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Basic Data Analysis for Quantitative Research
Copyright © 2010 by the McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin
11-2
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 Utilize perceptual mapping to present
research findings
11-3
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, and Hypothesis testing
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Measures of Central Tendency
MeanMeanArithmetic Average
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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 best
measure. for ordinal data, the median is generally
the best. for interval or ratio data, the mean is
generally used.
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Describes how close to the mean or other measure of central tendency, the rest of the values fall
Describes how close to the mean or other measure of central tendency, the rest of the values fall
Measures of Dispersions
RangeDistance between the smallest and largest value in a
set
Standard DeviationMeasure of the average dispersion of the values
about the mean
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Exhibit 11.3 Output for Measures of Dispersion
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Hypothesis Testing
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
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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
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Exhibit 11.7 Univariate Hypothesis Test Using X16
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Bivariate Statistical Tests
Compare characteristics 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
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Exhibit 11.8 Cross-Tabulation
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Chi-Square Analysis
Chi-square analysis enables the researcher to test for statistical significance between the frequency distributions of two or more nominally scaled variables in a cross-tabulation table to determine if there is any association between the variables
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Exhibit 11.9 SPSS Chi-Square Crosstabulation Example
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Comparing means
Requires interval or ratio data The t-test is the difference between the means
divided by the variability of random means The t-value is a ratio of the difference between
the two sample means and the std error The t-test tries to determine if the difference
between the two sample means occurred by chance
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Exhibit 11.10 Comparing Two Means with Independent Samples t-Test
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Exhibit 11.11 Paired Samples t-Test
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Analysis of Variance
Analysis of Variance (ANOVA) is a statistical technique that determines if three or more means are statistically different from each other
The dependent variable must be measurable; either interval or ratio scaled
The independent variable must be categorical “One-way ANOVA” means that there is only one
independent variable
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F-Test
The F-test is the test used to statistically evaluate the differences between the group means in ANOVA
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Determining Statistical Significance using F-Test
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Follow-up Tests
Anova does not tell us where the significant differences lie – just that a difference exists Tukey Duncan Scheffe
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n-way ANOVA
Appropriate for multiple independent variables and for experimental designs with multiple variables involved in groups Example: men and women are shown
humorous and non-humorous ads and then attitudes toward brand are measured. IV = gender and ad type
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Exhibit 11.12 Example ANOVA
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Exhibit 11.14 Post-hoc ANOVA Test
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Perceptual Mapping
Perceptual mapping is a process that is used develop maps showing the perceptions of respondents
The maps visually represent respondent perceptions in two dimensions
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Exhibit 11.19 Perceptual Map of Fast-Food Restaurants
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Marketing Research in Action: Remington’s Steak House
Based on the analysis, in what areas should Remington’s seek to improve?
What new marketing strategies would you suggest given the findings?