Chapter 17 – Analysis and Interpretation: Individual Variables Independently
I. Learning Objectives:
Upon completing this chapter, the student should be able to:
1. Distinguish between univariate and multivariate analyses.
2. Describe frequency analysis.
3. Describe descriptive statistics.
4. Discuss confidence intervals for proportions and means.
The confidence interval is the range within which the true proportion or mean
5. Overview the basic purpose of hypothesis testing.
Hypothesis testing is used to establish whether or not to accept study results based
on a sample as being true for the overall population from which the sample was
drawn.
II. Chapter Outline:
A. Basic Univariate Statistics: Categorical Measures
Manager’s Focus
1. Frequency Analysis
2. Other Uses for Frequencies
3. Confidence Intervals for Proportions
Exhibit 17.5: Avery Fitness Center: Services Utilized within Past 30 Days
B. Basic Univariate Statistics: Continuous Measures
2. Converting Continuous Measures to Categorical Measures
3. Confidence Intervals for Means
C. Hypothesis Testing
Exhibit 17.7: Avery Fitness Center: Two-Box Results, with Descriptive Statistics
1. Null and Alternative Hypotheses
3. Issues in Interpreting Statistical Significance
D. Testing Hypotheses about Individual Variables
1. Testing Statistical Significance with Categorical Variables
2. Testing Statistical Significance with Continuous Variables
E. Summary
III. Answers to Review Questions:
1. A frequency analysis is a univariate technique that involves counting the number
of responses that fall into various response categories. This is a very simple
2. Outliers are valid observations that are so different from the rest of the
3. Percentages should be rounded off to whole numbers because whole numbers
are easier to read and because decimals might make the results look more
4. A histogram is a form of column chart on which the values of the variable are
5. A confidence interval is the range within which the true proportion or mean for
the population will fall, with a given level of confidence (usually 95%). For means,
6. The confidence interval only takes sampling error into account. To the extent
that other types of error have entered the study—and you can be sure that they
7. The most commonly used descriptive statistics for continuous measures
8. With ordinal-, interval-, or ratio-level measures, it is often useful to identify the
median point as a measure of “average” for the distribution. The distribution of
9. Occasionally, a client will have a predetermined structure for categories. In other
10. The two box technique is a technique for converting an interval-level rating scale
into a categorical measure, usually used for presentation purposes. The
percentage of respondents choosing one of the top two positions on a rating
Chapter 17 – Analysis and Interpretation: Individual Variables Independently
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11. The null hypothesis means the result isn’t true for the population and can be
12. Marketing research studies can’t “prove” results. At best, it can indicate which of
13. The p-value represents the likelihood of obtaining the particular value of a test
statistic if the null hypothesis were true. Once you have the p-value, it is a simple
matter to compare it with the significance level of the test to determine whether
the result can be considered “statistically significant” (i.e., the sample results can
14. The chi square goodness-of-fit test is a statistical test used to determine whether
some observed pattern of frequencies corresponds to an expected pattern.
15. In almost all cases, it is important to report standard deviation along with mean
value. The sample mean is the arithmetic average value of the responses on a
variable. The sample standard deviation is a measure of the variation of
IV. Instruction Suggestions:
1. There are several approaches instructors can take to this discussion, depending on
their own interests and the students‘ statistical backgrounds. For some classes, the
techniques will already be familiar, and the instructor will simply want to
2. We think it’s a good idea to occasionally remind students that data analysis is
usually straightforward if two key issues are kept in mind. First, is the variable to be
analyzed by itself (univariate analyses) or in relationship to other variables
(multivariate analyses)? Second, what level of measurement was used in assessing
the variable?
3. Instructors may find it useful to demonstrate some of the analyses presented in the
chapter during class sessions using SPSS or another statistical software package. For
4. Given the usefulness and prevalence of simple univariate analyses in industry
settings, instructors will likely want to spend some time during class reinforcing the
5. In our experience, it seems that some undergraduate students have difficulty with
the concept of a confidence interval. While they have no doubt been exposed to
the concept in earlier statistics classes, the marketing research course affords them
the opportunity to understand how confidence intervals may be applied in practice.
into account only sampling error and that other types of error may actually be
more dangerous.
6. Some instructors desire to present the typical hypothesis testing procedure while
other instructors may wish to simply introduce the nature of hypothesis testing and
move on to specific tests, allowing students to focus on the p-values reported by
the statistical software. In either case, we believe that this information can be