9 Mann–Whitney U Numbers Tutorial
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maintain their internal environment, which is usually less salty than their surroundings.
For example, fish living in the ocean pump salts out of their bodies, and may use upward
of 50% of their energy budget to maintain homeostasis (Boeuf and Payan, 2001). One
adaptation of fishes in saltwater environments is to increase the number of mitochondrial
rich cells in their gills, which allows for increased transport of salts out of the body.
Researchers were interested in comparing the adaptations of a hypersaline population of
Limia perugiae, a small livebearer species that normally occupies freshwater habitats. To
investigate whether the hypersaline population had more mitochondrial rich cells in their
gills, they measured mitochondrial-dependent oxygen consumption in gill tissues from
the hypersaline population and a freshwater population of the same species.
*This
example was taken from the research conducted by Dr. Pablo Weaver.
Formulate a question about the data that can be addressed by performing a
Mann–Whitney U test.
Question: Do the gill tissues of the hypersaline and freshwater populations of L.
perugiae consume different amounts of oxygen?
Based on the question, formulate the null and alternative hypotheses that
address the question proposed.
Null Hypothesis (H0): Oxygen consumption is the same between populations.
Alternative Hypothesis (H1): Oxygen consumption differs between populations.
Now that an appropriate testable question has been developed, along with a set of testable
hypotheses, you can run the statistical analysis.
To run a Mann–Whitney U in Numbers, utilize the following tutorial.
More information on programming in Numbers is found in Chapter 14.
Check all assumptions prior to running the test.
Mann–Whitney U Test Numbers Tutorial
1. Start by creating a table similar to the one below. You need a Salinity column with a
nominal value assigned to each sample (1 = hypersaline and 2 = freshwater) and an
Oxygen Consumption column.
2. On the right side of the screen, select the Sort & Filter function. Select Sort Entire
Table, and select Add a Column, and Oxygen Consumption, then Ascending (1,
2, 3…).
3. Enter the rank of each value in the rank column. In this dataset, all the values have
the different values.
Note: If there were two numbers with the same value, you will average the rank of
those numbers (see the Numbers Wilcoxon signed-rank tutorial for an example).
4. Next sort by Salinity to separate the hypersaline from freshwater samples and split
the data into two columns.
Note: In the last image, we have added the values for N1 (the sample size of
hypersaline) and N2 (the sample size of freshwater). N1 = 9 and N2 = 12.
5. Next, calculate the sum of ranks for the hypersaline sample, the R1 value. Type =sum
and highlight the column of ranks for the hypersaline fish.
6. And, calculate the sum of ranks for the freshwater sample, the R2 value. Type =sum
and highlight the column of ranks for the freshwater fish.
7. Finally, set up the following table:
8. Fill in the numbers we have calculated so far.
9. Calculate U1 using the following equation:
10. Calculate U2 using the following equation:
11. Calculate
.
12. Calculate
.