The Mann Whitney U Test, also known as "Mann-Whitney-Wilcoxon (MWW)" test, is the same a as T-Test, but is used for ordinal (=ranked) data.
It is a test of difference between the medians rather than a test of
comparison between the means. The test can appear complicated to perform
and understand, but is actually very simple to interpret and very
useful. The U-values of each sample is given by the formula above where n is the number of value in each sample and Sum(R) is the sum of the rank scores of each sample: the lower the U-value, the more different the two samples are.
Let's say you've sampled two populations: just by looking at the means or the medians, it looks like two samples are different. What does that mean about the entire populations from which you've taken those samples?
There are THREE METHODS TO RUN THE MANN-WHITNEY U-TEST, depending on the size of your samples:
Let's say you've sampled two populations: just by looking at the means or the medians, it looks like two samples are different. What does that mean about the entire populations from which you've taken those samples?
- Does that mean that the entire populations are different as well in the same way?
- Or
was this just an accident? If that's the case, you would then need to
survey different (and maybe larger) samples, to draw a conclusion as to
whether the entire populations are different as well
- The Mann-Whitney U-Test can help you make a determination with at least 95% certainty!
There are THREE METHODS TO RUN THE MANN-WHITNEY U-TEST, depending on the size of your samples:
- If you have 8 values or less in each sample, watch the video below or follow these steps:
- Follow the step by step method to calculate the two U values. Once you have calculated the U-values, go to step 2 below directly
- Download the table of critical Mann-Whitney U-Values for samples of 8 values or less (below). That table will give your the % by which you can estimate that the two populations are different
- Calculate the median of sample 1 and the median of sample 2: find which one is higher/lower. The result of the test is formulated as follows: "Based on the samples, there is a p% chance that the median of the entire population #1 is not higher/lower than median of the entire population #2". Or, you can also say that "there is a (100 - p)% chance that the median of the entire population #1 is truly higher/lower than the median of the entire population #2)"
|
| ||||
- If you have fewer than 20 values in one sample, and 9-20 values in the other, use this online calculator or follow these steps:
- Copy your values on a new spreadsheet with values from sample 1 in the top half of a table and values from sample 2 in the bottom half.
- Create a new column: in each cell, enter a marker "1" or "2" if each value comes from sample 1 or sample 2
- Sort the values (along with their markers) from low (top) to high (bottom). Create a 2nd column and enter the rank for each entry from lowest to highest. If 2 lines or more are tied with the same rank, you must give them the same rank number, equal to the middle between those 2 or more lines: r = (t+2b+1)/2 (where t = # of lines which are tied and b is the # of the last rank immediately before the lines that are tied)
- Sort the values (and their ranks) by the marker so you can know again which values came from which sample.
- For convenience, split again the two samples (along with the corresponding ranks) into two separate tables
- For sample 1, calculate the number of value and the sum of the rank scores. Repeat for sample 2
- Apply the formula to calculate the U-values of each sample
- Compare the smallest of the two values U1 or U2 to the critical Mann-Whitney U-values: if the value of U is equal to or smaller than the relevant critical value, then the null hypothesis
can be rejected: there is a 5% chance or less that the difference
between the two samples occured by accident, or there is a 95% chance
that the difference between the two entire populations is different,
based on the samples
- Note: you can also this online U-value calculator and/or interpretation tool or use this online interpretation tool of the Mann-Whitney U Test
- If you have two samples with more than 20 values each, use this online calculator or follow these steps:
- Repeat the steps 1-7 above
- Calculate the Z-score using the formula below
- Use a Z-Table to find the corresponding critical Z-value (if you do not know how to read a Z-table, click here)
- Multiply the critical z-value found by 100: this will give you the % probability that the difference between the two entire populations could be due to chance, based on the samples (ie: a probability of 5% is less is usually enough to reject the Null Hypothesis)
- Note: you can also this online U-value calculator and/or interpretation tool or use this online interpretation tool of the Mann-Whitney U Test
 |