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StatXact Example 12
Jonckheere-Terpstra Test - Ecology/Ethology example
Do Birds with More Immaculate Plumage Frequent the Best Feeding Sites? This analysis is taken from the research of Peter N. Ferns and Alison Lang, in the article "The Value of Immaculate Mates: Relationships between Plumage Quality and Breeding Success in Sheldrakes", Ethology, volume 109, page 521-532, 2003.
Shelducks were studied at 20 feeding sites in the Severn Estuary, UK, to determine if an aspect of plumage coloring called immaculateness (the uniformity of a region of colored plumage and the regularity of its borders) was related to the quality of the feeding sites at which the birds ate. Immaculateness was measured on an eight-point scale, with a score of one being the worst and eight being the best. The quality of each feeding site was rated as poor, medium, or good.
The results for each gender were as follows:
Males:
| Quality of Site |
| Immaculateness |
PoorMedium |
Good |
| 1 |
00 |
0 |
| 2 |
00 |
0 |
| 3 |
00 |
0 |
| 4 |
32 |
0 |
| 5 |
00 |
0 |
| 6 |
1114 |
18 |
| 7 |
11 |
2 |
| 8 |
29 |
12 |
Females:
| Quality of Site |
|
Immaculateness |
PoorMedium |
Good |
| 1 |
00 |
1 |
| 2 |
03 |
1 |
| 3 |
02 |
0 |
| 4 |
1315 |
16 |
| 5 |
03 |
5 |
| 6 |
03 |
5 |
| 7 |
00 |
0 |
| 8 |
00 |
0 |
Because plumage score and breeding site quality are both ordered in these tables, the Jonckheere-Terpstra test is appropriate for each data set, and because the number of shelducks is so small, exact results are necessary to ensure accuracy. For the female data set, we get an exact p-value of .0815, which indicates an insignificant relationship between immaculateness and quality of feeding site. The Jonckheere-Terpstra test on the data for the males, however, returned an exact p-value of .0268, indicating that significantly more drakes with higher immaculateness scores frequented the best sites. Another test for doubly-ordered RxC tables, linear-by-linear association, returned similar conclusions, with an exact p-value of .2228 for females and .0148 for males.
| Exact p-values |
Jonckheere-Terpstra |
Linear-by-linear association |
| Males |
0.0268 |
0.0148 |
| Females |
0.0815 |
0.2228 |
StatXact v6.0 can now handle stratified RxC tables. When this data is put into a table stratified by gender, the appropriate test for a doubly-ordered RxC test is Cochran-Mantel-Haenszel test, which is a generalization of the linear-by-linear association test. The resulting exact p-value is .0064, indicating that, after controlling for gender, there is a highly significant relationship between immaculateness scores and the quality of feeding sites. The ability to analyze the data as a stratified table, a feature only available in StatXact version 6, has enabled us to see this relationship much more clearly.
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