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Chapter 11
Basic Data Analysis for Quantitative Research
Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin
11-2
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
11-3
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
Dialog Boxes for Calculating the Mean, Median, and Mode (in ‘Frequencies’ function)
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
SPSS Output for Measures of Dispersion
11-7
Type of Scale and Appropriate Statistic
11-8
Univariate Statistical Tests
• Used when the researcher wishes to test a proposition about a sample characteristic 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?”
11-9
Univariate Hypothesis Test Using X-16 – Reasonable Prices
11-10
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)
11-11
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
11-12
Cross-Tabulation:Ad Recall vs. Gender
11-13
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 cross-tabulation table to determine if there is any kind of association between the variables
SPSS Chi-Square Crosstab ExampleDo males and females recall the ads differently?
11-15
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 re-used (“Paired”) or not re-used (“Independent”) in order to obtain the data?
11-16
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,1
2
1 2
mean of sample 1
mean of sample 2
standard error of the difference between the two means
X
X
S X X
11-17
Comparing two means with Paired Samples t-Test
Do average scores on variables X-18 and X-20 differ from each other?
11-18
Do males and females differ with respect to their satisfaction?
Comparing Two Means with Independent Samples t-Test
11-19
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)
11-20
Analysis of Variance (ANOVA)
• F-test: The test used to statistically evaluate the differences between the group means in ANOVA
11-21
Example of One-Way ANOVA
Does distance driven affect customers’ likelihood of returning?
11-22
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
11-23
Results for Post-hoc Mean Comparisons
11-24
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
11-25
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)
11-26
n-Way ANOVA ExampleDoes distance driven and gender affect customers’ likelihood of
recommending Santa Fe Grill?
11-27
n -Way ANOVA Post-hoc Comparisons