistical packages which included Mann-Whitney U test, they were only valid when the data sample size was large. Hence, it is necessary and helpful to have a complete application of Mann-Whitney U test, including two conditions of small sample and large sample.

Part 1: an overview of Mann-Whitney U test

Part 2: an introduction to Mann-Whitney U test in Python

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Tool: Web Application

Package Source Code

Github

Demo

Installation

Download Mann-Whitney-U-Test to a directory of your choice and then run:

pip install -r requirements.txt

Use It

In order to use Mann-Whitney-U-Test, you need your data organized as a list like the following:

from mannwhitney import *
data1 = [1,2,3,4,4,5]
data2 = [4,5,6,6,9,10,14]

Then you could run it just as follows:

mwm = mannWhitney(data1,
                  data2, 
                  tail='two', 
                  significant_level=0.05) # two-tailed test
                                          # at 0.05 significance

Analyze

After testing, you could fetch the following results:

mwm.n1 & mwm.n2 int, e.g. 10

​ the number of sample size for a group

mwm.sample_size str, e.g. “small”

​ small or large sample size

mwm.significance bool, e.g. True

​ whether the test show significant difference

mwm.criticalu float, e.g. 3.0

​ the critical U value obtained from the table (only available when sample size is small)

mwm.p float, e.g. 0.05

​ the p value calculated from the testing data (only available when sample size is large)

mwm.stat_a float, e.g. 3.0

​ the U statistics calculated from the testing data

mwm.effectsize float, e.g. 0.8

​ the effect size

mwm.largergroup int, e.g. 1

​ the index of the larger group (1 or 2)

Web Application

You could also visit the webpage which is an application for this script if you don’t want to run the code.

Example

Similarly, just provide two groups of data and the application will run the test and show all the result.

The valid format of input data includes:

• copy directly from Excel (a row or a column)
• manual typing
  • separate with comma, e.g. 1, 2, 3, 4
  • separate with space, e.g. 1 2 3 4
  • mixture, e.g. 1 2 , 3, 4

Run the server on your instance

It is easy to set up your application and run it on your machine. After installing the required packages, simply run

python app.py runserver

Then it is on at http://127.0.0.1:5000/