Slide 1Slide 2The Value of Testing for AssociationExploring Relationships between VariablesThe Concept of CovariationTypes of Relationship: Positive and NegativeTypes of Relationship: Nonexistent & CurvilinearChi-Square AnalysisChi-Square Analysis: An ExampleCorrelation AnalysisRules of Thumb in Correlation AnalysisCorrelation Analysis: An ExampleSlide 13Spearman’s Rank Order CorrelationRegression AnalysisPatterns of Residuals: Three ExamplesSlide 17Multiple Regression AnalysisStandardized Residuals vs. Normal DistributionMulticollinearitySummary of Learning Objectives1995 7888 4320 000 000001 00023Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved.1995 7888 4320 000 000001 00023Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. CCHHAAPPTTEERR1234 0001 897251 000001717Data Analysis: Testing for Data Analysis: Testing for AssociationAssociation17-217-21995 7888 4320 000 000001 00023Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. The Value of Testing for AssociationUnderstanding relationships between buyer characteristics and their behavior is essential to a successful marketing strategy.Marketing managers are extremely interested in detailed descriptions of the people who are most inclined to purchase their products.It’s part of our human nature to seek out “associations” and “connections” between things and events in the marketplace – therefore, the concept of “covariation” is central to implementing and monitoring a marketing strategy.17-317-31995 7888 4320 000 000001 00023Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. Exploring Relationships between VariablesRelationships between variables can be described in several ways: Presence of A Relationship Direction of A Relationship Strength of Association Type of Relationship17-417-41995 7888 4320 000 000001 00023Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. The Concept of CovariationA research team draws upon the concept of “covariation” when they want to determine if two variables which describe customers are related.17-517-51995 7888 4320 000 000001 00023Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. Types of Relationship: Positive and Negative17-617-6Y YXXPositive Negative1995 7888 4320 000 000001 00023Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. Types of Relationship: Nonexistent & Curvilinear17-717-7YXCurvilinear RelationshipYXNo Relationship1995 7888 4320 000 000001 00023Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. Chi-Square AnalysisA chi-square test is often referred to as a “goodness of fit” test by people in the marketing research industry. Essentially, it is performed on categorical questions and allows a research team to assess how closely what’s “observed” fits the pattern of what was “expected”.17-817-81995 7888 4320 000 000001 00023Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. Chi-Square Analysis: An Example17-917-9C a s e P r o c e s s i n g S u m m a r y C a s e s V a l i d M i s s i n g T o t a l N P e r c e n t N P e r c e n t N P e r c e n t D i s t a n c e D r i v e n * 5 0 1 0 0 . 0 % 0 0 % 5 0 1 0 0 . 0 % G e n d e r D a t a A n a l y s i s : T e s t i n g f o r A s s o c i a t i o n D i s t a n c e D r i v e n * G e n d e r C r o s s - T a b u l a t i o n G e n d e r F e m a l e M a l e T o t a l D i s t a n c e D r i v e n 1 C o u n t 9 1 3 2 2 E x p e c t e d C o u n t 1 3 . 2 8 . 8 2 2 . 0 2 C o u n t 1 4 6 2 0 E x p e c t e d C o u n t 1 2 . 0 8 . 0 2 0 . 0 3 C o u n t 7 1 8 E x p e c t e d C o u n t 4 . 8 3 . 2 8 . 0 T o t a l C o u n t 3 0 2 0 5 0 E x p e c t e d C o u n t 3 0 . 0 2 0 . 0 5 0 . 0 C h i - S q u a r e T e s t s V a l u e d f A s y m p . S i g . ( 2 - s i d e d ) P e a r s o n 6 . 6 9 5 a 2 . 0 3 5 C h i - s q u a r e L i k e l i h o o d r a t i o 7 . 0 7 1 2 . 0 2 9 L i n e a r - b y - l i n e a r a s s o c i a t i o n 6 . 4 1 3 1 . 0 1 1 N o f v a l i d c a s e s 5 0 a . 2 c e l l s ( 3 3 . 3 % ) h a v e e x p e c t e d c o u n t l e s s t h a n 5 . T h e m i n i m u m e x p e c t e d c o u n t i s 3 . 2 0 .1995 7888 4320 000 000001 00023Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. Correlation AnalysisA correlation analysis is often referred to (affectionately) as “plus or minus one” by some practitioners of marketing research. Correlation allows a research team to determine the sturdiness of a linear relationship between two variables.17-1017-101995 7888 4320 000 000001 00023Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. Rules of Thumb in Correlation Analysis17-1117-11Range of Coefficient Description of Strength.81 to 1.00Very strong.61 to .80Strong.41 to .60Moderate.21 to .40Weak.00 to .20None1995 7888 4320 000 000001 00023Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. Correlation Analysis: An Example17-12a17-12aDescriptive StatisticsMeanStd. Deviation NRecommend to Friend 4.68 .98 50Satisfaction Level 4.78 .95 501995 7888 4320 000 000001 00023Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. Correlation Analysis: An Example17-12b17-12bCorrelationsRecommendto FriendSatisfactionLevelRecommend to FriendPearson correlation 1.000 .601**Sig. (2-tailed) .000N 50 50Satisfaction LevelPearson correlation .601** 1.000Sig. (2-tailed) .000N 50 50**. Correlation is significant at the .01 level (2-tailed)1995 7888 4320 000 000001 00023Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. Spearman’s Rank Order Correlation17-1317-13C o r r e l a t i o n s S p e a r m a n ’ s R h o F o o d Q u a l i t y R a n k F o o d V a r i e t y R a n k …