# Mann-Whitney U-test - The Grange School Blogs

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8/1/2011
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```							                                                                 Type the chart title here

35
30

25
20
15
10
5
Type the label for the first                         Type the label for the
0         data set here                                  second data set here

Type ? in the pink box to find out why this is the correct type of chart to use.                click here to go back to the main sheet
You need to compare the values for the two sets of data, making it clear which set of data is which. A line graph is not appropriate because the data
are not in any particular order.
Mann-Whitney U-Test
To use the Mann-Whitney U-test calculator, enter the actual values you got in the yellow boxes. Any cells you do not need should be left blank.
If there are values already there, type over them or delete them. You do not have to do anything else!
If you want to know where an answer has come from, type ? in the pink box beside the answers.

Enter the numbers you actually get in these boxes:                     6        10        8       7      12       6        4      2        5        5        5        5
20        20       22      23      29      26       23     29       23       24       27       30
12       12       12       12       12
0        0        0        0        0
0        0        0        0        0
0        0        0        0        0
The ranks for each site are:                                         17.5       14.0    15.0    16.0    13.0    17.5    23.0    24.0     20.5     20.5     20.5     20.5
11.5       11.5    10.0    8.0     2.5     5.0     8.0     2.5      8.0      6.0      4.0      1.0
Put all the data together and rank them. Give the rank 1 to the highest value, 2 to the second highest and so on. If there
are any tied values, the rank is calculated by giving them the average of the ranks they would have had. For example, if
two items tie for third place, they would have had the ranks 3 and 4, so we give them the rank (3 + 4)/2 = 3.5.

The sums of the ranks of the two samples are:                       222.00             Add up the ranks for each sample
78.00

The U-values are:                                                      0.0             U1 = n1n2 + 0.5(n1)(n1 + 1) - R1
144.0             U2 = n1n2 + 0.5(n2)(n2 + 1) - R2
n1, n2 are the sizes of samples 1 and 2, and R1, R2 are the sums of the ranks for samples 1 and 2

So the U-value you use is:                                             0.0
You use the smaller of the two values
The two sample sizes are:                                          12, 12

Are you doing a one or two tailed test?
Type 1 or 2 in the blue box.                                                1          Do a 2-tailed test if you weren't sure in advance whether you were looking for a
positive or negative difference. Do a 1-tailed test if you knew you were looking
for a particular type of difference. If you're not sure, do a 2-tailed test
You are carrying out a 1-tailed test

The values from the tables are:                                         5% 42           2.5% 37            1% 31
There is a 5% chance of getting below 42 if there was really no difference between
the categories - similarly, there's a 2.5% chance of getting below 37

So your conclusion is:   Your result is significant at the 1% level

Compare your U-value with the two values from the tables. If it is smaller, your result is
significant. This test and Wilcoxon are the only ones where you look for a smaller value.

```
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