Chapter 13: Q. 2 (page 547)
State the four assumptions for one-way ANOVA, and explain how those assumptions can be checked.
The factorial ANOVA requires the following assumptions: (1) interval data for the dependent variable, (2) normality, (3) homoscedasticity, and (4) no multicollinearity.
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Book Prices. The R. R. Bowker Company collects data on book prices and publishes its findings in The Bowker Annual Library and Book Trade Almanac. Independent simple random samples of hardcover books in law, science, medicine, and technology gave the data, in dollars, on the WeissStats site.
a. Obtain individual normal probability plots and the standard deviation 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 on the data is reasonable. If so. also do parts (d) and (e).
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 fewer than the samples were taken.
e. Interpret your results from part (d).
Discuss two methods for checking the assumptions of normal populations and equal standard deviations for a one-way ANOVA.
Explain the reason for the word variance in the phrase analysis of variance.
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:
Figure 13.7 shows side-by-side boxplots of independent samples from three normally distributed populations having equal standard deviations. Based on these boxplots, would you be inclined to reject the null hypothesis of equal population means? Why?
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