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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
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
6
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.
(c) The problems associated with two-way causation.
