TABLE 11-11
A physician and president of a Tampa Health Maintenance Organization (HMO) are attempting to show the benefits of managed health care to an insurance company. The physician believes that certain types of doctors are more cost-effective than others. One theory is that primary specialty is an important factor in measuring the cost-effectiveness of physicians. To investigate this, the president obtained independent random samples of 20 HMO physicians from each of 4 primary specialtiesGeneral Practice (GP), Internal Medicine (IM), Pediatrics (PED), and Family Physicians (FP)and recorded the total charges per member per month for each. A second factor which the president believes influences total charges per member per month is whether the doctor is a foreign or US medical school graduate. The president theorizes that foreign graduates will have higher mean charges than US graduates. To investigate this, the president also collected data on 20 foreign medical school graduates in each of the 4 primary specialty types described above. So information on charges for 40 doctors (20 foreign and 20 US medical school graduates) was obtained for each of the 4 specialties. The results for the ANOVA are summarized in the following table.
-Referring to Table 11-11, what assumption(s) need(s) to be made in order to conduct the test for differences between the mean charges of foreign and US medical school graduates?
A) There is no significant interaction effect between the area of primary specialty and the medical school on the doctors' mean charges.
B) The charges in each group of doctors sampled are drawn from normally distributed populations.
C) The charges in each group of doctors sampled are drawn from populations with equal variances.
D) All of the above are necessary assumptions.

Question

TABLE 11-11
A physician and president of a Tampa Health Maintenance Organization (HMO) are attempting to show the benefits of managed health care to an insurance company. The physician believes that certain types of doctors are more cost-effective than others. One theory is that primary specialty is an important factor in measuring the cost-effectiveness of physicians. To investigate this, the president obtained independent random samples of 20 HMO physicians from each of 4 primary specialtiesGeneral Practice (GP), Internal Medicine (IM), Pediatrics (PED), and Family Physicians (FP)and recorded the total charges per member per month for each. A second factor which the president believes influences total charges per member per month is whether the doctor is a foreign or US medical school graduate. The president theorizes that foreign graduates will have higher mean charges than US graduates. To investigate this, the president also collected data on 20 foreign medical school graduates in each of the 4 primary specialty types described above. So information on charges for 40 doctors (20 foreign and 20 US medical school graduates) was obtained for each of the 4 specialties. The results for the ANOVA are summarized in the following table. 
-Referring to Table 11-11, what assumption(s) need(s) to be made in order to conduct the test for differences between the mean charges of foreign and US medical school graduates?
A) There is no significant interaction effect between the area of primary specialty and the medical school on the doctors' mean charges. 
B) The charges in each group of doctors sampled are drawn from normally distributed populations. 
C) The charges in each group of doctors sampled are drawn from populations with equal variances. 
D) All of the above are necessary assumptions.

Quizplus · Accepted Answer

All three assumptions need to be made in order to conduct the test for differences between the mean charges of foreign and US medical school graduates. The first assumption (A) is necessary to ensure that there is no confounding effect between the area of primary specialty and the medical school on the doctors' mean charges. The second assumption (B) is necessary to ensure that the distribution of charges in each group of doctors sampled is normal, which is required for conducting the ANOVA F-test. The third assumption (C) is necessary to ensure that the variances of charges in each group of doctors sampled are equal, which is also required for conducting the ANOVA F-test.

TABLE 11-11 A Physician and President of a Tampa Health Maintenance Organization