15.17 Describing a two-way ANOVA.

A ANOVA was run with six observations per cell.

15.18 How large does the statistic need to be?

For each of the following situations, state how large the statistic needs to be for rejection of the null hypothesis at the 5% level. Sketch each distribution and indicate the region where you would reject.

15.19 Describe the design.

Each of the following situations is a two-way study design. For each case, identify the response variable and both factors, and state the number of levels for each factor ( and ) and the total number of observations .

15.20 Outline the ANOVA table.

For each part of the previous exercise, outline the ANOVA table, giving the sources of variation and the degrees of freedom. (Do not compute the numerical values for the sums of squares and mean squares.)

15.21 What can you conclude?

Analysis of data for a ANOVA with five observations per cell gave the statistics in the following table:

What can you conclude from the information given?

15.22 What additional information is needed?

A study reported the following results for data analysed using the methods that we studied in this chapter:

15.23 Where are your eyes?

The objectifying gaze, often referred to as “ogling” or “checking out,” can have many adverse consequences. A group of researchers used eye-tracking technology to better understand the nature and causes for this gaze. They asked 29 women and 36 men to look at images of college-aged women. Each woman had the same clothes and neutral expression but varied in body shape (ideal, average, and below average). Prior to looking at the images, each participant was told to focus on either the appearances or personalities of the women. Here is a summary of the amount of time (in milliseconds) the eyes focused on the chest of the women.

15.24 Acceptance of functional foods.

Functional foods are foods that are fortified with health-promoting supplements, like calcium-enriched orange juice or vitamin-enriched cereal. Although the number of functional foods is growing in the marketplace, very little is known about how the next generation of consumers views these foods. Because of this, a questionnaire was given to college students from the United States, Canada, and France.¹⁰ This questionnaire measured the students’ attitudes and beliefs about general food and functional food. One of the response variables collected concerned cooking enjoyment. This variable was the average of numerous items, each measured on a 10-point scale, where . Here are the means:

15.25 Estimating the within-group variance.

Refer to the previous exercise. Here are the cell standard deviations and sample sizes for cooking enjoyment:

Find the pooled estimate of the standard deviation for these data. Use the rule for examining standard deviations in ANOVA from Chapter 14 (page 720) to determine if it is reasonable to use a pooled standard deviation for the analysis of these data.

15.26 Comparing the groups. Challenge

Refer to Exercises 15.24 and 15.25. The researchers presented a table of means with different superscripts indicating pairs of means that differed at the 0.05 significance level, using the Bonferroni method.

15.27 More on acceptance of functional foods.

Refer to Exercise 15.24. The means for four of the response variables associated with functional foods are as follows.

For each of the four response variables, give a graphical summary of the means. Use this summary to discuss any interactions that are evident. Write a short report summarizing any differences in culture and gender with respect to the response variables measured.

15.28 Interpreting the results.

The goal of the study in the previous exercise was to understand cultural and gender differences in functional food attitudes and behaviors among young adults, the next generation of food consumers. The researchers used a sample of undergraduate students and had each participant fill out the survey during class time. How reasonable is it to generalize these results to the young adult population in these countries? Explain your answer.

15.29 Smart shopping carts.

In Example 7.10 (pages 381-382) we compared spending by shoppers on a budget using a shopping cart equipped with or without real-time feedback. In Exercise 7.67 (page 397) we compared spending by shoppers not on a budget using a shopping cart equipped with or without real-time feedback. Let’s now perform a two-factor ANOVA of these data.

15.30 Fuzzy fish?

Drugs used to treat anxiety persist in wastewater effluent, resulting in relatively high concentrations of these drugs in our rivers and streams. A regional commercial fishing business wants to better understand the effects of these drugs on fish. They hire researchers who expose fish to various levels of an anxiety drug in a laboratory setting and observe their behavior. In one study, researchers considered the effects of three doses of oxazepam on the behaviour of the European perch.¹¹ Twenty-five perch were each assigned to doses of 0, 1.8, or 910 micrograms per liter of water . Each fish was first observed prior to treatment and then observed seven days after treatment. The following table summarizes the results for activity (number of swimming bouts greater than 0.25 cm during 10 minutes).

15.31 The influences of transaction history and a thank you.

A service failure is defined as any service-related problem (real or perceived) that transpires during a customer’s experience with a firm. In the hotel industry, there is a high human component, so these sorts of failures commonly occur regardless of extensive training and established policies. As a result, hotel firms must learn to effectively react to these failures. One study investigated the relationship between a consumer’s transaction history (levels: long and short) and an employee’s statement of thanks (levels: yes and no) on a consumer’s repurchase intent.¹² Each subject was randomly assigned to one of the four treatment groups and asked to read some service failure/resolution scenarios and respond accordingly. Repurchase intent was measured using a 9-point scale. Here is a summary of the means:

15.32 Transaction history and a thank you.

Refer to the previous exercise. The numbers of subjects in each cell were not equal, so the researchers used linear regression to analyze the data. This was done by creating an indicator variable for each factor and the interaction. Here is a partial ANOVA table. Complete it and state your conclusions regarding the main effects and interaction described in the previous exercise.

15.33 The effect of humor.

In advertising, humor is often used to overcome sales resistance and stimulate customer purchase behavior. One experiment looked at the use of humor as an approach to offset the negative feelings often associated with website encounters.¹³ The setting of their experiment was an online travel agency, and they used a three-factor design, each factor with two levels. They were humor (used, not used), process (favorable, unfavorable), and outcome (favorable, unfavorable). For the humor condition, cartoons and jokes about skiing were used on the site. For the no-humor condition, standard pictures of ski sites were used. Two hundred and forty-one business students from a large Dutch university participated in the experiment. Each was randomly assigned to one of the eight treatment conditions. The students were asked to book a skiing holiday and then rate their perceived enjoyment and satisfaction with the process. All responses were measured on a 7-point scale. The following is a summary of the results for satisfaction.

15.34 Pooling the standard deviations.

Refer to the previous exercise. Find the pooled estimate of the standard deviation for these data. What are its degrees of freedom? Using the rule from Chapter 14 (page 720), is it reasonable to use a pooled standard deviation for the analysis? Explain your answer.

15.35 Describing the effects.

Refer to Exercise 15.33. The -values for all main and two-factor interactions are significant at the 0.05 level. Using the table, find the marginal means and use them to describe these effects.

15.36 Trust of individuals and groups.

Trust is an essential element in any exchange of goods or services. The following trust game is often used to study trust experimentally:

The value x is taken as a measure of the sender’s trust, and the value indicates the responder’s trustworthiness. A study used this game to study the dynamics between individuals and groups of three.¹⁴ The following table summarizes the average amount x sent by senders.

15.37 Trustworthiness of individuals and groups.

Refer to the previous exercise. Here is a summary of the percent returned to the sender.

Repeat parts (a)–(d) of Exercise 15.36 using these results. In this case, none of the effects is statistically significant.

15.38 Switching between work tasks.

In many businesses, employees are expected to handle multiple projects simultaneously. To work efficiently, this requires the employee to reduce or eliminate cognitions about one task and fully focus on another. Is this easy to do? A study looked at how having to transition between sequential tasks affects worker ability to dedicate their full attention to a given task.¹⁵ Each participant was asked to work on two tasks (each five minutes in length). The first task was a word puzzle, and the second involved reading four résumés and selecting the best candidate. The 78 participants were randomly assigned within a 2 (first task: finished/unfinished) × 2 (time pressure: high/low) design and were evaluated on how many characteristics of the résumés they recalled from Task 2. The following table summarizes the means.

Plot the means and describe the primary features of the data in terms of main effects and interaction.

15.39 Repeating an advertising message.

Does repetition of an advertising message increase its effectiveness? One theory suggests that there are two phases in the process. In the first phase, called “wearin,” negative or unfamiliar views are transformed into positive views. In the second phase, called “wearout,” the effectiveness of the ad is decreased because of boredom or other causes. One study designed to investigate this theory examined two factors. The first was familiarity of the ad, with two levels, familiar and unfamiliar; the second was repetition, with three levels, 1, 2, and 3.¹⁶ One of the response variables collected was attitude toward the ad. This variable was the average of four items, each measured on a 7-point scale, anchored by bad–good, low quality–high quality, unappealing–appealing, and unpleasant–pleasant. Here are the means for attitude:

15.40 Other response variables.

Refer to the previous exercise. In settings such as this, researchers collect data for several response variables. For this study, they also constructed variables that were called attitude toward the brand, total thoughts, support arguments, and counterarguments. Here are the means:

For each of the four response variables, give a graphical summary of the means. Use this summary to discuss any interactions that are evident. Write a short report summarizing the effect of repetition on the response variables measured, using the data in this exercise and the previous one.

15.41 Pooling the standard deviations.

Refer to the previous exercise. Here are the standard deviations for attitude toward brand:

Assuming that the cell sizes are equal, find the pooled estimate of the standard deviation for these data. Use the rule for examining standard deviations in ANOVA from Chapter 14 (page 720) to determine if it is reasonable to use a pooled standard deviation for the analysis of these data.

15.42 More pooling.

Refer to Exercise 15.40. Here are the standard deviations for total thoughts:

Assuming that the cell sizes are equal, find the pooled estimate of the standard deviation for these data. Use the rule for examining standard deviations in ANOVA from Chapter 14 (page 720) to determine if it is reasonable to use a pooled standard deviation for the analysis of these data.

15.43 Interpret the results.

Refer to Exercises 15.39 and 15.40. The subjects were 94 adult staff members at a West Coast university. They were evenly split into familiar and unfamiliar groups. Each subject watched a half-hour local news show from a different state that included ads at all the repetition levels. The selected ads were judged to be “good” by some experts and had been shown in regions other than where the study was conducted. The real names of the products were replaced by either familiar or unfamiliar brand names by a professional video editor. The ads were pretested, and no one in the pretest sample suggested that the ads were not real. Discuss each of these facts in terms of how you would interpret the results of this study.

15.44 Interpret the results.

Refer to Exercises 15.39 and 15.40. The ratings for this study were each measured on a 7-point scale, anchored by bad-good, low quality-high quality, unappealing-appealing, and unpleasant-pleasant. The results presented were averaged over three ads for different products: a bank, women’s clothing, and a health care plan. Write a short report summarizing the Normality assumption for two-way ANOVA and the extent to which it is reasonable for the analysis of these data.

15.45 A manufacturing problem.

One step in the manufacture of large engines requires that holes of very precise dimensions be drilled. The tools that do the drilling are regularly examined and are adjusted to ensure that the holes meet the required specifications. Part of the examination involves measurement of the diameter of the drilling tool. A team studying the variation in the sizes of the drilled holes selected this measurement procedure as a possible cause of variation in the drilled holes. They decided to use a designed experiment as one part of this examination. Some of the data are given in Table 15.1. The diameters in millimeters (mm) of five tools were measured by the same operator at three times (8:00 A.M., 11:00 A.M., and 3:00 P.M.). Three measurements were taken on each tool at each time. The person taking the measurements could not tell which tool was being measured, and the measurements were taken in random order.¹⁷

15.46 Convert from millimeters to inches.

Refer to the previous exercise. Multiply each measurement by 0.04 to convert from millimeters to inches. Redo the plots and rerun the ANOVA using the transformed measurements. Summarize what parts of the analysis have changed and what parts have remained the same.

15.47 Discounts and expected prices.

CASE 15.1 Case 15.1 (page 15-15) describes a study designed to determine how the frequency that a supermarket product is promoted at a discount and the size of the discount affect the price that customers expect to pay for the product. In the exercises that followed, we examined the data for two levels of each factor.

Table 15.2 gives the complete set of data.

15.48 Rerun the data as a one-way ANOVA.

CASE 15.1 Refer to the previous exercise. Rerun the analysis as a one-way ANOVA with treatments. Summarize the results of this analysis. Use the Bonferroni multiple-comparisons procedure to describe combinations of number of promotions and percent discounts that are similar or different.

15.49 Consumer-generated ads.

More and more companies involve consumers in the process of developing advertisements. Is it beneficial to let consumers know this? In one study, 125 undergraduate students were randomly assigned to a design.¹⁸ Each student watched one of two consumer-generated Doritos ads. Half of the students were told that the ad was consumer-generated and the other half were not. After viewing the ad, the students provided their reactions to the ad and the advertised brand with higher scores reflecting a more favorable opinion. Here is part of the ANOVA table for their reactions to the ad:

15.50 Use of animated agents in a multimedia environment.

Multimedia learning environments are designed to enhance learning by providing a more hands-on and exploratory investigation of a topic. Often, animated agents (human-like characters) are used with the hope of enhancing social interaction with the software and thus improving learning. One group of researchers decided to investigate whether the presence of an agent and the type of verbal feedback provided were actually helpful.¹⁹ To do this, they recruited 135 college students and randomly divided them among four groups: agent/simple feedback, agent/elaborate feedback, no agent/simple feedback, and no agent/elaborate feedback. The topic of the software was thermodynamics. The change in score on a 20-question test taken before and after using the software was the response.