12: Basic Data Analysis for Quantitative Research

12-2 Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved. Hair/Wolfinbarger/Ortinau/Bush, Essentials of Marketing Research 1e © McGraw-Hill/Irwin2008 Statistical Analysis  Summary Statistics  Central tendency and dispersion,  Relationships of the sample data, and  Hypothesis testing

12-3 Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved. Hair/Wolfinbarger/Ortinau/Bush, Essentials of Marketing Research 1e © McGraw-Hill/Irwin2008 Mode Response Most Often Given to a QuestionMode Response Most Often Given to a Question Median Middle Value of a Rank Ordered DistributionMedian Middle Value of a Rank Ordered Distribution Measures of Central Tendency Mean Arithmetic Average

12-4 Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved. Hair/Wolfinbarger/Ortinau/Bush, Essentials of Marketing Research 1e © McGraw-Hill/Irwin2008 Measures of Central Tendency  Each measure of central tendency describes a distribution in its own manner:  for nominal data, the mode is the only possible measure.  for ordinal data, the median is generally the best.  for interval or ratio data, the mean is generally used.

12-5 Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved. Hair/Wolfinbarger/Ortinau/Bush, Essentials of Marketing Research 1e © McGraw-Hill/Irwin2008 Describes how close to the mean or other measure of central tendency, the rest of the values fall Measures of Dispersion Range Distance between the smallest and largest value in a set Standard Deviation Measure of the average dispersion of the values about the mean

12-6 Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved. Hair/Wolfinbarger/Ortinau/Bush, Essentials of Marketing Research 1e © McGraw-Hill/Irwin2008 SPSS Output for Measures of Dispersion

12-7 Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved. Hair/Wolfinbarger/Ortinau/Bush, Essentials of Marketing Research 1e © McGraw-Hill/Irwin2008 Hypothesis Testing Independent Samples  two or more groups of responses that are tested as though they come from different populations Related (Matched) Samples  two or more groups of responses that are assumed to originate from the same population

12-8 Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved. Hair/Wolfinbarger/Ortinau/Bush, Essentials of Marketing Research 1e © McGraw-Hill/Irwin2008 Univariate Tests of Significance  Tests of one variable at a time  z-test  t-test  Appropriate for interval or ratio data  Test: “Is a mean significantly different from some number?”

12-9 Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved. Hair/Wolfinbarger/Ortinau/Bush, Essentials of Marketing Research 1e © McGraw-Hill/Irwin2008 Univariate Hypothesis Test Using X16 Variable (Reasonable Prices)

12-10 Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved. Hair/Wolfinbarger/Ortinau/Bush, Essentials of Marketing Research 1e © McGraw-Hill/Irwin2008 Bivariate Statistical Tests  Compare characteristics (means or frequencies) 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

12-11 Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved. Hair/Wolfinbarger/Ortinau/Bush, Essentials of Marketing Research 1e © McGraw-Hill/Irwin2008 Cross-Tabulation: Ad Recall vs. Gender

12-12 Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved. Hair/Wolfinbarger/Ortinau/Bush, Essentials of Marketing Research 1e © McGraw-Hill/Irwin2008 Chi-Square Analysis Chi-square analysis enables the researcher to test 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 association between the variables

12-13 Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved. Hair/Wolfinbarger/Ortinau/Bush, Essentials of Marketing Research 1e © McGraw-Hill/Irwin2008 SPSS Chi-Square Crosstab Example

12-14 Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved. Hair/Wolfinbarger/Ortinau/Bush, Essentials of Marketing Research 1e © McGraw-Hill/Irwin2008 Comparing means  Requires interval or ratio data  The t-test is the difference between the means divided by the average variability of the two random means  The t-value is a ratio of the difference between the two sample means and the std error of the difference in means  The t-test tries to determine whether the difference between the two sample means is significant or whether it occurred by chance

12-15 Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved. Hair/Wolfinbarger/Ortinau/Bush, Essentials of Marketing Research 1e © McGraw-Hill/Irwin2008 Comparing Two Means with Independent Samples t-Test

12-16 Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved. Hair/Wolfinbarger/Ortinau/Bush, Essentials of Marketing Research 1e © McGraw-Hill/Irwin2008 Comparing Two Means with Paired Samples t-Test

12-17 Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved. Hair/Wolfinbarger/Ortinau/Bush, Essentials of Marketing Research 1e © McGraw-Hill/Irwin2008 Analysis of Variance  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

12-18 Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved. Hair/Wolfinbarger/Ortinau/Bush, Essentials of Marketing Research 1e © McGraw-Hill/Irwin2008 F-Test The F-test is the test used to statistically evaluate the differences between the group means in ANOVA

12-19 Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved. Hair/Wolfinbarger/Ortinau/Bush, Essentials of Marketing Research 1e © McGraw-Hill/Irwin2008 Total variance in dataset can be separated into Between Group and Within Group Variance. Total variance in dataset can be separated into Between Group and Within Group Variance. The larger the variance Between Groups vs. Within Groups, the larger the F-Ratio. The larger the variance Between Groups vs. Within Groups, the larger the F-Ratio. The higher the F-Ratio, the more likely it is that the Null Hypothesis will be rejected and that the means are statistically different. The higher the F-Ratio, the more likely it is that the Null Hypothesis will be rejected and that the means are statistically different. Determining Statistical Significance using F-Test

12-20 Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved. Hair/Wolfinbarger/Ortinau/Bush, Essentials of Marketing Research 1e © McGraw-Hill/Irwin2008 SPSS One-way ANOVA example: Likelihood of Recommending vs. Gender

12-21 Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved. Hair/Wolfinbarger/Ortinau/Bush, Essentials of Marketing Research 1e © McGraw-Hill/Irwin2008 Follow-up Tests  ANOVA does not tell us where the significant differences lie – just that a difference exists  Pairwise Comparison Tests  Tukey  Duncan  Scheffe

12-22 Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved. Hair/Wolfinbarger/Ortinau/Bush, Essentials of Marketing Research 1e © McGraw-Hill/Irwin2008 SPSS Scheffe Test Example

12-23 Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved. Hair/Wolfinbarger/Ortinau/Bush, Essentials of Marketing Research 1e © McGraw-Hill/Irwin2008 n-way ANOVA  Appropriate for multiple independent variables  Example: men and women are shown humorous and non-humorous ads and then attitudes toward brand are measured. IVs = (1) gender, and (2) ad type; DV = attitude toward brand  Need 2-way ANOVA design here (also called “factorial design”) because we have 2 IVs

12-24 Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved. Hair/Wolfinbarger/Ortinau/Bush, Essentials of Marketing Research 1e © McGraw-Hill/Irwin2008 SPSS Example: 2-way ANOVA Likelihood of Recommending vs. (1) Gender & (2) Distance

12-25 Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved. Hair/Wolfinbarger/Ortinau/Bush, Essentials of Marketing Research 1e © McGraw-Hill/Irwin2008 SPSS Example: Repeated Measures ANOVA Does your version of SPSS have it?