1. Basic Data Analysis for Quantitative Research
Chapter 11
Basic Data Analysis for Quantitative Research
McGraw-Hill/Irwin
Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved.

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

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

4. Dialog Boxes for Calculating the Mean, Median, and Mode (in ‘Frequencies’ function)

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

6. SPSS Output for Measures of Dispersion

7. Type of Scale and Appropriate Statistic

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?”

9. Univariate Hypothesis Test Using X-16 – Reasonable Prices

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. 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

12. Cross-Tabulation: Ad Recall vs. Gender

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

14. SPSS Chi-Square Crosstab Example
Do males and females recall the ads differently?

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?

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,

17. Comparing two means with Paired Samples t-Test
Do average scores on variables X-18 and X-20 differ from each other?

18. Do males and females differ with respect to their satisfaction?
Comparing Two Means with Independent Samples t-Test
Do males and females differ with respect to their satisfaction?

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)

20. Analysis of Variance (ANOVA)
F-test: The test used to statistically evaluate the differences between the group means in ANOVA

21. Example of One-Way ANOVA
Does distance driven affect customers’ likelihood of returning?

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

23. Results for Post-hoc Mean Comparisons

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

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)

26. n-Way ANOVA Example
Does distance driven and gender affect customers’ likelihood of recommending Santa Fe Grill?

27. n -Way ANOVA Post-hoc Comparisons