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. Interpret the test for interaction shown in the ANOVA table. Use $\alpha = 0.025$ .

__________ is a particular combination of levels of the factors involved in a study.

The results of a Tukey multiple comparison are summarized below. Treatment Sample Mean B 35.4 C 31.5 A 20.7 a. How many pairwise comparisons of the three treatments are there? b. Which treatments are significantly different from each other? c. Which treatments are not significantly different from each other?

An appliance manufacturer is interested in determining whether the brand of laundry detergent used affects the average amount of dirt removed from standard household laundry loads. An Experiment is set up in which 12 laundry loads are randomly assigned to each of four laundry Detergents-- Brands A, B, C, and D. (A total of 40 loads in the experiment.)A manufacturer of Brand A claims that the design of the experiment is flawed. According to the manufacturer, Brand A is better in cold water than in hot water. If all 48 loads in the above experiment were run in hot Water, the results will be biased against Brand A. Explain how to redesign the experiment so that The main effects of both brand and water temperature (hot or cold)on amount of dirt removed, And their possible interaction, can be investigated.

A company that employs a large number of salespeople is interested in learning which of the salespeople sell the most: those strictly on commission, those with a fixed salary, or those with a reduced fixed salary plus a commission. The previous monthʹs records for a sample of salespeople are inspected and the amount of sales (in dollars)is recorded for each, as shown in the table. Commissioned Fixed Salary Commission Plus Salary \ 450 \ 507 \ 492 \ 425 \ 361 \ 492 \ 450 \ 437 \ 470 \ 483 \ 432 \ 439 \ 466 \ 444 \ 467 ANALYSIS OF VARIANCE DF SS MS F SOURCE 2 4195 2097.7 3.17 FACTOR 12 7945 662.1 ERROR TOTAL 14 12140 Test to determine if a difference exists in the mean sale amounts among the three compensation systems. Test using $\alpha = .025$ .

A multiple-comparison procedure for comparing four treatment means produced the confidence intervals shown below. For each pair of means, indicate which mean is larger or indicate that there Is no significant difference. - :(8,20) - :(-5,1) - :(12,18) - :(-22,-10) - :(-4,6) - :(12,22)

A certain HMO is attempting to show the benefits of managed care to an insurance company. The HMO believes that certain types of doctors are more cost-effective than others. One theory is that certification level is an important factor in measuring the cost-effectiveness of physicians. To investigate this, the HMO obtained independent random samples of 20 physicians from each of the three certification levels-Board certified (C); Uncertified, board eligible (E); and Uncertified, board ineligible (I)-and recorded the total per member per month charges for each (a total of 60 physicians). In order to compare the mean charges for the three groups, the data were subjected to an analysis of variance. The results of the ANOVA are summarized in the following table. Take $\alpha$ $= 0.01$ Source df SS MS F Value Prob > F Treatments 2 4083.81 2041.905 20.73 .0001 Error 57 5614.5 98.5 Total 59 9698.31 Interpret the $p$ -value of the ANOVA $F$ -test.

In a completely randomized design experiment, 10 experimental units were randomly chosen for each of three treatment groups and a quantity was measured for each unit within each group. In the first steps of testing whether the means of the three groups are the same, the sum of squares for treatments was calculated to be 3,110 and the sum of squares for error was calculated to be 27,000. Complete the ANOVA table. Source df SS MS F Treatments Error Total

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. Identify the dependent (response)variable for this experiment.

Four brands of baseball bats were tested to determine which bat allowed hitters to hit a baseball farthest. Eight different batters were thrown 25 pitches while hitting with each of the four bats (assigned in random order). The average distance of the five longest hits using each bat is shown In the table below. The goal is to determine if the average hit distance differs for the four brands of Baseball bats. Batter Brand 1 Brand 2 Brand 3 Brand 4 1 307 315 300 275 2 310 317 305 285 3 335 335 330 302 4 325 328 320 300 5 300 305 295 270 6 345 350 340 310 7 312 315 308 300 8 298 302 295 288 The ANOVA table output is shown here: Source DF SS MS F P Batter 7 6227.4 946.77 39.70 0.0000 Brand 3 4117.6 1372.54 57.55 0.0000 Error 21 500.9 23.85 Total 31 11245.9 Identify the test statistic that should be used for testing whether the average distance hit for the Four brands of baseball bats differ.

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 sample mean charges for each of the eight categories are shown in the Table. Primary Specialty Foreign Grad USA Grad GP 39.00 41.40 IM 52.90 50.60 PED 21.30 23.10 FP 32.80 36.60 What type of design was used for this experiment?

An industrial psychologist is investigating the effects of work environment on employee attitudes. A group of 44 recently hired sales trainees were randomly assigned to one of 11 different ʺhome Roomsʺ - four trainees per room. Each room is identical except for wall color, with 11 different Colors used. The psychologist wants to know whether room color has an effect on attitude, and, if So, wants to compare the mean attitudes of the trainees assigned to the 11 room colors. At the end Of the training program, the attitude of each trainee was measured on a 100-pt. scale (the lower the Score, the poorer the attitude). How many treatments are in this study?

A study was conducted to test the effectiveness of supermarket sales strategies. At one supermarket, the price level (regular, reduced price, and at cost to supermarket)and display level (normal display space, normal display space plus end-of-aisle display, and twice the normal Display space)were tested to determine if they had any effect on the weekly sales of a particular Supermarket product. Each of the combinations of price level and display level were put in place For a randomly selected week and the weekly sales of the product was recorded. Each combination Was used three times over the course of the experiment. The results of the study are shown here: Identify the response variable used in this experiment.

An advertising firm conducts 3 different campaigns, each in 14 different cities, to promote a certain product, and tracks the product sales attributable to each campaign in each city. Determine Whether the study is observational or designed.

Four different leadership styles used by Big-Six accountants were investigated. As part of a designed study, 15 accountants were randomly selected from each of the four leadership style Groups (a total of 60 accountants). Each accountant was asked to rate the degree to which their Subordinates performed substandard field work on a 10-point scale-called the ʺsubstandard work Scaleʺ. The objective is to compare the mean substandard work scales of the four leadership styles. The data on substandard work scales for all 60 observations were subjected to an analysis of Variance. ONE-WAY ANOVA FOR SUBSTAND BY STYLE SOURCE DF SS MS F P BETWEEN 3 1565.38 521.794 3.750 0.0159 WITHIN 56 7792.12 139.145 TOTAL 59 9357.50 Interpret the results of the ANOVA $F$ -test shown on the printout for $\alpha = 0.05$ .

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. Identify the response variable in this study.

The __________ in a designed experiment to compare k means is the probability of making at least one Type I error in a series of inferences about the population means, based on (1 - α)100% confidence intervals.

A study was conducted to test the effectiveness of supermarket sales strategies. At one supermarket, the price level (regular, reduced price, and at cost to supermarket)and display level (normal display space, normal display space plus end-of-aisle display, and twice the normal Display space)were tested to determine if they had any effect on the weekly sales of a particular Supermarket product. Each of the combinations of price level and display level were put in place For a randomly selected week and the weekly sales of the product was recorded. Each combination Was used three times over the course of the experiment. The results of the study are shown here: The ANOVA table is shown below: Source Display 2 1691393 845696 1709.37 0.0000 Price 2 3089054 154427 3121.89 0.0000 Display Price 4 510705 127676 258.07 0.0000 Error 18 8905 495 Total 26 5300057 Based on the results found in the ANOVA table, should the Main Effects tests for either Display or Price be conducted?

Four brands of baseball bats were tested to determine which bat allowed hitters to hit a baseball farthest. Eight different batters were thrown 25 pitches while hitting with each of the four bats (assigned in random order). The average distance of the five longest hits using each bat is shown In the table below. The goal is to determine if the average hit distance differs for the four brands of Baseball bats. Batter Brand 1 Brand 2 Brand 3 Brand 4 1 307 315 300 275 2 310 317 305 285 3 335 335 330 302 4 325 328 320 300 5 300 305 295 270 6 345 350 340 310 7 312 315 308 300 8 298 302 295 288 Identify the response variable in this experiment.

A study was conducted to test the effectiveness of supermarket sales strategies. At one supermarket, the price level (regular, reduced price, and at cost to supermarket)and display level (normal display space, normal display space plus end-of-aisle display, and twice the normal Display space)were tested to determine if they had any effect on the weekly sales of a particular Supermarket product. Each of the combinations of price level and display level were put in place For a randomly selected week and the weekly sales of the product was recorded. Each combination Was used three times over the course of the experiment. The results of the study are shown here: The ANOVA table is shown below: Source DF SS MS F P Display 2 1691393 845696 1709.37 0.0000 Price 2 3089054 154427 3121.89 0.0000 Display Price 4 510705 127676 258.07 0.0000 Error 18 8905 495 Total 26 5300057 Which of the following tests should be conducted first?