Chapter 15 EXERCISES
15.34 Plants and hummingbirds. Different varieties of the tropical flower Heliconia are fertilized by different species of hummingbirds. Over time, the lengths of the flowers and the forms of the hummingbirds’ beaks have evolved to match each other. Here are data on the lengths in millimeters of three varieties of these flowers on the island of Dominica:18 
H. bihai 47.12 46.75 46.81 47.12 46.67 47.43 46.44 46.64 48.07 48.34 48.15 50.26 50.12 46.34 46.94 48.36 H. caribaea red 41.90 42.01 41.93 43.09 41.47 41.69 39.78 40.57 39.63 42.18 40.66 37.87 39.16 37.40 38.20 38.07 38.10 37.97 38.79 38.23 38.87 37.78 38.01 H. caribaea yellow 36.78 37.02 36.52 36.11 36.03 35.45 38.13 37.10 35.17 36.82 36.66 35.68 36.03 34.57 34.63 Do a complete analysis that includes description of the data and a rank test for the significance of the differences in lengths among the three species.
15.35 Time spent studying. In Exercise 1.119 (page 69), you compared the time spent studying by men and women. The students in a large first-year college class were asked how many minutes they studied on a typical weeknight. Here are the responses of random samples of 30 women and 30 men from the class:
Women Men 170 120 180 360 240 80 120 30 90 200 120 180 120 240 170 90 45 30 120 75 150 120 180 180 150 150 120 60 240 300 200 150 180 150 180 240 60 120 60 30 120 60 120 180 180 30 230 120 95 150 90 240 180 115 120 0 200 120 120 180 Summarize the data numerically and graphically.
Use the Wilcoxon rank sum test to compare the men and women. Write a short summary of your results.
Use a two-sample t test to compare the men and women. Write a short summary of your results.
Which procedure is more appropriate for these data? Give reasons for your answer.
15.36 Response times for telephone repair calls. A study examined the time required for the telephone company Verizon to respond to repair calls from its own customers and from customers of CLEC, another phone company that pays Verizon to use its local lines. Here are the data, which are rounded to the nearest hour:
Verizon 1 1 1 1 2 2 1 1 1 1 2 2 1 1 1 1 2 2 1 1 1 1 2 3 1 1 1 1 2 3 1 1 1 1 2 3 1 1 1 1 2 3 1 1 1 1 2 3 1 1 1 1 2 3 1 1 1 1 2 4 1 1 1 1 2 5 1 1 1 1 2 5 1 1 1 1 2 6 1 1 1 1 2 8 1 1 1 1 2 15 1 1 1 2 2 CLEC 1 1 5 5 5 1 5 5 5 5 Does Verizon appear to give CLEC customers the same level of service it gives its own customers? Compare the data using graphs and descriptive measures and express your opinion.
We would like to see if times are significantly longer for CLEC customers than for Verizon customers. Why would you hesitate to use a t test for this purpose? Carry out a rank test. What can you conclude?
Explain why a nonparametric procedure is appropriate in this setting.
- 15.37 Multiple comparisons for plants and hummingbirds. As in ANOVA, we often want to carry out a multiple comparisons method following a Kruskal-Wallis test to tell us which groups differ significantly.19 The Bonferroni method (page 374) is a simple method: if we carry out k tests at fixed significance level
Write down all the pairwise comparisons we can make (for example, bihai versus caribaea red). There are three possible pairwise comparisons.
Carry out three Wilcoxon rank sum tests, one for each of the three pairs of flower varieties. What are the three two-sided P-values?
For purposes of multiple comparisons, any of these three tests is significant if its P-value is no greater than
PUTTING IT ALL TOGETHER
Iron-deficiency anemia is the most common form of malnutrition in developing countries. Does the type of cooking pot affect the iron content of food? A study in Ethiopia measured the iron content (milligrams per 100 grams of food) for three types of food cooked in each of three types of pots:20 Here are the data:
| Type of pot | Iron content | |||
|---|---|---|---|---|
| Meat | ||||
| Aluminum | 1.77 | 2.36 | 1.96 | 2.14 |
| Clay | 2.27 | 1.28 | 2.48 | 2.68 |
| Iron | 5.27 | 5.17 | 4.06 | 4.22 |
| Legumes | ||||
| Aluminum | 2.40 | 2.17 | 2.41 | 2.34 |
| Clay | 2.41 | 2.43 | 2.57 | 2.48 |
| Iron | 3.69 | 3.43 | 3.84 | 3.72 |
| Vegetables | ||||
| Aluminum | 1.03 | 1.53 | 1.07 | 1.30 |
| Clay | 1.55 | 0.79 | 1.68 | 1.82 |
| Iron | 2.45 | 2.99 | 2.80 | 2.92 |
Exercises 15.38 to 15.41 use these data.
15.38 Cooking vegetables in different pots. Let’s first concentrate on the 12 observations for the vegetable dish. Does the vegetable dish vary in iron content when cooked in aluminum, clay, and iron pots?
What do the data appear to show? Check the conditions for one-way ANOVA. Which requirements are a bit dubious in this setting?
Instead of using ANOVA, do a rank test. Summarize your conclusions about the effect of pot material on the iron content of the vegetable dish.
15.39 Cooking meat and legumes in aluminum and clay pots. Is there a significant difference between the iron content of meat cooked in aluminum and clay? Is the difference between aluminum and clay significant for legumes? Use rank tests.
15.40 Iron in food cooked in iron pots. The raw data appear to show that food cooked in iron pots has the highest iron content. They also suggest that the three types of food differ in iron content. Is there significant evidence that the three types of food differ in iron content when all are cooked in iron pots?
15.41 Multiple comparisons for cooking pots. Exercise 15.37 outlines how to use the Wilcoxon rank sum test several times for multiple comparisons with overall significance level 0.05 for all comparisons together. Apply this procedure to the data used in Exercises 15.38 and 15.40. Why is is not needed for Exercise 15.39?