12.42 The effect of increased variation within groups. The One-Way ANOVA applet lets you see how the F statistic and the P-value depend on the variability of the data within groups, the sample size, and the differences among the means.

12.43 The effect of increased variation between groups. Set the pooled standard error for the One-Way ANOVA applet at a middle value. Drag the black dots so that they are approximately equal.

12.44 The effect of increased sample size. Set the pooled standard error for the One-Way ANOVA applet at a middle value and drag the black dots so that the means are roughly 5.00, 4.50, and 5.25, respectively.

12.45 The multiple-play strategy. Multiple play is a bundling strategy through which multiple services are provided over a single network. A common triple-play service these days is Internet, television, and telephone. The market for this service has become a key battleground among telecommunication, cable, and broadband service providers. A study compared the pricing (average monthly cost in U.S. dollars) among triple-play providers using DSL, cable, or fiber platforms.¹¹ The following table summarizes the results for 47 providers.

12.46 The two-sample t test and one-way ANOVA. Refer to the diet and mood data in Exercise 7.68 (page 457). Find the two-sample pooled t statistic for comparing the two energy-restricted diets. Then formulate the problem as an ANOVA and report the results of this analysis. Verify that F = t².

12.47 Winery websites. As part of a study of British Columbia wineries, each of the 193 wineries were classified into one of three categories based on their website features. The Presence stage just had information about the winery. The Portals stage included order placement and online feedback. The Transactions Integration stage included direct payment or payment through a third party online. The researchers then compared the number of market integration features of each winery (for example, in-house touring, a wine shop, a restaurant, in-house wine tasting, gift shop, etc.). Here are the results:¹²

12.48 Time levels of scale. Recall Exercise 7.62 (page 456). This experiment actually involved three groups. The last group was told the construction project would last 12 months. Here is a summary of the interval lengths (in days) between the earliest and latest completion dates.

12.49 Time levels of scale, continued. Refer to the previous exercise.

12.50 Facebook recruitment of young adult smokers. Studies about tobacco use have had difficulties recruiting young adults. Because Facebook is visited daily by a very large percent of young adults, researchers decided to investigate the effectiveness of using Facebook to recruit young adults for a smoking cessation trial. Thirty-six ads were run over a seven-week period, with each ad classified based on its image type. The effectiveness of each ad was assessed using the ad cost per unique click (CUC).

12.51 Organic foods and morals? Organic foods are often marketed using moral terms such as “honesty’’ and “purity.’’ Is this just a marketing strategy, or is there a conceptual link between organic food and morality? In one experiment, 62 undergraduates were randomly assigned to one of three food conditions (organic, comfort, and control).¹³ First, each participant was given a packet of four food types from the assigned condition and told to rate the desirability of each food on a seven-point scale. Then, each was presented with a list of six moral transgressions and asked to rate each on a seven-point scale ranging from 1 = not at all morally wrong to 7 = very morally wrong. The average of these six scores was used as the response.

12.52 Organic foods and morals, continued. Refer to the previous exercise.

12.53 Organic foods and friendly behavior? Refer to Exercise 12.51 for the design of the experiment. After rating the moral transgressions, the participants were told “that another professor from another department is also conducting research and really needs volunteers.’’ They were told that they would not receive compensation or course credit for their help and then were asked to write down the number of minutes (out of 30) that they would be willing to volunteer. This sort of question is often used to measure a person’s prosocial behavior.

12.54 Massage therapy for osteoarthritis of the knee. Various studies have shown the benefits of massage to manage pain. In one study, 125 adults suffering from osteoarthritis of the knees were randomly assigned to one of five eight-week regimens.¹⁴ The primary outcome was the change in the Western Ontario and McMaster Universities Arthritis Index (WOMAC-Global). This index is used extensively to assess pain and functioning in those suffering from arthritis. Negative values indicate improvement. The following table summarizes the results of those completing the study.

12.55 Financial incentives for weight loss. The use of financial incentives has shown promise in promoting weight loss and healthy behaviors. In one study, 104 employees of the Children’s Hospital of Philadelphia, with BMIs of 30 to 40 kilograms per square meter (kg/m²), were each randomly assigned to one of three weight-loss programs.¹⁵ Participants in the control program were provided a link to weight-control information. Participants in the individual-incentive program received this link but were also told that $100 would be given to them each time they met or exceeded their target monthly weight loss. Finally, participants in the group-incentive program received similar information and financial incentives as the individual-incentive program but were also told that they were placed in secret groups of five and at the end of each four-week period, those in their group that met their goals throughout the period would equally split an additional $500. The study ran for 24 weeks and the total change in weight (in pounds) was recorded.

12.56 Financial incentives for weight loss, continued. Refer to the previous exercise.

12.57 Changing the response variable. Refer to the previous two exercises, where we compared three weight-loss programs using change in weight measured in pounds. Suppose that you decide to instead make the comparison using change in weight measured in kilograms.

12.58 Do labels matter? A study was performed to examine the self-identification of college students of Asian descent with various identity categories and assess whether there are attitudinal differences across these categories. Undergraduates at a large midwestern university who had identified themselves as being of Asian descent on their admission application were asked to participate in the study.¹⁶ A total of 620 undergraduates filled out the survey. One question classified the participants into groups by asking them to indicate the option with which they primarily identify: (a) Asian American, (b) specific ethnicity (for example, Chinese), (c) ethnicity American (for example, Chinese American), and (d) other. The responses to the remaining survey questions were then compared across these four groups. One item was “The campus is supportive of Asian American students.’’ Responses were on a four-point scale (1 = strongly disagree, 4 = strongly agree). A summary of the results follows:

12.59 Do we experience emotions differently? Do people from different cultures experience emotions differently? One study designed to examine this question collected data from 410 college students from five different cultures.¹⁷ The participants were asked to record, on a 1 (never) to 7 (always) scale, how much of the time they typically felt eight specific emotions. These were averaged to produce the global emotion score for each participant. Here is a summary of this measure:

Note that the convention of giving the standard deviations in parentheses after the means saves a great deal of space in a table such as this.

12.60 The emotions study, continued. Refer to the previous exercise. The experimenters also measured emotions in some different ways. For a period of a week, each participant carried a device that sounded an alarm at random times during a three-hour interval five times a day. When the alarm sounded, participants recorded several mood ratings indicating their emotions for the time immediately preceding the alarm. These responses were combined to form two variables: frequency, the number of emotions recorded, expressed as a percent; and intensity, an average of the intensity scores measured on a scale of 0 to 6. At the end of the one-week experimental period, the subjects were asked to recall the percent of time that they experienced different emotions. This variable was called “recall.’’ Here is a summary of the results:

12.61 Shopping and bargaining in Mexico. Price haggling and other bargaining behaviors among consumers have been observed for a long time. However, research addressing these behaviors, especially in a real-life setting, remains relatively sparse. A group of researchers performed a small study to determine whether gender or nationality of the bargainer has an effect in the final price obtained.¹⁸ The study took place in Mexico because of the prevalence of price haggling in informal markets. Salespersons working at various informal shops were approached by one of three bargainers looking for a specific product. After an initial price was stated by the vendor, bargaining took place. The response was the difference between the initial and the final price of the product. The bargainers were a Spanish-speaking Hispanic male, a Spanish-speaking Hispanic female, and an Anglo non-Spanish-speaking male. The following table summarizes the results:

12.62 Restaurant ambiance and consumer behavior. There have been numerous studies investigating the effects of restaurant ambiance on consumer behavior. One study investigated the effects of musical genre on consumer spending.¹⁹ At a single high-end restaurant in England over a three-week period, there were a total of 141 participants; 49 of them were subjected to background pop music (for example, Britney Spears, Culture Club, and Ricky Martin) while dining, 44 to background classical music (for example, Vivaldi, Handel, and Strauss), and 48 to no background music. For each participant, the total food bill, adjusted for time spent dining, was recorded. The following table summarizes the means and standard deviations (in British pounds):

12.63 Do isoflavones increase bone mineral density? Kudzu is a plant that was imported to the United States from Japan and now covers over seven million acres in the South. The plant contains chemicals called isoflavones that have been shown to have beneficial effects on bones. One study used three groups of rats to compare a control group with rats that were fed either a low dose or a high dose of isoflavones from kudzu.²⁰ One of the outcomes examined was the bone mineral density in the femur (in grams per square centimeter). Here are the data:

12.64 Do poets die young? According to William Butler Yeats, “She is the Gaelic muse, for she gives inspiration to those she persecutes. The Gaelic poets die young, for she is restless, and will not let them remain long on earth.’’ One study designed to investigate this issue examined the age at death for writers from different cultures and genders.²¹ Three categories of writers examined were novelists, poets, and nonfiction writers. Most of the writers are from the United States, but Canadian and Mexican writers are also included.

12.65 Exercise and healthy bones. Many studies have suggested that there is a link between exercise and healthy bones. Exercise stresses the bones and this causes them to get stronger. One study examined the effect of jumping on the bone density of growing rats.²² There were three treatments: a control with no jumping, a low-jump condition (the jump height was 30 centimeters), and a high-jump condition (60 centimeters). After eight weeks of 10 jumps per day, five days per week, the bone density of the rats (expressed in milligrams per cubic centimeter) was measured. Here are the data:

12.66 Exercise and healthy bones, continued. Refer to the previous exercise.

12.67 Contrasts of interest. Refer to Exercise 12.61 (page 692). Given the group means and F statistic, we can determine that MSE = 2.421. Use this value and the other information in Exercise 12.61 to do the following.

12.68 Orthogonal polynomial contrasts. Recall the Facebook friends study (page 648). Previous research has shown that the bigger one’s social network, the higher one’s social attractiveness. In fact, the relationship between the number of friends and social attractiveness is approximately linear. A reasonable question to ask is whether this is same sort of pattern exists within an online social network. With orthogonal polynomial contrasts, we can assess the contributions of different polynomial trends to the overall pattern. Given the five equally spaced levels of the factor in this study, we can investigate up to a quartic (x⁴) trend. The derivation of the coefficients is beyond the scope of this book, so we will just investigate the trends here. The coefficients for the linear, quadratic, and cubic trends follow:

12.69 A comparison of different types of scaffold material. One way to repair serious wounds is to insert some material as a scaffold for the body’s repair cells to use as a template for new tissue. Scaffolds made from extracellular material (ECM) are particularly promising for this purpose. Because they are made from biological material, they serve as an effective scaffold and are then resorbed. Unlike biological material that includes cells, however, they do not trigger tissue rejection reactions in the body. One study compared six types of scaffold material.²³ Three of these were ECMs and the other three were made of inert materials (MAT). There were three mice used per scaffold type. The response measure was the percent of glucose phosphated isomerase (Gpi) cells in the region of the wound. A large value is good, indicating that there are many bone marrow cells sent by the body to repair the tissue.

12.70 A comparison of different types of scaffold material, continued. Refer to the previous exercise.

12.71 Contrasts for the massage study. Refer to Exercise 12.54 (page 690). There are several comparisons of interest in this study. They are (1) usual care versus the average of the massage groups; (2) the average of the two 30-minute massage groups versus the average of the two 60-minute massage groups; and (3) the difference between a 30-minute massage once a week and twice a week versus the difference between a 60-minute massage once a week and twice a week.

12.72 A dandruff study. Analysis of variance (ANOVA) methods are often used in clinical trials where the goal is to assess the effectiveness of one or more treatments for a particular medical condition. One such study compared three treatments for dandruff and a placebo. The treatments were 1% pyrithione zinc shampoo (PyrI), the same shampoo but with instructions to shampoo two times (PyrII), 2% ketoconazole shampoo (Keto), and a placebo shampoo (Placebo). After six weeks of treatment, eight sections of the scalp were examined and given a score that measured the amount of scalp flaking on a 0 to 10 scale. The response variable was the sum of these eight scores. An analysis of the baseline flaking measure indicated that randomization of patients to treatments was successful in that no differences were found between the groups. At baseline, there were 112 subjects in each of the three treatment groups and 28 subjects in the Placebo group. During the clinical trial, three dropped out from the PyrII group and six from the Keto group. No patients dropped out of the other two groups.

12.73 The dandruff study, continued. Refer to the previous exercise.

12.74 Comparing each pair of dandruff treatments. Refer to Exercise 12.72. Use the Bonferroni or another multiple-comparisons procedure that your software provides to compare the individual group means in the dandruff study. Write a short summary of your conclusions.

12.75 Testing several contrasts from the dandruff study. Refer to Exercise 12.72. There are several natural contrasts in this experiment that describe comparisons of interest to the experimenters. They are (1) Placebo versus the average of the other three treatments, (2) Keto versus the average of the two Pyr treatments, and (3) PyrI versus PyrII.

12.76 Changing the response variable. Refer to Exercise 12.69 (page 694), where we compared six types of scaffold material to repair wounds. The data are given as percents ranging from 5 to 75.

12.77 More on changing the response variable. Refer to the previous exercise and Exercise 12.69 (page 694). A calibration error was found with the device that measured Gpi, which resulted in a shifted response. Add 5% to each response and redo the calculations. Summarize the effects of transforming the data by adding a constant to all responses.

12.78 Linear transformation of the response variable. Refer to the previous two exercises. Can you suggest a general conclusion regarding what happens to the test statistic, degrees of freedom, P-value, and conclusion when you perform analysis of variance on data that have been transformed by multiplying the raw data by a constant and then adding another constant? (That is, if y is the original data, we analyze y*, where y* = a + by and a and b ≠ 0 are constants.)

12.79 More on the Facebook friends study. Refer to the Facebook friends study that we began to examine in Example 12.3 (page 648). The explanatory variable in this study is the number of Facebook friends, with possible values of 102, 302, 502, 702, and 902. When using ANOVA, we treat the explanatory variable as categorical. An alternative analysis is to use simple linear regression. Perform this analysis and summarize the results. Plot the residuals from the regression model versus the number of Facebook friends. What do you conclude?

12.80 Using the table of group means and standard deviations. Refer to Exercise 12.6 (page 655). Using the table of group means and standard deviations, construct an ANOVA table similar to that on page 662.

12.81 Planning another emotions study. Scores on an emotional scale were compared for five different cultures in Exercise 12.59 (page 691). Suppose that you are planning a new study using the same outcome variable. Your study will use European American, Asian American, and Hispanic American students from a large university.

12.82 Planning another isoflavone study. Exercise 12.63 (page 692) gave data for a bone health study that examined the effect of isoflavones on rat bone mineral density. In this study, there were three groups. Controls received a placebo, and the other two groups received either a low or a high dose of isoflavones from kudzu. You are planning a similar study of a new kind of isoflavone. Use the results of the study described in Exercise 12.63 to plan your study. Write a proposal explaining why your study should be funded.

12.83 Planning another restaurant ambiance study. Exercise 12.62 (page 693) gave data for a study that examined the effect of background music on total food spending at a high-end restaurant. You are planning a similar study but intend to look at total food spending at a more casual restaurant. Use the results of the study described in Exercise 12.62 to plan your study.