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

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?”

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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

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Cross-Tabulation:Ad Recall vs. Gender

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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

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Example of One-Way ANOVA

Does distance driven affect customers’ likelihood of returning?

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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

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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

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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)

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n-Way ANOVA ExampleDoes distance driven and gender affect customers’ likelihood of

recommending Santa Fe Grill?

11-27

n -Way ANOVA Post-hoc Comparisons