Basic Data Analysis for Quantitative Research

Copyright © 2010 by the McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

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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

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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?