In Problem, refer to the specified problem and use the technology of your choice to do the following tasks.
a. Decide whether conducting a Kruskal?Wallis test on the data is reasonable. If so, also do parts (b)?(d).
b. Use a Kruskal?Wallis test to decide, at the 5% 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.
c. Interpret your results from part (b).
d. If a one-way ANOVA test was performed on the data, compare the results of that test with those of the Kruskal?Wallis test, paying particular attention to the P-values.
Note: All data sets are on the WeissStats site.
Weight Loss and Leg Power. The data from Problem 1 on the Maximum Nottingham leg power of three weight-loss groups of older men.
Problem1
In Problems, use the technology of your choice to do the following tasks.
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 on the data is reasonable. If so, also do parts (d)–(f).
d. Use a one-way ANOVA test to decide, at the 5% 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).
*f. If the result of the one-way ANOVA test is statistically significant, perform and interpret a Tukey multiple comparison.
Weight Loss and Leg Power. Another characteristic compared in the hip bone density study discussed in Problem 2 wasMaximum Nottingham leg power, in watts. On the WeissStats site, we provide the leg-power data for the three groups, based on the results obtained by the researchers.
Problem2
In Problems, use the technology of your choice to do the following tasks.
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 on the data is reasonable. If so, also do parts (d)–(f).
d. Use a one-way ANOVA test to decide, at the 5% 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).
*f. If the result of the one-way ANOVA test is statistically significant, perform and interpret a Tukey multiple comparison.
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. 1998–2004), 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 1.8 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 5%, weight gain of more than 5%, and stable weight (between 5% loss and 5% gain). For purposes of the hip bone density study, other characteristics were compared, one such being body mass index (BMI). On theWeissStats site, we provide the BMI data for the three groups, based on the results obtained by the researchers