Question

Dual energy X-ray absorptiometry (DXA) is a technique for measuring bone health. One of the most common measure is total body bone mineral content (TBBMC). A highly skilled operator is required to take the measurements. Recently, a new DXA machine was purchased by a research lab and two operators were trained to take measurements. TBBMC (grams) for eight subjects was measured by both operators. A comparison of the means for the two operators provides a check on the training they received and allows us to determine if the averages are different between the two operators. Data are in Supp52data.

Subject	1	2	3	4	5	6	7	8
Operator 1	1.328	1.342	1.075	1.228	0.939	1.004	1.178	1.286
Operator 2	1.323	1.322	1.073	1.233	0.934	1.019	1.184	1.304

A. Compute the differences between the measured for the two operators. Display the distribution of the differences using a histogram or stem and leaf plot.   Describe briefly.

B. Address whether the “assumption of normality” holds for this problem.

C. Test the null hypothesis that the two averages of the operators are the same. (Include the hypotheses, test statistic, distribution, p value and conclusion).

d) Calculate a 95% CI.

e) Describe relationship between your answers in c) and d).

Answer 1

A. Compute the differences between the measured for the two operators. Display the distribution of the differences using a histogram or stem and leaf plot.   Describe briefly.

Ans:

The histogram of the values from the Operator 1-Operator 2 is drawn. This plot shows that the difference may or may not be followed a normal distribution. This may be due to less number of sample size.

B. Address whether the “assumption of normality” holds for this problem.

The probability plot of the difference values satisfied the assumption of normal distribution at 0.05 level of significance. Hence, the test of the difference between the Operator 1 and Operator 2 can be used paired t-test.

C. Test the null hypothesis that the two averages of the operators are the same. (Include the hypotheses, test statistic, distribution, p value and conclusion).

Ans:

Test statistic under Ho is

Therefore, t= -0.35

P-Value = 0.739

Conclusion: The estimated p-value is 0.739 and more than 0.05 level of significance. Hence, retain the null hypothesis and conclude that there is no difference the averages between the two operators.

d) Calculate a 95% CI.

Ans The 95% CI for mean difference is (-0.01172, 0.00872).

e) Describe relationship between your answers in c) and d).

Ans: The p-value from c) is more than 0.05 level of significance and retain the null hypothesis. Whereas, the confidence interval from d) include the value zero and can conclude that there is no difference in two operators at 0.05 level of significance. Both the results give the same conclusions.