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Association Analyses (1)

Learn how to characterize relationships between variables, test statistical significance, calculate correlation coefficients, and interpret results in marketing research. Understand when and how to use association analyses effectively.

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Association Analyses (1)

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  1. Association Analyses (1) BUS ADM 462: Marketing Research I-Hsuan (Shaine) Chiu

  2. Learning Objectives • Describe different types of association analyses • Demonstrate when and how to use association analyses

  3. Motivating Example • Are levels of worry about global warming related to the desirability of a hybrid car? • Is there a relationship between the importance of free shipping and the importance of free return? • Are different housing types related to different modes of transportation among college students?

  4. Characterizing Relationships between Variables • Presence • Does the relationship exist in the population?  Test of statistical significance

  5. Characterizing Relationships between Variables • Direction or Pattern • Direction of a linear relationship • Pattern of a nonlinear relationship Decreasing Increasing

  6. Characterizing Relationships between Variables • Strength of relationships Strong Increasing Strong Decreasing Moderate Increasing Moderate Decreasing

  7. Procedure for Analyzing the Relationship

  8. Step 3: Procedure for Test of Significance of Association

  9. Step 3: Procedure for Test of Significance of Association Step 1: State hypotheses • H0: There is no relationship between two variables • H1: There exists a true relationship between two variables Step 2: Calculate the test statistic Step 3: Evaluate the test statistic Step 4: Draw conclusion

  10. Step 3: Procedure for Test of Significance of Association Step 1: State hypotheses • Compute p-value Step 2: Calculate the test statistic Step 3: Evaluate the test statistic Step 4: Draw conclusion

  11. Step 3: Procedure for Test of Significance of Association Step 1: State hypotheses • Compare p-value with significance level ⍺ • Significance level ⍺ = 1- confidence level • 90% confidence level  ⍺ = 1-0.9 = 0.1 • 95% confidence level  ⍺ = 1-0.95 = 0.05 • 99% confidence level  ⍺ = 1-0.99 = 0.01 Step 2: Calculate the test statistic Step 3: Evaluate the test statistic Step 4: Draw conclusion

  12. Step 3: Procedure for Test of Significance of Association Step 1: State hypotheses • Compare p-value with significance level ⍺ • p-value < ⍺  Reject H0 and conclude H1 • H0: There is no relationships between two variables • H1: There exists a true relationships between two variables • p-value > ⍺  Do not reject H0 and conclude H0 • H0: There is no relationships between two variables • H1: There exists a true relationships between two variables Step 2: Calculate the test statistic Step 3: Evaluate the test statistic Step 4: Draw conclusion

  13. Relationships between two Continuous Variables

  14. Motivating Example • Is there a relationship between the importance of free shipping and the importance of free return? • Is there a relationship between the importance of free return and age?

  15. The Pearson Correlation Coefficient • Pearson Correlation Coefficient (rxy) • A statistic that indicates the degree of linear association between two continuous variables • Ranges between -1 and 1

  16. The Pearson Correlation Coefficient • Correlation coefficient captures both direction and strength of the linear relationship • Positive  Increasing linear relationship • Negative  Decreasing linear relationship

  17. Example – Correlation Coefficient • A manager is wondering if the following relationships exist at 90% confidence level: • The importance of free return and the importance of free shipping (7-point Likert scale) • The importance of free return and the age of their customers • The importance of free shipping and the age of their customers

  18. Example – Correlation Coefficient • Step 1: State hypotheses • For the importance of free return vs the age of customers • H0: There is no relationship between the importance of free return and the age of customers • H1: There exists a true relationship between the importance of free return and the age of customers

  19. Example –Correlation Coefficient • Step 2: Calculate the p-value • Step 3: Evaluate the p-value at a given significance level p-value

  20. Example – Correlation Coefficient • Step 4: Generate conclusion based on Step 3 • p-value=.440 > ⍺ = 0.1, Do not reject H0 and conclude H0 p-value • We do not reject the null hypothesis and conclude that there is no relationship between the importance of free shipping and the age of customers. • H0: There is no relationship between the importance of free return and the age of customers • H1: There exists a true relationship between the importance of free return and the age of customers

  21. What about other relationships? • For the importance of free return vs the importance of free shipping • H0: There is no relationship between the importance of free return and the importance of free shipping • H1: There exists a true relationship between the importance of free return and importance of free shipping • For the importance of free shipping vs the age of customers • H0: There is no relationship between the importance of free shippingand the age of customers • H1: There exists a true relationship between the importance of free shippingand the age of customers

  22. Example –Correlation Coefficient • Step 2: Calculate the p-value • Step 3: Evaluate the p-value at a given significance level p-value

  23. Example – Correlation Coefficient • Step 4: Generate conclusion based on Step 3 p-value • We reject the null hypothesis and conclude that there exists a relationship between the importance of free return and the importance of free shipping. • H0: There is no relationship between the importance of free return and the importance of free shipping • H1: There exists a true relationship between the importance of free return and importance of free shipping

  24. Example – Correlation Coefficient • The Pearson correlation coefficient is .685, indicating an increasing linear relationship between the importance of free shipping and the importance of free return. That is, customers who value free shipping highly usually value free return a lot as well.

  25. Example – Correlation Coefficient • Moreover, the Pearson correlation coefficient is .685, indicating the relationship between the importance of free shipping and the importance of free return is strong.

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