Exam 10: Analysis of Variance: Comparing More Than Two Means

A certain HMO is attempting to show the benefits of managed health care to an insurance company. The HMO believes that certain types of doctors are more cost-effective than others. One theory is that both primary specialty and whether the physician is a foreign or USA medical school graduate are an important factors in measuring the cost-effectiveness of physicians. To investigate this, the president obtained independent random samples of 40 HMO physicians, half foreign graduates and half USA graduates, from each of four primary specialties?General Practice (GP), Internal Medicine (IM), Pediatrics (PED), and Family Physician (FP)?and recorded the total per-member, per-month charges for each. Thus, information on charges were obtained for a total of n = 160 doctors. The ANOVA results are summarized in the following table. dfSSMSF ValueProb > F Source df SS MS F Value Prob > F Specialty 3 22855 7618 60.94 .0001 Medschool 1 105 105 0.84 .6744 Interaction 3 890 297 2.38 .1348 Error 152 18950 125 Total 159 42800 Assuming no interaction, is there evidence of a difference between the mean charges of USA and foreign medical school graduates? Use ? = 0.025.

A certain HMO is attempting to show the benefits of managed health care to an insurance company. The HMO believes that certain types of doctors are more cost-effective than others. One theory is that both primary specialty and whether the physician is a foreign or USA medical school graduate are an important factors in measuring the cost-effectiveness of physicians. To investigate this, the president obtained independent random samples of 40 HMO physicians, half foreign graduates and half USA graduates, from each of four primary specialties?General Practice (GP), Internal Medicine (IM), Pediatrics (PED), and Family Physician (FP)?and recorded the total per-member, per-month charges for each. Thus, information on charges were obtained for a total of n = 160 doctors. The ANOVA results are summarized in the following table. Source df SS MS F Value Prob > F Specialty 3 22855 7618 60.94 .0001 Medschool 1 105 105 0.84 .6744 Interaction 3 890 297 2.38 .1348 Error 152 18950 125 Total 159 42800 Interpret the test for interaction shown in the ANOVA table. Use ? = 0.05.

Given that the mean square for treatments (MST) for an ANOVA F-test is 5,000 and the mean square for error (MSE) is 3,750, find the value of the test statistic F.

In a study to determine the least amount of time necessary to clean an SUV while maintaining a high quality standard, the owner of a chain of car washes designed an experiment where 20 employees were divided into four groups, each with five members. Each member of each group was assigned an SUV to clean within a certain time limit. The time limits for the groups were 20 minutes, 25 minutes, 30 minutes, and 35 minutes. After the time limits for each group had expired, the owner inspected each SUV and rated the quality of the cleaning job on a scale of 1 to 10. What are the factor levels for this study?

A scientist is hoping to compare the mean levels of DDT toxin found in three species of fish in a local river. He randomly samples 50 of each species to use in the analysis. For each fish, he measures the amount of DDT toxin present. Ideally he will be able to rank the species based on the mean level of toxin found in each of the three species. How many factors are present in this study?

Psychologists have found that people are generally reluctant to transmit bad news to their peers. This phenomenon has been named the "MUM effect." To investigate the cause of the MUM effect, 40 undergraduates at a university participated in an experiment. Each subject was asked to administer an IQ test to another student and then provide the test taker with his or her percentile score. (Unknown to the subject, the test taker was a bogus student who was working with the researchers.) The experimenters manipulated two factors, subject visibility and success of test taker, each at two levels. Subject visibility was either visible or not visible to the test taker. Success of test taker was either top 20% or bottom 20%. Ten subjects were randomly assigned to each of the 2 x 2 = 4 experimental conditions, then the time (in seconds) between the end of the test and the delivery of the percentile score from the subject to the test taker was measured. (This variable is called the latency to feedback.) The data was subject to an analysis of variance, with the following results: Source df SS MS F PR > F Subject visibility 1 1380.24 1380.24 4.25 0.430 Test taker success 1 1325.16 1325.16 -1371.89 0.05 Visibility x success 1 3385.80 3385.80 10.45 .002 Error 36 11,664.00 324.00 Total 39 17,755.20 Is there evidence to indicate that subject visibility and test taker success interact? Use α = .01.

A city monitors ozone levels monthly over a 7 year period in order to relate the ozone levels to the seasons. Determine whether the study is observational or designed.

A certain HMO is attempting to show the benefits of managed health care to an insurance company. The HMO 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 HMO obtained independent random samples of 26 HMO physicians from each of four primary specialties-- General Practice (GP), Internal Medicine (IM), Pediatrics (PED), and Family Physician (FP)-- and recorded the total per-member, per-month charges for each. Identify the treatments for this group.

Which method generally produces wider confidence intervals?

A local consumer reporter wants to compare the average costs of grocery items purchased at three different supermarkets, A, B, and C. Prices (in dollars) were recorded for a sample of 60 randomly selected grocery items at each of the three supermarkets. In order to reduce item-to-item variation, the prices were recorded for each item on the same day at each supermarket. The results of the ANOVA test are summarized in the following table. Source df Anova SS Mean Square F Value Pr > Supermkt 2 2.6412678 1.3206399 39.23 0.0001 Item 59 215.5949311 3.6541514 108.54 0.0001 Error 118 3.9725322 0.0336655 Corrected Total 179 222.2087311 What is the value of the test statistic for determining whether the three supermarkets have the same average prices?