Statistics for Biologists
STT 464
Homework # 8
Due Friday November 20, 2015

Question 1: Refer to the data from Exercise 7 on page 315 of Freund et al. (2010), drawing conclusions based only the ANOVA F-test.

Question 2: Revisit Exercise 7 from page 315 in Freund et al. (2010).

a) Conduct Fisher’s LSD to separate the means. Is this test being used in a “protected” sense? Why or why not?
b) Use a Tukey’s test to separate the means using either underscore or letter superscript notation.
c) Use a Bonferroni test to separate the means using either underscore or letter superscript notation. Would you prefer this test over the other two? Why or why not?

Question 3: Previous studies suggest that vegetarians may not receive enough zinc in their diets. As the zinc requirement is particularly important during pregnancy, researchers conducted a study to determine whether vegetarian pregnant women are at greater risk from low zinc levels than are nonvegetarian pregnant women. Twenty-three women were monitored: twelve vegetarians who were pregnant, six nonvegetarians who were pregnant and five vegetarians who were not pregnant. None of these women were smokers, and none of the nonpregnant women were taking oral contraceptives (I’m not sure why that might be even important..that information was just provided -> perhaps they influence zinc levels?). The zinc status in each woman was measured by zinc content in the blood, urine, and hair. The following table presents the zinc level in the hair (Data from King et al., 1981. American Journal of Clinical Nutrition 34: 1049-1055).

Pregnant Nonvegetarians (Population 1) Pregnant Vegetarians
(Population 2) Nonpregnant Vegetarians
(Population 3)
185 171 210
189 174 139
187 202 172
181 171 198
150 207 177
176 125
189
179
163
174
184
186
a) Check the basic ANOVA assumption using a residual plot and modified Levene’s test. What would you conclude?

b) Carry on with this problem assuming that there is no need to transform the data. Consider the following null hypotheses:

Ho: 1 – 1/2 2 – 1/2 3 = 0
Ho: 2 – 3 = 0

(i) Describe (in layperson terms) what two hypotheses are being tested.
(ii) Carry out the two-tailed tests and draw some conclusions.
Question 4: Arthritis is a very commonly occurring affliction. It is a major cause of lost work time and often results in serious disability. Of the many types of arthritis, the most common type is osteoarthritis. This condition is frequently due to wear and tear in the joints and is more likely to be found in people over 50. It is very painful in the weight-bearing joints, such as the knees and hips. Cartilage wears away on the bone ends, causing pain and swelling. Osteoarthritis may develop after an injury such as bone fracture or a joint dislocation. In order to reduce the amount of time osteoarthritis patients are absent from work, it is important for them to have effective pain relief. An experiment was conducted to compare the effectiveness of three new analgesics, A1, A2, A3. A clinic evaluated a large group of patients and identified 42 patients with a moderate level of pain. Each of the 42 persons was then randomly assigned to one of the three analgesics. The patients were then placed on the therapies and the percentage reduction in pain level was assessed for each patient. These values are recorded below.
Subject A1 A2 A3
1 3 1.8 1.3
2 1.2 6.3 12.6
3 1 5.2 10
4 0.7 3.7 10.5
5 1.1 5.4 10.8
6 0.6 2.9 5.9
7 1.2 6 12.1
8 0.1 0.3 0.6
9 0.7 3.6 18.6
10 1.9 9.3 18.7
11 0.6 2.8 5.5
12 1.6 8.1 18.2
13 4 19.9 22.3
14 0.1 0.3 0.6
a) Provide side-by-side box plots of the data from the three analgesics. What do you think you should do? Confirm your action based on conclusions derived from a more formal test.
b) Use a Tukey’s test to separate the means, making sure that estimates are reported on the scale of measurement.

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