1. MARKETING RESEARCH ESSENTIALS WITH DATA ANALYSIS IN EXCEL AND SPAA McDaniel │ Gates │ Sivaramakrishnan │ Main Chapter Fourteen: Statistical Tests of Relation and Difference

2. LEARNING OBJECTIVES Learn the commonly used statistical tests of relation, conduct data analyses using these tests, and interpret the results. Learn the commonly used statistics tests of difference, conduct data analyses using these tests, and interpret the results. Know how to manage the dataset for some special data analysis situations. Chapter Fourteen: Statistical Tests of Relation and Difference

3. Tests of Relation Bivariate Techniques: –Statistical methods of analyzing relationships between variables Multivariate techniques: –Statistical methods of analyzing the relationship using more than two variables

4. Chi-Square Test of Independence A statistical test to determine whether or not two nominal variables are unrelated (independent) to each other

5. Correlation Analysis Correlation Analysis: –Analysis of the degree to which changes in one variable are associated with changes in another Pearson Correlation: –Analysis technique for use with interval or ratio data

6. Correlation Analysis Measures of Association: Do not mean there is a causal relationship between the relevant variables Could simply represent coincidence between the variables Should be taken in context and with timeliness of both data sets Can be used in conjunction with cross-tabulations of relevant data to add another perspective to the results

7. Regression Analysis Independent variable – the variable believed to affect the value of the dependent variable Dependent variable – the variable expected to be explained or caused by the independent variable Bivariate regression analysis – the analysis of the nature of the relationship between two variables when one is considered the independent (predictor) variable and the other the dependent (predicted) variable

8. Nature of the Relationship: Scatterplot

9. Least-Squares Estimation Procedure Used to fit data for X and Y not plotted Enables estimation of non-plotted data points Results in a straight line that fits the actual observations (plotted dots) better than any other line that could be fit to the observations

10. Least-Squares Estimation Procedure Estimating regression analysis equation:

11. Least-Squares Estimation Procedure Values for “a” and “b” can be calculated as follows:

12. Multiple Regression Analysis The analysis of the nature of the relationship between two or more independent (predictor) variables and a dependent (predicted) variable.

13. Tests of Difference Examination of the differences between variables or groups 4 statistical techniques can be used

14. Independent Samples T-Test Determines if the means of two groups are significantly different from each other Used with the Levene’s Test for Equality of Variances (to compare variances rather than means) – ensures correct conclusion regarding hypotheses

15. Analysis of Variance (ANOVA) Determines if three or more group means are significantly different from each other

16. Non-Parametric Chi-Square Test of Difference Between Proportions Determines if two or more proportions are equal Used for testing proportions rather than relations between two variables

17. Paired-Samples T-Test Determines if the means of two variables are significantly different from each other within the same group

18. Special Data Analysis Situations Data can be reconfigured to complete analysis in different ways in order to look for important conclusions: –By group –By excluding a group –By creating a new variable

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