A study compares changes in bone density in 22 women who are neither pregnant nor breastfeeding to that of 47 comparably aged women who are breastfeeding. Table 12.13 lists percent changes in bone mineral content in the spines of these women. Compare these groups with back-to-back stemplots on a common stem. How do the groups differ? Does either group show a major departure from Normality? Calculate the 95% confidence interval for the mean difference in bone loss in the two groups. Discuss your findings. 290CHAPTER 12COMPARING INDEPENDENT MEANSTABLE 12.13 Percent change in bone mineral content over three months in the spines of women.Controls0.00.9-0.21.01.72.9-0.61.1-0.12.40.31.2-1.6-0.1-1.50.7-0.42.2-0.4-0.4-2.2-0.1Breastfeeders-2.7-0.8-5.3 -8.3 --2.1-6.8-4.3-4.7-2.5 -4.9-1.0-6.5-1.8-5.2-5.7-7.0-2.22.2-7.8-3.1-3.0-3.6-5.2-2.0-2.1-5.6-4.4-3.3-6.5-1.0-4.9-4.7-3.8-5.9-2.5-0.3-6.2-6.81.7-4.00.3-2.30.4-5.30.2-2.2-5.1Data from Y axis of Figure 3 in Laskey, M. A., Prentice, A., Hanratty, L. A., Jarjou, L. M., Dibba,B., Beavan, S. R., et al. (1998). Bone changes after 3 mo of lactation: Influence of calcium intake,breast-milk output, and vitamin D-receptor genotype. American Journal of Clinical Nutrition, 67(4),685-692.Data are stored online in the file LACTATION.SAV.

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Description: A study compares changes in bone density in 22 women who are neither pregnant nor breastfeeding to that of 47 comparably aged women who are breastfeeding. Table 12.13 lists percent changes in bone mineral content in the spines of these women. Compare

1) The stem and leaf plot is Control Breast-feeders -8 3 -7 8,0 -6 8,8,5,5,2 -5…

Answered: Controls 2.4 0.0 0.9 -0.2 1.0 1.7 2.9…

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A study compares changes in bone density in 22 women who are neither pregnant nor breastfeeding to that of 47 comparably aged women who are breastfeeding. Table 12.13 lists percent changes in bone mineral content in the spines of these women.

Compare these groups with back-to-back stemplots on a common stem. How do the groups differ? Does either group show a major departure from Normality?

Calculate the 95% confidence interval for the mean difference in bone loss in the two groups. Discuss your findings.

290
CHAPTER 12
COMPARING INDEPENDENT MEANS
TABLE 12.13 Percent change in bone mineral content over three months in the spines of women.
Controls
0.0
0.9
-0.2
1.0
1.7
2.9
-0.6
1.1
-0.1
2.4
0.3
1.2
-1.6
-0.1
-1.5
0.7
-0.4
2.2
-0.4
-0.4
-2.2
-0.1
Breastfeeders
-2.7
-0.8
-5.3 -8.3 --2.1
-6.8
-4.3
-4.7
-2.5 -4.9
-1.0
-6.5
-1.8
-5.2
-5.7
-7.0
-2.2
2.2
-7.8
-3.1
-3.0
-3.6
-5.2
-2.0
-2.1
-5.6
-4.4
-3.3
-6.5
-1.0
-4.9
-4.7
-3.8
-5.9
-2.5
-0.3
-6.2
-6.8
1.7
-4.0
0.3
-2.3
0.4
-5.3
0.2
-2.2
-5.1
Data from Y axis of Figure 3 in Laskey, M. A., Prentice, A., Hanratty, L. A., Jarjou, L. M., Dibba,
B., Beavan, S. R., et al. (1998). Bone changes after 3 mo of lactation: Influence of calcium intake,
breast-milk output, and vitamin D-receptor genotype. American Journal of Clinical Nutrition, 67(4),
685-692.
Data are stored online in the file LACTATION.SAV.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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