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Chapter 13: Q. 13.32 (page 542)
Suppose that a one-way ANOVA is being performed to compare the means of three populations and that the sample sizes are and Determine the degrees of freedom for the statistic.
The degrees of freedom for suchstatistics are
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| Sample 1 | Sample 2 | Sample 3 | Sample 4 |
| 7 | 5 | 6 | 3 |
| 4 | 9 | 7 | 7 |
| 5 | 4 | 5 | 7 |
| 4 | 4 | 4 | |
| 8 | 4 |
In section\(13.2\) we considered two hypothetical examples to explain the logic behind one-way ANOVA. Now you are to further examine those examples.
a. Refer to Table \(13.1\) on page \(528\). Perform a one-way ANOVA on the data and compare your conclusion to that stated in the corresponding "what does it mean"? box. Use \(\alpha =0.05\).
b. Repeat part (a) for the data in Table \(13.2\) on page \(528\).
Rock Sparrows breeding in northern Italy are the subject of a long-term ecology and conservation study due to their wide variety of breeding patterns. Both males and females have a yellow patch on their breasts that is thought to play a significant role in their sexual behavior. A Pilastro et al. conducted an experiment in which they increased or reduced the size of a female's breast patch by dying feathers at the edge of a patch and then observed several characteristics of the behavior the male. Their results were published in the paper "Male Rock Sparrow Adjust Their Breeding Strategy According to Female Ornamentation: Parental or Mating Investment? Eight mating pairs were observed in each of three groups: a reduced patch size group, a group control and an enlarged patch size group. The data on the WeissStats site, based on the results reported by the researchers, give the number of minutes per hour that makes sang in the vicinity of the nest after the patch size manipulation was done on the females.
Denosumab and Osteoporosis. A clinical study was conducted to see whether an antibody called denosumab is effective in the treatment of osteoporosis in postmenopausal women, as reported in the article "Denosumab in Postmenopausal Women with Low Bone Mineral Density (New England Journal of Medicine, Vol. . No. , pp. ) by M. McClung et al. Postmenopausal women with osteoporosis were randomly assigned into groups that received either a placebo a six-month regimen of Denosumab at doses of mg, mg,mg, or mg. The following table provides summary statistics for the body-mass indexes (BMI) of the women in each treatment group.
At the significance level, do the data provide sufficient evidence to conclude that a difference exists in mean BMI for women in the five different treatment groups? Note: For the degrees of freedom in this exercise:
We stated earlier that a one-way ANOVA test is always right-tailed because the null hypothesis is rejected only when the test statistic, , is too large. Why is the null hypothesis rejected only when is too large?
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