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. 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

3. 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

4. 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

5. Exhibit 11.2 - Dialog Boxes for Calculating the Mean, Median, and Mode

6. 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

7. Exhibit 11.3 - Measures of Dispersion

8. 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

9. 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

10. 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. 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

12. Choosing the Appropriate Statistical Technique
Considerations that influence the choice of a particular technique:
Number of variables
Scale of measurement
Parametric versus nonparametric statistics

13. Exhibit 11.6 - Type of Scale and Appropriate Statistic

14. 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

15. Exhibit 11.7 - Univariate Hypothesis Test Using X 16 –Reasonable Prices

16. 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

17. 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

18. Exhibit 11.8 - Example of a Cross-Tabulation: Gender by Ad Recall

19. Chi-Square Analysis
Assesses how closely the observed frequencies fit the pattern of the expected frequencies
Referred to as a “goodness-of-fit” test

20. 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

21. 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,

22. Exhibit 11.11 - Paired Samples t-Test

23. 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

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

25. Exhibit 11.12 - Example of One-Way ANOVA

26. 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

27. Exhibit 11.13 - Results for Post-hoc ANOVA Tests

28. 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

29. Exhibit 11.14 - n-Way ANOVA Results—Santa Fe Grill

30. Exhibit 11.15 - n -Way ANOVA Means Result

31. 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

32. Perceptual Mapping Applications in Marketing Research
New-product development
Image measurement
Advertising
Distribution

33. Exhibit 11.17 - Perceptual Map of Six Fast-Food Restaurants

34. Run post-hoc ANOVA tests between the competitor groups
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?