Marketing Chapter 18 Yes Ice Cream Purchases And Murder Rates Are Correlated But This Way

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Chapter 18 – Analysis and Interpretation: Multiple Variables Simultaneously

I. Learning Objectives:

Upon completing this chapter, the student should be able to:

2. Explain the purpose and importance of cross tabulation.

3. Describe a technique for comparing groups on a continuous dependent variable.

• When there are only two groups, the independent samples t-test is used

4. Explain the difference between an independent sample t-test for means and a

paired sample t-test for means.

6. Describe a technique for examining the influence of one or more predictor

variables on an outcome variable.

II. Chapter Outline:

A. Cross Tabulation

Exhibit 18.1: Univariate versus Multivariate Analysis: Enhanced Meaning

Exhibit 18.2: Avery Fitness Center: Therapy Pool Usage by Doctor’s

Recommendation (SPSS Output)

Manager’s Focus

Exhibit 18.3: Avery Fitness Center: Banner Table

1. Presenting Cross-Tab Results: Banner Table

B. Independent Samples T-Test for Means

C. Paired Sample T-Test for Means

Exhibit 18.4: Avery Fitness Center: Number of Visits (Past 30 Days) by Exercise

Circuit Usage (SPSS Output)

D. Pears Product-Moment Correlation Coefficient

Exhibit 18.7: Avery Fitness Center: Correlation between Age and Revenues (SPSS

Output)

1. Caution in the Interpretation of Correlations

E. Regression Analysis

III. Answers to Review Questions:

1. Multivariate analysis often provides a much deeper understanding of the data.

3. Cross tabulation is a multivariate technique used for studying the relationship

between two or more categorical variables. The technique considers the joint

distribution of sample elements across variables. The “row percentage” is

cell is the “column percentage” and is calculated using the column total as the

denominator. To answer this question, think about which of the variables being

studied is likely to be the independent variable (cause) and which is likely to be

the dependent variable (effect). Percentages are always calculated in the

direction of the causal variable. That is, the marginal totals for the causal

variable are always used as the denominator when calculating percentages in

cross tabulations.

4. You will need to use multivariate analyses to get the information you need.

Here’s an example: In an awareness test for an ice-cream shop, 58% of survey

respondents could name the shop in a recall task. Closer analysis revealed

5. What happens when you need to compare two means when both measures are

provided by the same people? In that case, you would use the paired sample t-

7. Here’s an example: If we did the math, we would discover that ice cream

purchases are positively correlated with murder rates. What? Does this mean

that purchasing ice cream can cause someone to commit a murder? Of course

not. What we know is that people purchase more ice cream when the weather is

warmer and the days are longer. And murder rates tend to be higher when more

people are outside. So, what do these two activities have in common? If you said

8. Regression analysis is a statistical technique used to derive an equation

representing the influence of a single (simple regression) or multiple (multiple

regression) independent variables on a continuous dependent, or outcome,

variable.

9. Sometimes you will be tempted to assume that one variable caused the other

one when you obtain a statistically significant correlation coefficient between

two variables. Just because two variables are correlated doesn’t mean that one

10. The coefficient of multiple determination is a measure representing the relative

proportion of the total variation in the dependent variable that can be explained

IV. Instruction Suggestions:

1. The first thing instructors should decide is whether they are going to employ the

examples in the text to develop the discussion or use other examples taken from

their own research. Some prefer to use a single dataset so that all analyses

2. We think it is important for instructors to re-emphasize to students that applied

data analysis is not nearly as difficult as they probably think it is. The

fundamental questions are (a) how many variables do we need to consider? and

(b) what level of measurement was used to assess each variable? This chapter

Once an appropriate technique is selected, it is usually a relatively easy process

of applying formulas or interpreting computer output.

3. There are two general approaches that may be taken to the presentation of this

material, depending upon the degree of detail the instructor wants to provide in

the classroom. The first approach is to try to cover all of the techniques included

in the chapter, more or less, using examples from the text or other sources. We

expect that it would take 2-3 class sessions to present the multivariate

techniques we have included in the text.

A second approach to presenting the material is to select the most commonly

4. Because most multivariate analyses will be performed by computer, the

6. It is obvious that we excluded many types of analysis from the text, instead

choosing to include only common and/or straightforward techniques that we felt

were appropriate for the target audience. The instructor may want to go further

to include one or more additional techniques (e.g., conjoint analysis, factor

Chapter 18 – Analysis and Interpretation: Multiple Variables Simultaneously

7. Regardless of whether the instructor chooses to use the example of cross

tabulation from the text or supply one of his or her own (or one using one of the

other data sets in the text or supplemental materials), experience suggests that

few students initially appreciate how cross-tabs are developed and in what

direction percentages should be calculated.

8. If preferred, the instructor can next detail what can happen when a third

variable is added to an initial cross-tab analysis. The instructor might ask the

class “Why stop with three variables?” with the goal of making several important

points, including

• The analyst never knows for sure when to stop, in that he or she is always

in a position of INFERRING a relationship does or does not exist.

9. T-tests are quite common in research and can be obtained easily via computer

analysis or relatively easily by hand calculation. As a result, we recommend that

instructors spend at least a little time on them in class. Some students may

already be familiar with the different types of t-tests, but most will probably

10. The text includes discussions of three primary correlational techniques, (a) the

Pearson product-moment correlation coefficient, (b) simple regression analysis,

and (c) multiple regression analysis. As with the other techniques, we believe

that there is greater value for undergraduate students through discussion of

when they should be applied and how to interpret the results rather than

through learning the mathematical calculations.

The instructor should point out the similarities between correlation and simple

regression. For example, the instructor might note that the standardized beta in

highlighted, the discussion can profitably be directed at some of the problems of

multiple regression analysis that do not seem to be appreciated fully by

beginning research students. Some of the points that can be made are:

(a) The statement of relationship is still an inference and that the nature of

the inference might change drastically with the introduction of the “right”

additional variable. The situation here parallels that for cross-tabulation

analysis.

(b) The fact that we have assumed a linear relationship between the

variables.