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Chapter 13: Q. 6 (page 547)
In one-way ANOVA,
a. list and interpret the three sums of squares.
b. state the one-way ANOVA identity and interpret its meaning with regard to partitioning the total variation among all the data.
(a) Three sum of squares are SSE, SSTR, and SST.
(b) The One-way ANOVA identity is.
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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.
An -curve has . In each case, find the -value having the specified area to its right.
a.
b.
c.
| SAMPLE 1 | SAMPLE 2 | SAMPLE 3 |
| 1 | 10 | 4 |
| 9 | 4 | 16 |
| 8 | 10 | |
| 6 | ||
| 2 |
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?
Fill in the missing entries in the partially completed one-way ANOVA table
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