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**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.

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**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

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**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

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

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**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

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**SPSS Output for Measures of Dispersion**

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**Type of Scale and Appropriate Statistic**

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**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**

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**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)

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**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

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**SPSS Chi-Square Crosstab Example**

Do males and females recall the ads differently?

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**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?

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**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,

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**Comparing two means with Paired Samples t-Test**

Do average scores on variables X-18 and X-20 differ from each other?

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**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?

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**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)

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**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

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**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 Example Does distance driven and gender affect customers’ likelihood of recommending Santa Fe Grill?

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**n -Way ANOVA Post-hoc Comparisons**

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