Marketing Chapter 11 Homework The owners of the Santa Fe Grill would like to know if there is a difference in the like li hood of returning to the restaurant

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Chapter 11 – Basic Data Analysis for Quantitative Research

comparison involves only one independent variable. Researchers also can use ANOVA to

examine the effects of several independent variables simultaneously. This enables analysts to

estimate both the individual and combined effects of several independent variables on the

dependent variable.

ANOVA requires that the dependent variable be metric. That is, the dependent variable must be

either interval or ratio scaled. A second data requirement is that the independent variable, in this

case the coffee consumption variable, be categorical (nonmetric).

ANOVA examines the variance within a set of data. The variance of a variable is equal to the

average squared deviation from the mean of the variable. The logic of ANOVA is that if we

calculate the variance between the groups and compare it to the variance within the groups, we

can make a determination as to whether the group means (attitudes toward the advertising

campaign) are significantly different. When within-group variance is high, it swamps any

between group differences we see unless those differences are large.

Researchers use the F-test with ANOVA to evaluate the differences between group means for

statistical significance (PPT slide 11-19).

The larger the difference in the variance between groups, the larger the F ratio. Since the total

variance in a data set is divisible into between- and within-group components, if there is more

variance explained or accounted for by considering differences between groups than there is

within groups, then the independent variable probably has a significant impact on the dependent

variable. Larger F ratios imply significant differences between the groups. Thus, the larger the

F ratio, the more likely it is that the null hypothesis will be rejected.

Chapter 11 – Basic Data Analysis for Quantitative Research

O. SPSS Application—ANOVA (PPT slides 11-20 to 11-22)

The owners of the Santa Fe Grill would like to know if there is a difference in the likelihood of

returning to the restaurant based on how far customers have driven to get to the restaurant. They

believe it is important to know the answer not only for their customers but for customers of

Jose’s as well. They therefore ask the researcher to test the hypothesis that there are no

differences in likelihood of returning (X23) and distance driven to get to the restaurant (X30). To

test this hypothesis the researchers may use the SPSS compare means test. The results are

shown in Exhibit 11.13 (PPT slide 11-20).

A weakness of ANOVA, however, is that the test enables the researcher to determine only that

statistical differences exist between at least one pair of the group means. The technique cannot

identify which pairs of means are significantly different from each other.

To run the Scheffé post-hoc test, the researchers use the SPSS compare means test. Results for

the Scheffé test for the restaurant example are shown in Exhibit 11.14 (PPT slide 11-22).

IV. n-Way ANOVA (PPT slide 11-21)

n-way ANOVA is a type of ANOVA that can analyze several independent variables at the same

time (PPT slide 11-21). Using multiple independent factors creates the possibility of an

interaction effect. That is, the multiple independent variables can act together to affect dependent

variable group means.

Chapter 11 – Basic Data Analysis for Quantitative Research

Another situation that may require n-way ANOVA is the use of experimental designs (causal

research), where the researcher uses different levels of a stimulus (e.g., different prices or ads) and

then measures responses to those stimuli.

A. SPSS Application—n-Way ANOVA

To help students understand how ANOVA is used to answer research questions, the text refers

to the restaurant database to answer a typical question. The owners want to know first whether

customers who come to the restaurant from greater distances differ from customers who live

nearby in their willingness to recommend the restaurant to a friend. Second, they also want to

know whether that difference in willingness to recommend, if any, is influenced by the gender

of the customers.

The purpose of the ANOVA analysis is to see if the differences that do exist are statistically

significant and meaningful. To statistically assess the differences, ANOVA uses the F-ratio.

The bigger the F-ratio, the bigger the difference among the means of the various groups with

respect to their likelihood of recommending the restaurant.

SPSS can help you conduct the statistical analysis to test the null hypotheses. The best way to

analyze the restaurant survey data to answer the owner’s questions is to use a factorial model. A

factorial model is a type of ANOVA in which the individual effects of each independent

variable on the dependent variable are considered separately, and then the combined effects (an

interaction) of the independent variables on the dependent variable are analyzed.

Chapter 11 – Basic Data Analysis for Quantitative Research

The means (see Total rows) show that the average likelihood of recommending the Santa Fe

Grill to a friend increases as the distance driven by the respondent decreases.

B. Perceptual Mapping (PPT slide 11-23 and 11-24)

Perceptual mapping is a process that is used to develop maps that show the perceptions of

respondents (PPT slide 11-23). The maps are visual representations of respondents’ perceptions

of a company, product, service, brand, or any other object in two dimensions. A perceptual map

typically has a vertical and a horizontal axis that are labeled with descriptive adjectives.

C. Perceptual Mapping Applications in Marketing Research (PPT slide 11-32)

While the fast-food example illustrates how perceptual mapping groups pairs of restaurants

together based on perceived ratings, perceptual mapping has many other important applications

in marketing research. Other applications are given below.

• New-product development: Perceptual mapping can identify gaps in perceptions and

thereby help to position new products.

• Image measurements: Perceptual mapping can be used to identify the image of the

company to help to position one company relative to the competition.

Marketing Research in Action

Examining Restaurant Image Positions—Remington’s Steak House (PPT slide 11-25)

The Marketing Research in Action in this chapter provides an overview of an image study

conducted for Remington’s Steak House, a retail theme restaurant located in a large midwestern

city. A copy of the questionnaire used for the image study is in Exhibit 11.19. Exhibit 11.20 shows

Chapter 11 – Basic Data Analysis for Quantitative Research

Remington’s Steak House.

Answers to Hands-On Exercise

1. What are other areas of improvement for Remington’s?

Students’ answers will vary. In the importance-performance chart, Remington’s is rated low

in “Speed of Service” but that is an important selection criterion for people evaluating places

to dine out. Remington’s should do something about that. Either actually changing their

2. Run post-hoc ANOVA tests between competitor groups. What additional problems or

challenges does this reveal?

Students’ answers will vary. Listed below are the additional problems or challenges.

• Food quality: Remington’s is rated significantly better than both Outback and

Longhorn.

• Speed of service: Remington’s is rated at a (statistically significant) poor third behind

both Outback and Longhorn.

3. What new marketing strategies would you suggest?

Students’ answers will vary. But, following are some of the possible marketing strategies

that could be suggested.

• Food quality: Maintain the lead. Stress this difference in promotional messages.

• Speed of service: Do something about the disadvantage. See Question 1 above for

strategies.

Chapter 11 – Basic Data Analysis for Quantitative Research

Answers to Review Questions

1. Explain the difference between the mean, the median, and the mode.

The mean, median, and mode are the three key measures of central tendency. The mean is

the arithmetical average of responses. The median is the number that sits in the middle of the

data set when you line the numbers up from lowest to highest. The mode is defined as the

most common number in the data set.

2. Why and how would you use Chi-square and t-tests in hypothesis testing?

Students’ answers will vary. Both the t-test and Chi-square tests are used to examine

hypotheses that propose differences between groups. The Chi-square analysis enables

researchers to test for statistical significance between the frequency distributions of two or

more nominally scaled variables in a cross-tabulation table to determine if there is any

association between the variables. An analyst can use the t-test to compare two means when

the sample size is smaller than 30 and the standard deviation is unknown. The t value is a

ratio of the difference between the two sample means and the standard error. The t test

3. Why and when would you want to use ANOVA in marketing research?

Students’ answers will vary. Analysis of variance (ANOVA) is a statistical technique that

determines whether three or more means are statistically different from one another. Thus, it

is similar to the t-test but allows for more than two groups to be examined. For example, if

one wanted to assess whether people of different ethnic backgrounds were more or less

4. What will ANOVA tests not tell you, and how can you overcome this problem?

While ANOVA can tell the research team statistical differences exist somewhere between

the sampled means, it can’t identify which specific means are different from each other.

Answers to Discussion Questions

1. The measures of central tendency discussed in this chapter are designed to reveal

information about the center of a distribution of values. Measures of dispersion provide

information about the spread of all the values in a distribution around the center values.

Assume you were conducting an opinion poll on voters’ approval ratings of the job

performance of the mayor of the city where you live. Do you think the mayor would be more

interested in the central tendency or the dispersion measures associated with the responses to

your poll? Why?

The best way to begin getting started with this question is to nail down a facet or two about

the survey instrument which was used to collect the data. For example, suggest to your

students that, above and beyond some categorical and continuous questions used at the

Chapter 11 – Basic Data Analysis for Quantitative Research

2. If you were interested in finding out whether or not young adults (21–34 years old) are more

likely to buy products online than older adults (35 or more years old), how would you phrase

your null hypothesis? What is the implicit alternative hypothesis accompanying your null

hypothesis?

Null Hypothesis: There isn’t a significant and measurable relationship between age and

purchasing products online. (Assumption: The age ranges are 21–34 years of age and 35+

3. The level of significance (alpha) associated with testing a null hypothesis is also referred to

as the probability of a Type I error. Alpha is the probability of rejecting the null hypothesis

on the basis of your sample data when it is, in fact, true for the population of interest.

Because alpha concerns the probability of making a mistake in your analysis, should you

always try to set this value as small as possible? Why, or why not?

A short answer to this question is that “It depends.” The more appropriate answer is that “It

depends on the amount of risk regarding the accuracy of the test that the research team (in

consultation with the client) is willing to accept.” The most prevalent significance levels

4. Analysis of variance (ANOVA) allows you to test for the statistical difference between two

or more means. Typically, there are more than two means tested. If the ANOVA results for a

set of data reveal that the four means that were compared are significantly different from

each other, how would you find out which individual means were statistically different from

Chapter 11 – Basic Data Analysis for Quantitative Research

each other? What statistical techniques would you apply to answer this question?

Note that ANOVA can’t identify which pairs of means are significantly different from each

other. In this case, we have four means to consider, so it’s clear (by virtue of what is and isn’t

5. EXPERIENCE MARKETING RESEARCH: Nike, Reebok, and Converse are strong

competitors in the athletic shoe market. The three use different advertising and marketing

strategies to appeal to their target markets. Use one of the search engines on the Internet to

This is a very comprehensive discussion question. A number of directives and “tips” which

should help guide them toward the necessary items to bring closure to this question are

provided below for your information.

Nike: Once you arrive at the home page for Nike, it’s best to begin to collect information for

this discussion question by clicking on the “About Nike” link. Information about Nike’s

target market and market share is located under the link entitled “investors.” However, there

are a number of other links where students can find “added value,” especially when it comes

to constructing a questionnaire which drills down into consumer perception about image;

products; and related aspects like diversity, job opportunities, and the like. Exploring the

FAQ section is always an interesting side.

Chapter 11 – Basic Data Analysis for Quantitative Research

6. SPSS EXERCISE: Form a team of three to four students in your class. Select one or two

local franchises to conduct a survey on, such as Subway or McDonald’s. Design a brief

survey (10–12 questions) including questions like ratings on quality of food, speed of service,

knowledge of employees, attitudes of employees, and price, as well as several demographic

variables such as age, address, how often individuals eat there, and day of week and time of

day. Obtain permission from the franchises to interview their customers at a convenient time,

usually when they are leaving. Assure the franchiser you will not bother customers and that

you will provide the franchise with a valuable report on your findings. Develop frequency

charts, pie charts, and similar graphic displays of findings, where appropriate. Use statistics

to test hypotheses, such as “Perceptions of speed of service differ by time of day or day of

week.” Prepare a report, and present it to your class; particularly point out where statistically

significant differences exist and why.

7. SPSS EXERCISE: Using SPSS and the Santa Fe Grill employee database, provide

frequencies, means, modes, and medians for the relevant variables on the questionnaire. The

questionnaire is shown in Chapter 10. In addition, develop bar charts and pie charts where

appropriate for the data you analyzed. Run an ANOVA using the work environment

perceptions variables to identify any differences that may exist between male and female

employees, and part-time versus full-time employees. Be prepared to present a report on

your findings.

Chapter 11 – Basic Data Analysis for Quantitative Research

8. SPSS EXERCISE: Review the Marketing Research in Action case for this chapter. There

were three restaurant competitors—Remington’s, Outback, and Longhorn. Results for a

one-way ANOVA of the restaurant image variable were provided. Now run post-hoc

ANOVA follow-up tests to see where the group differences are. Make recommendations for

new marketing strategies for Remington’s compared to the competition.

This is pretty much a repeat of the questions at the end of the Hands-On Exercise. The

answer is the same. Follow-up tests yield the following results:

• Food quality: Remington’s is rated significantly better than either Outback or

Longhorn.

• Speed of service: Remington’s is a (statistically significant) poor third behind both

Outback and Longhorn.

Based upon the above, the following marketing strategies are suggested:

• Food quality: Maintain the lead. Stress this difference in promotional messages.

• Speed of service: Do something about the disadvantage.

• Reasonable prices: This is a bad place to try to compete. Match Outback, but don’t get

into a price war. That’s too costly and there are no winners. Stress food quality and

value in the promotional messages.

Chapter 11 – Basic Data Analysis for Quantitative Research

efforts to create “atmosphere” are costly, it might cut back a little on the expense.

• Competent employees: Remington’s is a poor third in this relatively unimportant area.

One strategy would be not to worry about it. A better strategy would be to try to improve

the rating without spending a lot of money. A little more attention to employee selection

and a little more training can make a big difference.