burns05 im 17

CHAPTER 17

TESTING FOR DIFFERENCES BETWEEN TWO GROUPS OR AMONG MORE THAN TWO GROUPS

LEARNING OBJECTIVES

To learn how differences are used for market segmentation decisions

To understand when t-tests or z-tests are appropriate and why you do not need to

worry about this issue

To be able to test the differences between two percentages or means for two

independent groups

To know what is a pair samples difference test and when to use it

To comprehend “ANOVA” and how to interpret ANOVA output

To learn how to perform differences tests for means using SPSS

CHAPTER OUTLINE

MARKET SEGMENTATION IN THE NEW ZEALAND WINE MARKETWHY DIFFERENCES ARE IMPORTANTSMALL SAMPLE SIZES: THE USE OF A T-TEST OR A Z-TEST AND HOW SPSS ELIMINATES THE WORRYTESTING FOR SIGNIFICANT DIFFERENCES BETWEEN TWO GROUPS - RETURN TO YOUR INTEGRATED CASE

Differences between Percentages with Two Groups (Independent Samples)Using SPSS for Differences Between Percentages of Two Groups Differences between Means with Two Groups (Independent Samples)The Hobbits’ Choice Restaurant Survey: How to Perform an Independent Samples Significance of Differences between Means Test with SPSS

DIFFERENCES BETWEEN TWO MEANS WITHIN THE SAME SAMPLE (PAIRED SAMPLE)

The Hobbits’ Choice Restaurant Survey: How to Perform a Paired Samples Significance of Differences Between Means Test with SPSS

ONLINE SURVEYS AND DATABASES – A “SIGNIFICANCE” CHALLENGE TO MARKETING RESEARCHERTESTING FOR SIGNIFICANT DIFFERENCES IN MEANS AMONG MORE THAN TWO GROUPS: ANALYSIS OF VARIANCE

Basic Logic in Analysis of Variance

297

Chapter 17: Testing for Differences Between Two Groups or Among More Than Two Groups

How to Determine Statistically Significant Differences Among Group MeansThe Hobbits’ Choice Restaurant Survey: How to Run Analysis of Variance on SPSSApplying ANOVA (Analysis of Variance)n-Way ANOVA

KEY TERMS

Statistical significance of differences Meaningful difference

Stable difference Actionable difference

t test z test

Null hypothesis

Significance of differences between two percentages

Significance of difference between two means

Paired samples test for the difference between two means

ANOVA (analysis of variance) Flagging procedure

Post hoc tests Duncan’s multiple range test

One-way ANOVA n-way ANOVA

Interaction effects

TEACHING SUGGESTIONS

1. This chapter perpetuates the improvement over previous versions of the textbook instituted in the fourth edition. Prior editions which included confidence intervals, hypothesis tests, mean differences, and ANOVA in a single, long chapter. Also, there are fewer statistical differences formulas although those that remain are simplified somewhat. Greater emphasis is placed on identifying and interpreting relevant parts of SPSS output. Hopefully, instructors will find this material less difficult for students to understand and easier to teach.

298


2. The chapter begins by claiming that market segmentation is a very important and the basis for market researchers to investigate statistically significant differences among identifiable groups of consumers. One may use one’s favorite or most familiar market segmentation example to augment or emphasize the segmentation differences central point.

To identify market segments is only the beginning point of the marketing research notion of significant differences. Once the segments are identified, marketing research requires that data be gathered about the consumption patterns of the market segments, and then, these patterns are assessed statistically for significant differences. The statistical concepts used to compare segments are percentages and means.

It is important to emphasize that marketing segmentation is a conceptual notion, for whereas segments can be identified in a great many ways, they are not managerially relevant until statistically significant differences between them are shown that are useful from a marketing strategy standpoint.

As a simple example, take a florist that segments the local market by geographic area: North, East, West, and South. The average dollars spent per purchase is calculated for three flower-giving days in the year. Assume that differences of ±$5 are not significant.

Area Father’s Day Mother’s Day Valentine’s DayNorth $20 $17 $50

East $21 $31 $14

West $15 $17 $25

South $55 $36 $10

What are the promotional implications of these findings?

Answer by day.

Father’s Day – promote heavily to the SouthMother’s Day – promote heavily to the South and EastValentine’s Day – Promote heavily to the North, moderately to the West and lightly to the East and South

3. The differences between groups is taken with percentages first because the formulas are less complicated, and students can relate to them easier than they can relate to the means differences formulas. The chapter moves quickly from percentage differences to means differences to SPSS independent samples t test procedure because the intent is to have students understand the SPSS output and not become bogged down on computations. Instructors who are more concerned with their students’ learning of

299


the formulas may wish to dwell longer on the formulas and have students do in-class or other exercises that require them to use these formulas correctly.

4. Students sometimes appear traumatized by their experiences in their business statistics course. The section on “Small Sample Sizes: The Use of a t Test or a z Test and How SPSS Eliminates the Worry” is included to convince students that SPSS will always issue the proper statistical significance level. It may be valuable to go over this section at least briefly to help students understand that they are not responsible for determining the proper statistic and how to look up its significance.

5. The “flag waving” Marketing Research Insight is not meant to be simply “cute.” Students often find statistical concepts and terminology intimidating, and the flag waving analogy gives them something tangible to lock onto. The authors, of course, realize that statistical significance is greatly affected by sample size, and the flag waving MRI does not admit to the role of sample size. The intent it to give students a signal as to when to look further into the post hoc findings. This signal is especially useful for cross-tabulation and correlation treated in chapter 18 (next) because students typically overlook the significance test with these analyses. If they learn the signal with differences tests, this learning is generalizable to working with associative and predictive analyses.

6. The assumption of equal variances in the two samples of a t test for the significance of the difference between two means is not discussed in the text’s coverage of these computations. However, students will encounter it when they perform t tests with SPSS for Windows. The description includes comments on “Levene’s Test for Equality of Variances,” which is included in the SPSS output for a t test. Instructors who wish may want to cover the equal variances assumption test in class presentation and introduce students to the formulas with their own materials.

7. The paired samples t test procedure is much less commonly used than is the independent samples t test. The latter is the basis for finding statistically significant differences between two groups (market segments), while the pair samples test determines differences within a market segment. For example, males may differ from females on their satisfaction with an online catalog purchasing system, determined via an independent samples t test. At the same time males may prefer to purchase catalog items online more than on the telephone, and this would be determined using a paired-samples t test. Women, although a separate market segment, may prefer telephone purchases over online purchases with catalog items.

8. Instructors should be forewarned that the section on “Online Surveys and Databases – A ‘Significance’ Challenge to Marketing Researchers” may be misinterpreted by inattentive students. The point here is that with very large samples, practically everything becomes statistically significant because the sample size plays a key role in determining statistical significance. As the sample size increases, more statistical significance is found, and with gigantic databases, statistical tests are unnecessary. Inattentive students may jump to the conclusion that statistical significance tests are

300


never needed if one uses the rules of thumb provided in the Marketing Research Insight. This conclusion is gravely wrong for “traditional” marketing research situations, and instructors may wish to emphasize that database marketing research is emerging but not fully in place. So, the significant tests in this and other chapters are something students must understand.

9. The description of one-way analysis of variance is not in depth. Instructors who desire students to have more knowledge of ANOVA may use this description as a foundation and move to a more in-depth coverage with their own materials. SPSS for Windows will accommodate advanced use of one-way and n-way ANOVA.

10. The Duncan’s Multiple Range post hoc test was selected above other post hoc tests due to its descriptive presentation of significant differences between group means. The tests not discussed can be assigned to individual students with the requirement to perform background research and to make a presentation of their findings on the test to the class. Alternatively, instructors may want to assign students the task of performing various post hoc tests with SPSS for Windows and comparing their findings.

ACTIVE LEARNING EXERCISES

Calculations to Determine Significant Differences Between Percents

The calculations are provided in the last column. Note that the frequencies have been computed to percentages in the table. The only statistically significant difference is in FM radio ads where the computed z is 2.40 and greater than the 95% level of confidence z of 1.96.

Joined Did not Join Difference FindingTotal 100 30Recall newspaper ads 45

(45%)15

(50%)

301


Recall FM radio station ads 89(89%)

20(67%)

Recall Yellow Pages ads 16(16%)

5(17%)

Recall local TV news ads 21(21%)

6(20%)

Perform Means Differences Analysis with SPSS

For this active learning exercise, students must use SPSS and the Hobbit’s Choice Restaurant survey dataset to determine if there is a difference in the total monthly restaurant expenditures for the subscribers to City Magazine versus the nonsubscribers. The SPSS output follows and shows that there is a significant difference: subscribers spend about $208, while nonsubscribers spend about $101 per month on the average.

302


Group Statistics

181 $208.2983 $83.30793 $6.19223

219 $101.9132 $69.67768 $4.70838

Do you subscribeto City Magazine?Yes

No

How many total dollarsdo you spend permonth in restaurants(for your meals only)?

N Mean Std. DeviationStd. Error

Mean

Independent Samples Test

10.161 .002 13.908 398 .000 $106.3851 $7.64909 $91.34744 $121.423

13.676 351.337 .000 $106.3851 $7.77898 $91.08587 $121.684

Equal variancesassumed

Equal variancesnot assumed

How many total dollarsdo you spend permonth in restaurants(for your meals only)?

F Sig.

Levene's Test forEquality of Variances

t df Sig. (2-tailed)Mean

DifferenceStd. ErrorDifference Lower Upper

95% ConfidenceInterval of the

Difference

t-test for Equality of Means

Perform Analysis of Variance with SPSS

Students must use SPSS’s ANOVA routine to select the factor of newspaper section most read and the dependent variable of how much is typically spent in restaurants per month. The following output indicates that the overall F is significant, and the Duncan’s post hoc test table reveals that each radio programming listening group is different from all other groups.

ANOVA

How many total dollars do you spend per month in restaurants (for your meals only)?

1618591 3 539530.432 125.879 .000

1633008 381 4286.109

3251599 384

Between Groups

Within Groups

Total

Sum ofSquares df Mean Square F Sig.

303


How many total dollars do you spend per month in restaurants (for your meals only)?

Duncana,b

66 $51.1364

159 $126.4780

82 $191.5366

78 $247.7692

1.000 1.000 1.000 1.000

To which type of radioprogramming do youmost often listen?Country&Western

Rock

Talk/News

Easy Listening

Sig.

N 1 2 3 4

Subset for alpha = .05

Means for groups in homogeneous subsets are displayed.

Uses Harmonic Mean Sample Size = 86.102.a.

The group sizes are unequal. The harmonic mean of the group sizes is used.Type I error levels are not guaranteed.

b.

ANSWERS TO END-OF-CHAPTER QUESTIONS

1. What are differences and why should market researchers be concerned with them? Why are marketing managers concerned with them?

Review question. Students will need to review the section on “Why Differences Are Important.”

Differences in consumers are the bases for marketing segmentation, effective marketing positioning strategy, and competitive advantage. In order to be useful to the researcher (and manager), differences must be: significant, meaningful, stable, and actionable.

2. What is considered to be a “small sample,” and why is this concept a concern to statisticians? To what extent do market researchers concern themselves with small samples? Why?

Review question. Students will need to understand the appropriate use of z tests versus t tests and to refer to the large databases that are now prevalent in marketing research.

The statistician refers to a “small sample” as any sample that has less than or equal to 30 respondents, and this condition requires the use of a t test. Market researchers are not concerned with small samples because statistical programs automatically adjust for the correct statistic. Also, with databases and huge samples that can accompany online surveys, market researchers rarely work with such small samples.

3. When a market researcher compares the responses of two identifiable groups with respect to their answers to the same question, what is this called?

Review question. This question requires an understanding of the test of the significance of the difference between means of two groups (independent samples t test).

304


It is a difference of means test (or means difference test). The two groups constitute independent groups, and with SPSS, the test is called an independent samples t test.

4. With regard to differences tests, briefly define and describe each of the following:

Review question. Students are required to define each notion. The descriptions follow each term.

a. Null hypothesis

The hypothesis that the difference in their population parameters is equal to zero.

b. Sampling distribution

The assumption is made that the differences have been computed for comparisons of the two sample statistics for many repeated samplings. If the null hypothesis is true, this distribution of differences follows the normal curve with a mean equal to zero and a standard error equal to one.

c. Significant difference

Statistical significance of differences means that the differences found in the sample(s) may be assumed to exist in the population(s) from which the random samples are drawn.

5. Relate the formula and identify each formula’s components in the test of significant differences between two groups for when the question involved is…

Review question. To answer these questions, students must be able to distinguish between percentages and means differences tests.

a. A “yes/no” type of question

This is a nominal scale situation, so the percentage formula must be used. The formula is…

305


Where:

= percentage found in sample 1

= percentage found in sample 2

= standard error of the difference between two percentages

b. A metric scale-type of question

This is an interval or ratio scale variable situation, so the mean formula must be used. This formula is…

Where:

mean found in sample 1

mean found in sample 2

= standard error of the difference between two means

6. Are the following two sample results significantly different?

Application question. Students must determine what formula to use, make correct computations, and interpret the findings.

Sample Sample Confidence Your

1 2 Level Finding?_____

Mean: 10.6 Mean: 11.7 95%

Std. dev:1.5 Std. dev: 2.5

n = 150 n = 300

306


Means and standard deviations are provided in this example, so the formula for mean differences must be used.

The computed z is greater than 1.96, so the difference is significant at the 95% level.


1 2 Level Finding?____

Percent: 45% Percent: 54% 99%

n = 350 n = 250

Percentages are involved, so the difference between percentages formula must be used.

The computed z is -2.18 which is less than 2.56, so the difference between these two percentages is not significant at the 99% level.


307


1 2 Level Finding?____

Mean: 1500 Mean: 1250 95%

Std. dev: 550 Std. dev: 500

n = 1200 n= 500

Means and standard deviations are involved, so the means difference formula must be used.

The computed z value is greater than 1.96, so the difference between these two means is statistically significant at the 95% level of confidence.

7. What is a paired-samples test? Specifically how are the samples “paired”?

Review question. Students must show an understanding of comparing means of two questions answered by the same sample.

If a researcher has a questionnaire with identically or very similarly scaled questions (such as several 5-point disagree-agree Likert statements) that are rated by a sample of respondents, the significance of the difference between the means of any two compared questions can be assessed with a paired-samples test. Any two variables that are scaled similarly can be “paired” and tested.

308


8. When should one-way ANOVA be used and why?

Review question. This question requires students to review the basics of ANOVA.

ANOVA is used when comparing means for 3 or more groups. It is used because it is more efficient than performing many independent t tests for the significance of the difference between two means because a single F test is used.

9. When a researcher finds a significant F value in analysis of variance, why can it be considered a “flagging” device?

Review question. Students must demonstrate a conceptual understanding of the interpretation of the significance level in an ANOVA output.

ANOVA is a “flagging” device. If at least one pair of means has a statistically significant difference, ANOVA will signal this by indicating significance. Then, it is up to the researcher to conduct further tests to determine precisely how many statistically significant differences actually exist and which ones they are.

10. The circulation manager of the Daily Advocate commissions a market research study to determine what factors underlie the circulation attrition. Specifically, the survey is designed to compare current Daily Advocate subscribers with those who have dropped their subscriptions in the past year. A telephone survey is conducted with both sets of individuals. Following is a summary of the key findings from the study.

Item Current Subscribers

Lost Subscribers

Significance

B Length of residence in the city 20.1 yrs 5.4 yrs .000 Length of time as a subscriber 27.2 yrs 1.3 yrs .000 Watch local TV news program (s) 87% 85% .372 Watch national news program(s) 72% 79% .540 Obtain news from the Internet 13% 23% .025 Satisfaction* with...

Delivery of newspaper 5.5 4.9 .459 Coverage of local news 6.1 5.8 .248 Coverage of national news 5.5 2.3 .031 Coverage of local sports 6.3 5.9 .462 Coverage of national sports 5.7 3.2 .001 Coverage of local social news 5.8 5.2 .659 Editorial stance of the newspaper 6.1 4.0 .001 Value for subscription price 5.2 4.8 .468

*Based on a 7-point scale where 1=very dissatisfied and 7=very satisfied

Interpret these findings for the Circulation Manager.

309


Application question. Students must correctly interpret the findings of the differences reported here.

The findings reveal 6 significant differences at the 95% level of confidence. Strictly speaking, there are just differences and not “greater” or “lesser” difference unless the significance level is .025 or less.

The interpretation is that lost subscribers are: younger, shorter subscribers, more likely to use the Internet for news, less satisfied with the Daily Advocate’s coverage of national news and sports, and less favorable about the editorial stance of the newspaper.

11. A researcher is investigating different types of customers for a sporting goods store. In a survey, respondents have indicated how much they exercise in approximate minutes per week. These respondents have also rated the performance of the sporting goods store across 12 difference characteristics such as good value for the price, convenience of location, helpfulness of the sales clerks, and so on. The researcher used a 1-7 rating scale for these 12 characteristics where 1=“poor performance” and 7=“excellent performance.” How can the researcher investigate differences in the ratings based on the amount of exercise reported by the respondents?

Application question: Students must realize that for this question, groups must be identified in order to compare differences.

The researcher could use a median split on the number of minutes of exercise per week to identify the low versus the high exercise groups. Then, he or she could use tests of the differences in the performance means. Alternatively, the researcher could use quartiles or some other splitting method to identify more than two groups. With more than 2 groups, ANOVA should be used.

12. A marketing manager of Collections, Etc, a Web-based catalog sales company, uses a segmentation scheme based on the incomes of target customers. The segmentation system has four segments: (1) low income, (2) moderate income, (3) high income, and (4) wealthy. The company database holds information on every customer’s purchases over the past several years, and the total dollars spent at Collections, Etc. is one of the prominent variables. Using Microsoft Excel on this database, the marketing manager finds that the average total dollar purchases for the four groups are as follows.

Market Segment Average Total Dollar Purchases

Low income $101

Moderate income $120

High income $231

Wealthy $595

310


Construct a table that is based on the Duncan’s Multiple Range test table concept discussed in the chapter that illustrates that the Low and Moderate Income groups are not different from each other, but the other groups are significantly different from one another.

Application question. This questions requires that students understand and can apply the mean differences visual approach used by the Duncan’s Multiple Range test table presentation.

The table would look like the following.

Market Segment Average Total Dollar Purchases Group Group Group

Low income $101 A

Moderate income $120 A

High income $231 B

Wealthy $595 C

13. How would a grocery store chain company go about constructing and validating a market segmentation system? Take the possible segmentation variables of family type (single, couple, or with children) and occupation (skilled labor, professional, or retired). Indicate the steps you would take and any considerations you would take into account as a researcher investigating if there was a useful segmentation system for the grocery store chain company using these two demographic variables as the basis.

Application question. This question requires an understanding of analysis of variance.

There are two factors involved: family type with 3 different levels and occupation with 3 levels. The store would need to determine a metric measure such as total dollar purchases per week across a sample of customers representing all (3x3) nine possible combinations. Then, a researcher could perform a 2-way ANOVA to find what significant differences exist among the nine different segments. Scanner data could be used if the researcher wanted to replicate or compare the findings across many weeks to insure that the market segments are indeed different.

CASE SOLUTIONS

Case 17.1 Don’t You Just Hate it When…? (Part II)

Case Objective

This case requires students to identify what differences analysis tests should be conducted based on identification of nominal or metric scaled variables.

311


Answers to Case QuestionsIndicate the specific differences statistical tests that should be conducted to answer each of the research questions 1, 2, and 3 in the email attachment Marsha sent to Josh. In each of your answers, tell precisely what is the grouping variable, what is the variable being used to compare the groups to each other, and if percentages or means are to be compared.

The answers follow.

Research Question Grouping Variable Target Variables Differences Test

1. Do regular PPP patrons differ from those who are not regular patrons, and if so, how?

Use Pets, Pets, & Pets how often?

1= do not use regularly 2= use regularly

Times visited PPP in past year

Actual number of times

Amount spent on last visit to PPP

Actual dollar amount rounded to dollars

How likely to buy at PPP next time (1-7 scale)

1-7 scale where: 1=unlikely, 7=very likely

Number of pets owned

Actual number of pets

Independent samples t-test as the target variable are ratio or interval

2. Do regular PPP patrons recall seeing PPP newspaper advertising more or less than those who do not use PPP regularly?

Use Pets, Pets, & Pets how often?


Recall seeing a PPP newspaper ad in the past month?

1=yes 2=no

Percentage differences test as the target variable is nominal

3. Do PPP customers differ by household income level, and if so how?

Use Pets, Pets, & Pets how


Income level

1=below $20,000 Etc.

First, use the midpoints of the income ranges for the target variable, than do

312


often? independent samples t-test as the target variable is metric

Case 17.2 Washington Street Bistro Importance-Performance Survey

Case Objective

Students are required to assess the results of significance tests performed on the means of two independent groups, and they must glean managerial implications from their assessments.

Answers to Case Questions

1. Interpret these findings for Ms. Wilson What do they say about the two subpopulations of lunch and dinner patrons?

The two tables in the case are given below with annotations of significance/ nonsignificance in the right-hand column. Attributes that have significant differences are in bold.

Table A

Importance* of Selected Restaurant Attributes by Type of Patron

Cafeteria Attribute Lunch Dinner Sig. Assessment

Courteous employees 5.28 5.18 0.978 Not sig

Helpful employees 5.20 5.15 0.876 Not sig

Quality of service 5.07 4.98 0.540 Not sig

Freshness of salad items 5.07 4.50 0.034 Sig

High nutritional value of meals 5.03 4.44 0.045 Sig

Overall quality of meals 4.97 4.53 0.035 Sig

Comfortable seating 4.96 4.95 0.986 Not sig

Discounts for frequent patrons 4.89 4.75 0.752 Not sig

Appetizing look of items 4.88 4.02 0.052 Not sig

Speed of service 4.83 4.97 0.650 Not sig

Relaxed atmosphere 4.83 5.23 0.001 Sig

313


Good-tasting dishes 4.80 4.02 0.012 Sig

Adequate lighting 4.71 4.80 0.659 Not sig

Good variety of entrees 4.60 3.53 0.002 Sig

Low price of specials 4.52 4.20 0.102 Not sig

Large portions 4.34 3.87 0.034 Sig

Clean surroundings 4.25 4.50 0.286 Not sig

*Based on a scale where 1 = “unimportant” and 7 = “very important”

Directional tests are not called for as there was no a priori indication that one group’s mean(s) would be greater or less than the other group’s mean(s).

There are eight significant differences (at the 95% level of confidence), and lunch patrons attach more importance to six of these attributes than do dinner patrons. “Relaxed atmosphere” is the only attribute held more important for dinner patrons than for lunch patrons.

Table B

Evaluation of Washington Street Bistro Performance** on Selected Attributes by Type of Patron

Bistro Attribute Lunch Dinner Sig. Assessment

Courteous employees 5.79 5.46 0.182 Not sig

Helpful employees 5.83 5.51 0.044 Sig

Quality of service 5.54 5.60 0.276 Not sig

Freshness of salad items 5.80 4.46 0.001 Sig

High nutritional value of meals 5.29 5.23 0.197 Not sig

Overall quality of meals 4.48 4.46 0.568 Not sig

Comfortable seating 4.63 4.53 0.389 Not sig

Discounts for frequent patrons 5.45 4.56 0.009 Sig

Appetizing look of items 5.65 4.64 0.045 Sig

Speed of service 5.52 4.22 0.010 Sig

Relaxed atmosphere 4.96 5.63 0.061 Sig

Good-tasting dishes 5.31 4.37 0.048 Sig

Adequate lighting 4.52 4.62 0.369 Not sig

Good variety of entrees 4.98 3.75 0.019 Sig

314


Low price of specials 5.35 6.86 0.045 Sig

Large portions 4.43 5.43 0.038 Sig

Clean surroundings 5.56 5.24 0.286 Not sig

**Based on a scale where 1 = “very dissatisfied” and 7 = “very satisfied”

Ten of the attributes have resulted in significant differences (at the 95% level of confidence), and seven of them are rated higher in performance by lunch patrons than they are rated by dinner patrons. The attributes “relaxed atmosphere,” “low price of specials,” and “large portions” are rated higher by dinner patrons than they are rated by lunch patrons.

2. What managerial implications are apparent from these findings?

Table A ranks the attributes, roughly, by overall importance for both groups. Ms. Wilson should note that employee factors are most important, so she should make sure that the Bistro employees are courteous, helpful, and provide good service. The lunch patrons are more demanding than are the dinner patrons as evidenced in the higher importance ratings they gave for specific cafeteria attributes. She should be especially concerned with “running a tight ship” during the lunch hours.

Table B reveals that there is room for improvement. The averages range from a low of 3.75 to a high of 6.86, but most are in the 4-5 range. On the 7-point satisfaction scale, a 4 is the neutral position, so Washington Street Bistro’s performance can certainly be improved. The reasons for differences in the two groups’ satisfaction levels is not known, but two possibilities exist. First, there may be real differences in the Bistro’s performance during lunch versus dinner hours. Ms. Wilson should determine any systematic differences in the Bistro’s operations for the lunches versus dinners using the significantly different characteristics as a basis.

For instance, “freshness of salad items” is rated higher by lunch patrons than by dinner patrons workers. Are the dinner patrons getting leftovers from the lunch menu items not sold? Second, Ms. Wilson has already noted demographic segmentation differences: dinner patrons are more likely to be young professionals are more casual than the lunch patrons. The dinner patrons may be looking for a place to relax after a hard day, while the lunch patrons may want a nutritious lunch quickly in the middle of a busy workday.

315


Case 17.3 The Hobbit’s Choice Restaurant Survey Differences Analysis

Case Objective

The objective of this integrated case item is to have students identify what differences tests are appropriate, to run them, and interpret them correctly.

1. Jeff wonders if The Hobbit’s Choice Restaurant is more appealing to women that it is to men or vice versa. Perform the proper analysis, interpret it, and answer Jeff’s question.

The question concerns two groups: men and women. The “appealing” variable is the “how likely would it be for you to patronize this restaurant.” The proper analysis is an independent samples t test, and the output follows.

Group Statistics

204 3.02 1.251 .088

196 2.98 1.226 .088

What is your gender?Male

Female

How likely would it befor you to patronizethis restaurant (newupscale restaurant)?

N Mean Std. DeviationStd. Error

Mean

Independent Samples Test

.380 .538 .282 398 .778 .03 .124 -.209 .279

.282 397.852 .778 .03 .124 -.209 .278

Equal variancesassumed

Equal variancesnot assumed

How likely would it befor you to patronizethis restaurant (newupscale restaurant)?

F Sig.

Levene's Test forEquality of Variances

t df Sig. (2-tailed)Mean

DifferenceStd. ErrorDifference Lower Upper


Difference

t-test for Equality of Means

As can be seen, the means are quite similar (3.02 and 2.98). The Levene’s test indicates that the “equal variances assumed” condition is in effect, and the Sig (2-tailed) value of .778 means that the null hypothesis is supported. Men and women do not differ with respect to their likelihood to use the upscale restaurant described in the questionnaire.

2. With respect to the location of The Hobbit’s Choice Restaurant, is a waterfront viewer preferred more than a drive less than 30 minutes?

Here, two questions are being compared. Both are measured with a Likert disagree-agree scale, so it is appropriate to use a paired-samples t test. The output follows.

316


Paired Samples Statistics

3.42 400 1.333 .067

2.73 400 1.311 .066

Prefer Waterfront View

Prefer Drive Less than30 Minutes

Pair1

Mean N Std. DeviationStd. Error

Mean

Paired Samples Correlations

400 -.805 .000Prefer Waterfront View& Prefer Drive Lessthan 30 Minutes

Pair1

N Correlation Sig.

Paired Samples Test

.69 2.513 .126 .45 .94 5.532 399 .000Prefer Waterfront View- Prefer Drive Lessthan 30 Minutes

Pair1

Mean Std. DeviationStd. Error

Mean Lower Upper


Difference

Paired Differences

t df Sig. (2-tailed)

The means arithmetically different (3.42 versus 2.73), and the Sig (2-tailed) value is .000. The interpretation is that these two restaurant features are not preferred equally. In fact, the waterfront view is more preferred than a 30-minute drive.

3. With respect to the restaurant’s atmosphere is a string quartet preferred over a jazz combo?

Again, two questions are being compared, so the paired-samples t test procedure should be used. Output follows.


2.50 400 1.420 .071

3.70 400 1.221 .061

Prefer String Quartet

Prefer Jazz Combo

Pair1


Mean


400 -.620 .000Prefer String Quartet& Prefer Jazz Combo

Pair1

N Correlation Sig.

317


Paired Samples Test

-1.19 2.378 .119 -1.43 -.96 -10.030 399 .000Prefer String Quartet- Prefer Jazz Combo

Pair1


Mean Lower Upper


Difference

Paired Differences


There is quite a bit of difference (3.7 versus 2.5), and the significance level of .000 indicates that the difference is statistically significant. Jazz is preferred over classical (string quartet) music.

4. What about unusual entrees versus unusual desserts?

The paired-sample t test procedure yields the following results.


2.41 400 1.514 .076

2.40 400 1.550 .077

Prefer Unusual Desserts

Prefer Unusual Entrees

Pair1


Mean


400 .868 .000Prefer Unusual Desserts& Prefer Unusual Entrees

Pair1

N Correlation Sig.

Paired Samples Test

.00 .787 .039 -.07 .08 .064 399 .949Prefer Unusual Desserts- Prefer Unusual Entrees

Pair1


Mean Lower Upper


Difference

Paired Differences


The means are almost equal, and the significance level of .949 indicates support for the null hypothesis. So, there is no difference in the preference of unusual entrees versus unusual deserts.

5. In general, establishments are appealing to higher income households, while they are less appealing to lower income households. Is this pattern the case for The Hobbit’s Choice Restaurant?

As noted in Question 1, preference is measured by the “likely to patronize” variable. In this case, there are 7 different income groups, so one-way analysis of variance (ANOVA) is called for. The output follows.

318


ANOVA

How likely would it be for you to patronize this restaurant (new upscale restaurant)?

453.301 6 75.550 188.280 .000

157.697 393 .401

610.998 399

Between Groups

Within Groups

Total


Post Hoc TestsHomogeneous Subsets


Duncana,b

34 1.15

26 1.23

82 2.68

133 2.74

16 4.00

66 4.33

43 4.56

.569 .714 1.000 .127

Which of the followingcategories bestdescribes your beforetax household income?$15,000 to $24,999

<$15,000

$25,000 to $49,999

$50,000 to $74,999

$75,000 to $99,999

$150,000+

$100,000 to $149,999

Sig.

N 1 2 3 4




The group sizes are unequal. The harmonic mean of the group sizes is used.Type I error levels are not guaranteed.

b.

The ANOVA table reports a significance level of .000 that signifies that at least one pair of income levels has a significant difference in preference. The Duncan’s test table reveals that four groups of significant differences exist. The two lowest income levels have the lowest preference for an upscale restaurant, and they are not statistically different from each other. The next two income levels are not different from each other, but they are different from all other levels. The fifth level occupies a significantly different level of preference, while the two highest income levels represent the highest level of preference for an upscale restaurant. Although these two income levels are not significantly different from each other, they are significantly different from all other income levels. The pattern is consistent with the notion of greater preference for upscale restaurants with greater income.

6. Jeff and Cory speculated that the different geographic areas that they identified by zip codes would have different reactions to the prospect of patronizing a new upscale restaurant. Are these anticipated differences substantiated by the survey? Perform the proper analysis and interpret your findings.

319


There are 4 zip code geographic areas (A, B, C, and D). Because more than two groups are being compared, a one-way ANOVA is required. Output follows.

ANOVA


370.710 3 123.570 203.647 .000

240.287 396 .607

610.998 399

Between Groups

Within Groups

Total


Post Hoc Tests

Homogeneous Subsets

How likely would it be for you to patronize this restaurant (new upscalerestaurant)?

Duncana,b

40 1.18

20 1.20

220 2.85

120 4.18

.878 1.000 1.000

Please check theletter that includes theZip Code in which youlive (coded by letter).D (10, 11, & 12)

A (1 & 2)

C (6, 7, 8, & 9)

B (3, 4, & 5)

Sig.

N 1 2 3




The group sizes are unequal. The harmonic mean of the groupsizes is used. Type I error levels are not guaranteed.

b.

The output indicates that significant differences do exist between the various groups, and the Duncan’s table reveals that zip code area B has the highest preference for an upscale restaurant while areas D and A have the lowest preference. This finding is consistent with Jeff’s thinking about the preferences of these areas.

320

burns05 im 17

Documents

groups differences

spss differences

differences tests

significant differences

mean differences

means test

groups chapter

samples test