Directions for using SigmaStat
Mann-Whitney Test

Start SigmaStat as before.

If you saved your file from the two-sample t-test, then go to File, then Open and pick the file with your data in it. This will bring up a screen called the notebook, with the spreadsheet as the active window. If the Data screen is not active, then click on the section called Data, which will bring up the spreadsheet with your numbers in it. If you did not save the file, then you will need to re-enter the data.

Enter data into the spreadsheet. These are condylobasal length measurements of Microtus mexicanus. Population #1 is from Arizona and population #2 is from New Mexico. Be sure to label your columns.
```pop #1                pop #2
23.1                    24.0
24.2                    22.3
23.7                    24.0
23.7                    23.3
26.1                    24.2
24.6                    21.3
24.4                    24.3
25.2                    22.3
24.4                    23.5
24.6                    24.3
26.0                    24.5
26.4                    23.2
25.4                    24.8
24.0                    25.3
25.6                    24.6
23.3```
Run the Mann-Whitney Test: The procedure is essentially identical to that of the t-test, except that you do a rank sum test. Go to Statistics, then Compare two groups, then rank sum test. This brings up another window, which is used to assign columns in your spreadsheet. The box may be too low on your screen, in which case you will need to drag it higher on your screen to be able to see the bottom of the window. Data format is Raw. Then use the cursor to point to the top of column #1; this highlights column #1 as one of your populations. Then click on the Next button at the bottom of the window. Then click on column #2, and then click on the Finish button. The results of the t-test are then displayed on the screen.

In this case, the tests of the assumption for normality and equality of variances will be satisfied and the program will then ask you if you want to run a t-test instead. Click on No, to continue with the rank sum test. Remember, if you meet the assumptions of a t-test, then a t-test is a more porwerful test than a Mann-Whitney Test

Export the file if you want to use the output in another program.

The output:
 ```Mann-Whitney Rank Sum Test Friday, July 16, 1999, 10:25:06 Data source: Data 1 in Notebook Normality Test: Passed (P = 0.643) Equal Variance Test: Passed (P = 0.651) Group N Missing arizona 16 0 new mexico 15 0 Group Median 25% 75% arizona 24.500 23.850 25.500 new mexico 24.000 23.225 24.450 T = 189.000 n(small)= 15 n(big)= 16 (P = 0.046) The differences in the median values among the two groups are greater than would be expected by chance; there is a statistically significant difference (P = 0.046)```

Explanation of the output:

Normality Test: This is the results of the K-S distance value that would have been calculated if we had run basic statistics. The P value, in this case, is equal to 0.643, thus we fail to reject the null hypothesis that the populations have a normal distribution.
Equal Variance Test: This is the variance ratio test, where the larger sample variance is divided by the smaller sample variance. The P value, in this case, is equal to 0.651, thus we fail to reject the null hypothesis that the variances of the two population are equal.
In general, we would only be running a Mann-Whitney Test if the P values for one or both of the above tests were less than 0.05. Because a t-test is so robust, we would still get good results even at the P = 0.01 level to reject for these tests of the assumptions.

Group is the labels that you gave your columns.
N is the sample size for each sample.
Missing is the number of blank cells in your data set. In this case missing values will have no affect on the results of your test.
Median is the Xbar for each sample.
25% is the first quartile
75% is the third quartile

T is the value that you look up in table B11. Zar calls this number U. Note a capital T is used for this value while a lower case t is used for the t-test. Sample sizes are given and the P value associated with this test (P = 0.046).

The difference in the median values ... This is simply a statement about wether to reject your null hypothesis that the two populations have the same condyobasal length. The phrase "greater than would be expected by chance" means that you reject your null hypothesis. The P value is equal to 0.046, which is less than the level to reject at 0.05.

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