### Chapter 11

```Chapter 11
Basic Data Analysis for Quantitative
Research
McGraw-Hill/Irwin
Statistical Analysis - Overview
• Every set of data collected needs some
summary information that describes the
numbers it contains
– Central tendency and dispersion
– Relationships of the sample data
– Hypothesis testing
11-2
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
11-3
Dialog Boxes for Calculating the Mean, Median, and
Mode (in ‘Frequencies’ function)
11-4
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
11-5
SPSS Output for Measures of Dispersion
11-6
Type of Scale and Appropriate Statistic
11-7
Univariate Statistical Tests
• Used when the researcher wishes to test a
against a known or given standard
• Appropriate for interval or ratio data
• Test: “Is a mean significantly different from
some number?”
– Example: “Is the ‘Reasonable Prices’ average
different from 4.0?”
11-8
Univariate Hypothesis Test Using X-16 –
Reasonable Prices
11-9
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 (ANOVA)
11-10
Cross-Tabulation (“Cross-tabs”)
• Used to examine relationships and report
findings for two categorical (i.e. ‘nominal’)
variables
• Purpose is to determine:
– if differences exist between subgroups of the
total sample on a key measure
– whether there is an association between two
categorical variables
• A frequency distribution of responses on two
or more sets of variables
11-11
Cross-Tabulation:
11-12
Chi-Square Analysis
• Assesses how closely the observed frequencies fit
the pattern of the expected frequencies
– Referred to as a “goodness-of-fit”
• Tests for statistical significance between the
frequency distributions of two or more nominally
scaled (i.e. “categorical”) variables in a crosstabulation table to determine if there is any kind of
association between the variables
11-13
SPSS Chi-Square Crosstab Example
Do males and females recall the ads differently?
Comparing Means: Independent
Versus Related Samples
• Independent samples: Two or more groups of
responses that supposedly come from different
populations
• Related samples: Two or more groups of responses
that supposedly originated from the same
population
– Also called “Matched” or “Dependent” samples
– SPSS calls them “Paired” samples
• Practical tip: Ask yourself, “Were the subjects reused (“Paired”) or not re-used (“Independent”) in
order to obtain the data?
11-15
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
11-16
Comparing two means with
Paired Samples t-Test
Do average scores on variables X-18 and X-20 differ from each other?
11-17
Comparing Two Means with
Independent Samples t-Test
Do males and females differ with respect to their satisfaction?
11-18
Analysis of Variance (ANOVA)
• 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
• “n-way ANOVA” means that there is more
than one independent variable (i.e. ‘n’ IVs)
11-19
Analysis of Variance (ANOVA)
• F-test: The test used to statistically evaluate
the differences between the group means in
ANOVA
11-20
Example of One-Way ANOVA
Does distance driven affect customers’ likelihood of returning?
11-21
Analysis of Variance (ANOVA)
• ANOVA does not tell us where the significant
differences lie – just that a difference exists
• Follow-up (Post-hoc) tests: Analysis that flags the
specific means that are statistically different from
each other
– Performed after an ANOVA determines there is an
“Omnibus” differenc between means
• Some Pairwise Comparison Tests (there are
others)
– Tukey
– Duncan
– Scheffé
11-22
Results for Post-hoc Mean Comparisons
11-23
n-Way ANOVA
• ANOVA that analyzes several independent
variables at the same time
– Also called “Factorial Design”
• Multiple independent variables in an ANOVA
can act in concert together to affect the
dependent variable – this is called Interaction
Effect
11-24
n-way ANOVA: Example
• Men and women are shown humorous and
non-humorous ads and then attitudes toward
the brand are measured.
• IVs (factors) = (1) gender (male vs. female),
and (2) ad type (humorous vs. non-humorous)
• DV = attitude toward brand
• Need 2-way ANOVA design here (also called
“factorial design”) because we have two
factors
– 2 x 2 design (2 levels of gender x 2 levels of ad type)
11-25
n-Way ANOVA Example
Does distance driven and gender affect customers’ likelihood of
recommending Santa Fe Grill?
11-26
n -Way ANOVA Post-hoc Comparisons
11-27
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