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Chapter 13: Q. 3 (page 547)
On what distribution does one-way ANOVA rely?
The F-distribution is used in one-way ANOVA.
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Discuss two methods for checking the assumptions of normal populations and equal standard deviations for a one-way ANOVA.
a. Obtain individual normal probability plots and the standard deviations of the samples.
b. Perform a residual analysis.
c. Use your results from parts (a) and (b) to decide whether conducting a one-way ANOVA test and the data is reasonable. If so, also do parts .
d. Use a one-way ANOVA test to decide, at the significance level, whether the data provide sufficient evidence to conclude that a difference exists among the means of the populations from which the samples were taken.
e. Interpret your results from part (d).
Weight Loss and BMI. In the paper "Voluntary Weight Reduction in Older Men Increases Hip Bone Loss: The Osteoporotic Fractures in Men Study" (Journal of Clinical Endocrinology & Metabolism, Vol. 90, Issue 4. Pp. ), K. Ensrud et al. reported on the effect of voluntary weight reduction on hip bone loss in older men. In the study, 1342 older men participated in two physical examinations an average of years apart. After the second exam, they were categorized into three groups according to their change in weight between exams: weight loss of more than , weight gain of more than , and stable weight (between loss and gain). For purposes of the hip bone density study, other characteristics were compared, one such being body mass index (BMI). On the Weissstats site, we provide the BMI data for the three groups, based on the results obtained by the researchers.
Income by Age. The U.S. Census Bureau collects information on the incomes of employed persons and publishes the results in Historical Income Tables. Independent simple random samples of ployed persons in each of four age groups gave the data on annual income, in thousands of dollars, presented on the WeissStats site.
Copepod Cuisine. Copepods are tiny crustaceans that are an essential link in the estuarine food web. Marine scientists G. Weiss et al. at the Chesapeake Biological Laboratory in Maryland designed an experiment to determine whether dietary lipid (fat) content is important in the population growth of a Chesapeake Bay copepod. Their findings were published in the paper "Development and Lipid Composition of the Harpacticoid Copepod Nitocra Spinipes Reared on Different Diets" (Marine Ecology Progress Series, Vol. , pp. ). Independent random samples of copepods were placed in containers containing lipid-rich diatoms, bacteria, or leafy macroalgae. There was containers total with four replicates per diet. Five gravid (egg-bearing) females were placed in each container. After days, the number of copepods in each container was as follows.
At the significance level, do the data provide sufficient evidence to conclude that a difference exists in the mean number of copepods among the three different diets? (Note:
Fill in the missing entries in the partially completed one-way ANOVA tables.
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