Chapter 13: Q.13.13 (page 532)
Explain the reason for the word variance in the phrase analysis of variance.
Variance is just a statistical method for separating identified variance data into various elements for further analysis.
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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 \(528\).
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:
Movie fans use the annual Leonard Maltin Movie Guide for facts, cast members, and reviews of more than films. The movies are rated from stars , indicating a very good movie, to 1 star , which Leonard Maltin refers to as a BOMB. The following table gives the running times, in minutes, of a random sample of films listed in one year's guide.
At the significance level, do the data provide sufficient evidence to conclude that a difference exists in mean running times among films in the four rating groups? (Note:,,
We have provided data from independent simple random samples from several populations. In each case, determine the following items.
a. SSTR
b. MSTR
c. SSE
d. MSE
e. F
Popular Diets. In the article "Comparison of the Atkins, Ornish, Weight Watchers, and Zone Diets for Weight Loss and Heart Disease Risk Reduction" (Journal of the American Medical Association, Vol. , No. 1, Pp, ), M. Dansinger et al. conducted a randomized trial to assess the effectiveness of four popular diets for weight loss. Overweight adults with an average body mass index ofand agesyears participated in the randomized trial for 1 year. The weight losses, in kilograms, based on the results of the experiment are given on the WeissStats site. Negative losses are gains. Weight Watchers.
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)
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