Chapter 11
Basic Data Analysis for Quantitative
Research
McGraw-Hill/Irwin
Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved.
Learning Objectives
• Explain measures of central tendency and
dispersion
• Describe how to test hypotheses using
univariate and bivariate statistics
• Apply and interpret analysis of variance
(ANOVA)
• Utilize perceptual mapping to present
research findings
11-2
Statistical Analysis
• Every set of data collected needs some
summary information developed that
describes the numbers it contains
– Central tendency and dispersion
– Relationships of the sample data
– Hypothesis testing
11-3
Measures of Central Tendency
Mean
• The arithmetic average of the sample
• All values of a distribution of responses are summed and divided by
the number of valid responses
Median
• The middle value of a rank-ordered distribution
• Exactly half of the responses are above and half are below the median
value
Mode
• The most common value in the set of responses to a question
• The response most often given to a question
11-4
Exhibit 11.2 - Dialog Boxes for Calculating the
Mean, Median, and Mode
11-5
Measures of Dispersion
Range
• The distance between the smallest and largest values in a set of
responses
Standard deviation
• The average distance of the distribution values from the mean
Variance
• The average squared deviation about the mean of a distribution
of values
11-6
Exhibit 11.3 - Measures of Dispersion
11-7
Preparation of Charts
• Charts and other visual communication
approaches should be used whenever
practical
– Help information users to quickly grasp the
essence of the results developed in data analysis
– Can be an effective visual aid to enhance the
communication process
• Add clarity and impact to research reports and
presentations
11-8
How to Develop Hypotheses
• Researchers have preliminary ideas regarding
data relationships based on research
objectives
– Hypotheses - Ideas derived by researchers from
previous research, theory and/or the current
business situation
• Developed prior to data collection
– As a part of the research plan
11-9
How to Develop Hypotheses
• Null hypothesis - Based on the notion that any
change from the past is due entirely to
random error
• Alternative hypothesis - States the opposite of
the null hypothesis
11-10
Sample Statistics and Population
Parameters
• Sample statistics are useful in making
inferences regarding the population’s
parameter
– Population parameter - A variable or some sort of
measured characteristic of the entire population
11-11
Choosing the Appropriate Statistical
Technique
• Considerations that influence the choice of a
particular technique:
– Number of variables
– Scale of measurement
– Parametric versus nonparametric statistics
11-12
Exhibit 11.6 - Type of Scale and
Appropriate Statistic
11-13
Univariate Statistical Tests
• Used to test hypotheses when the researcher
wishes to test a proposition about a sample
characteristic against a known or given
standard
11-14
Exhibit 11.7 - Univariate Hypothesis
Test Using X 16 –Reasonable Prices
11-15
Bivariate Statistical Tests
• Test hypotheses that compare the
characteristics of two groups or two variables
• Three types of bivariate hypothesis tests
– Chi-square
– t-test
– Analysis of variance
11-16
Cross-Tabulation
• Useful for examining relationships and
reporting the findings for two variables
• Purpose is to determine if differences exist
between subgroups of the total sample
• A frequency distribution of responses on two
or more sets of variables
11-17
Exhibit 11.8 - Example of a CrossTabulation: Gender by Ad Recall
11-18
Chi-Square Analysis
• Assesses how closely the observed
frequencies fit the pattern of the expected
frequencies
– Referred to as a “goodness-of-fit” test
11-19
Comparing Means: Independent
Versus Related Samples
• Independent samples: Two or more groups of
responses that are tested as though they may
come from different populations
• Related samples: Two or more groups of
responses that originated from the sample
population
11-20
Using the t -Test to Compare Two
Means
• t-test: A hypothesis test that utilizes the t
distribution
– Used when the sample size is smaller than 30 and
the standard deviation is unknown
• Where,
X 1  m ean of sam ple 1
X 2  m ean of sam ple 2
S X 1  X 2  standard error of the difference betw ee n the tw o m eans
11-21
Exhibit 11.11 - Paired Samples t-Test
11-22
Analysis of Variance (ANOVA)
• A statistical technique that determines
whether three or more means are statistically
different from one another
• Null hypothesis for ANOVA always states that
there is no difference between the dependent
variable group
11-23
Analysis of Variance (ANOVA)
• F-test: The test used to statistically evaluate
the differences between the group means in
ANOVA
11-24
Exhibit 11.12 - Example of One-Way
ANOVA
11-25
Analysis of Variance (ANOVA)
• Follow-up tests: A test that flags the means
that are statistically different from each other
– Performed after an ANOVA determines there are
differences between means
11-26
Exhibit 11.13 - Results for Post-hoc
ANOVA Tests
11-27
n-Way ANOVA
• A type of ANOVA that can analyze several
independent variables at the same time
• Multiple independent variables in an ANOVA
can act together to affect dependent variable
group means
11-28
Exhibit 11.14 - n-Way ANOVA
Results—Santa Fe Grill
11-29
Exhibit 11.15 - n -Way ANOVA Means
Result
11-30
Perceptual Mapping
• Used to develop maps showing the
perceptions of respondents
– Maps are visual representations of respondents’
perceptions of a company, product, service,
brand, or any other object in two dimensions
• Approaches used to develop perceptual maps
– Rankings
– Medians
– Mean ratings
11-31
Perceptual Mapping Applications in
Marketing Research
•
•
•
•
New-product development
Image measurement
Advertising
Distribution
11-32
Exhibit 11.17 - Perceptual Map of Six
Fast-Food Restaurants
11-33
Marketing Research In Action:
Examining Restaurant Image Positions—Remington’s Steak
House
• Run post-hoc ANOVA tests between the
competitor groups
– What additional problems or challenges did this
reveal?
• What new marketing strategies can be
suggested?
11-34