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12: Basic Data Analysis for
Quantitative Research
Statistical Analysis
Summary Statistics
Central tendency and dispersion,
Relationships of the sample data, and
Hypothesis testing
Hair/Wolfinbarger/Ortinau/Bush, Essentials of
Marketing Research 1e © McGraw-Hill/Irwin2008
Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved.
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Measures of
Central Tendency
Mean
Arithmetic
Average
Mode
Response Most
Often Given
to a Question
Median
Middle Value
of a Rank Ordered
Distribution
Hair/Wolfinbarger/Ortinau/Bush, Essentials of
Marketing Research 1e © McGraw-Hill/Irwin2008
Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved.
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Measures of
Central Tendency
Each measure of central tendency
describes a distribution in its own
manner:
for nominal data, the mode is the only
possible measure.
for ordinal data, the median is generally the
best.
for interval or ratio data, the mean is
generally used.
Hair/Wolfinbarger/Ortinau/Bush, Essentials of
Marketing Research 1e © McGraw-Hill/Irwin2008
Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved.
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Measures of Dispersion
Describes how close to the mean or other measure
of central tendency, the rest of the values fall
Range
Distance between the
smallest and largest
value in a set
Hair/Wolfinbarger/Ortinau/Bush, Essentials of
Marketing Research 1e © McGraw-Hill/Irwin2008
Standard Deviation
Measure of the average
dispersion of the values
about the mean
Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved.
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SPSS Output for Measures
of Dispersion
Hair/Wolfinbarger/Ortinau/Bush, Essentials of
Marketing Research 1e © McGraw-Hill/Irwin2008
Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved.
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Hypothesis Testing
Independent Samples
two or more groups
of responses that are
tested as though they
come from different
populations
Hair/Wolfinbarger/Ortinau/Bush, Essentials of
Marketing Research 1e © McGraw-Hill/Irwin2008
Related (Matched) Samples
two or more groups of
responses that are assume
to originate from the same
population
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Univariate Tests of
Significance
Tests of one variable at a time
z-test
t-test
Appropriate for interval or ratio data
Test: “Is a mean significantly different
from some number?”
Hair/Wolfinbarger/Ortinau/Bush, Essentials of
Marketing Research 1e © McGraw-Hill/Irwin2008
Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved.
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Univariate Hypothesis Test Using X16
Variable (Reasonable Prices)
Hair/Wolfinbarger/Ortinau/Bush, Essentials of
Marketing Research 1e © McGraw-Hill/Irwin2008
Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved.
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Bivariate
Statistical Tests
Compare characteristics (means or
frequencies) of two groups or two
variables
Cross-tabulation with Chi-Square
t-test to compare two means
Analysis of variance (ANOVA) to compare
three or more means
Hair/Wolfinbarger/Ortinau/Bush, Essentials of
Marketing Research 1e © McGraw-Hill/Irwin2008
Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved. 12-10
Cross-Tabulation:
Ad Recall vs. Gender
Hair/Wolfinbarger/Ortinau/Bush, Essentials of
Marketing Research 1e © McGraw-Hill/Irwin2008
Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved. 12-11
Chi-Square Analysis
Chi-square analysis enables the
researcher to test for statistical
significance between the frequency
distributions of two or more nominally
scaled (i.e. “categorical”) variables in a
cross-tabulation table to determine
if there is any association
between the variables
Hair/Wolfinbarger/Ortinau/Bush, Essentials of
Marketing Research 1e © McGraw-Hill/Irwin2008
Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved. 12-12
SPSS Chi-Square Crosstab
Example
Hair/Wolfinbarger/Ortinau/Bush, Essentials of
Marketing Research 1e © McGraw-Hill/Irwin2008
Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved. 12-13
Comparing means
Requires interval or ratio data
The t-test is the difference between the
means divided by the average variability of
the two random means
The t-value is a ratio of the difference
between the two sample means and the
std error of the difference in means
The t-test tries to determine whether the
difference between the two sample means
is significant or whether it occurred by
chance
Hair/Wolfinbarger/Ortinau/Bush, Essentials of
Marketing Research 1e © McGraw-Hill/Irwin2008
Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved. 12-14
Comparing Two Means with
Independent Samples t-Test
Hair/Wolfinbarger/Ortinau/Bush, Essentials of
Marketing Research 1e © McGraw-Hill/Irwin2008
Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved. 12-15
Comparing Two Means with
Paired Samples t-Test
Hair/Wolfinbarger/Ortinau/Bush, Essentials of
Marketing Research 1e © McGraw-Hill/Irwin2008
Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved. 12-16
Analysis of Variance
ANOVA determines whether three or more
means are statistically different from each
other
The dependent variable must be either
interval or ratio data
The independent variable(s) must be
categorical (i.e. nominal or ordinal)
“One-way ANOVA” means that there is
only one independent variable
Hair/Wolfinbarger/Ortinau/Bush, Essentials of
Marketing Research 1e © McGraw-Hill/Irwin2008
Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved. 12-17
F-Test
The F-test is the test used
to statistically evaluate the differences
between the group means in ANOVA
Hair/Wolfinbarger/Ortinau/Bush, Essentials of
Marketing Research 1e © McGraw-Hill/Irwin2008
Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved. 12-18
Determining Statistical
Significance using F-Test
Total variance in dataset can be separated
into Between Group and Within Group Variance.
The larger the variance Between
Groups vs. Within Groups, the larger the F-Ratio.
The higher the F-Ratio, the more likely it is that
the Null Hypothesis will be rejected
and that the means are statistically different.
Hair/Wolfinbarger/Ortinau/Bush, Essentials of
Marketing Research 1e © McGraw-Hill/Irwin2008
Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved. 12-19
SPSS One-way ANOVA example:
Likelihood of Recommending vs. Gender
Hair/Wolfinbarger/Ortinau/Bush, Essentials of
Marketing Research 1e © McGraw-Hill/Irwin2008
Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved. 12-20
Follow-up Tests
ANOVA does not tell us where the
significant differences lie – just that a
difference exists
Pairwise Comparison Tests
Tukey
Duncan
Scheffe
Hair/Wolfinbarger/Ortinau/Bush, Essentials of
Marketing Research 1e © McGraw-Hill/Irwin2008
Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved. 12-21
SPSS Scheffe Test Example
Hair/Wolfinbarger/Ortinau/Bush, Essentials of
Marketing Research 1e © McGraw-Hill/Irwin2008
Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved. 12-22
n-way ANOVA
Appropriate for multiple independent
variables
Example: men and women are shown
humorous and non-humorous ads and then
attitudes toward brand are measured. IVs =
(1) gender, and (2) ad type; DV = attitude
toward brand
Need 2-way ANOVA design here (also
called “factorial design”) because we have 2
IVs
Hair/Wolfinbarger/Ortinau/Bush, Essentials of
Marketing Research 1e © McGraw-Hill/Irwin2008
Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved. 12-23
SPSS Example: 2-way ANOVA
Likelihood of Recommending vs.
(1) Gender & (2) Distance
Hair/Wolfinbarger/Ortinau/Bush, Essentials of
Marketing Research 1e © McGraw-Hill/Irwin2008
Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved. 12-24
SPSS Example:
Repeated Measures ANOVA
Does your version of SPSS have it?
Hair/Wolfinbarger/Ortinau/Bush, Essentials of
Marketing Research 1e © McGraw-Hill/Irwin2008
Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved. 12-25