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Chapter18 Determining and Interpreting Associations Among Variables

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Associative Analyses Associative analyses: determine where stable relationships exist between two variables

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Types of Relationships Between Two Variables Relationship: a consistent, systematic linkage between the levels or labels for two variables Four basic types of relationships: Nonmonotonic Monotonic Linear Curvilinear

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Types of Relationships Between Two Variables…cont. Nonmonotonic: two variables are associated, but only in a very general sense Monotonic: the general direction of a relationship between two variables is known Increasing Decreasing

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Types of Relationships Between Two Variables…cont. Linear: “straight-line” association between two variables Curvilinear: some smooth curve pattern describes the association

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Characterizing Relationships Between Variables Presence: whether any systematic relationship exists between two variables of interest Direction: whether the relationship is positive or negative Strength of association: how consistent the relationship is

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Cross-Tabulations Bar charts can be used to “see” nonmonotonic relationships Cross-tabulation: consists of rows and columns defined by the categories classifying each variable Cross-tabulation table: four types of number in each cell Frequency Raw percentage Column percentage Row percentage Figure 18.3

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Chi-Square Analysis Chi-square analysis: assesses nonmonotonic associations in cross-tabulation tables Observed frequencies: counts for each cell found in the sample Expected frequencies: calculated on the null of no association between the two variables under examination

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Chi-Square Analysis Computed chi-square values:

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Chi-Square Analysis The chi-square distribution’s shape changes depending on the number of degrees of freedom The computed chi-square value is compared to a table value to determine statistical significance

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Chi-Square Analysis How do I interpret a Chi-square result? The chi-square analysis yields the probability that the researcher would find evidence in support of the null hypothesis is he or she repeated the study many, many times with independent samples. A significant chi-square result means the researcher should look at the cross-tabulation row and column percentages to “see” the association pattern.

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Correlation Coefficients and Covariation Correlation coefficient: standardizes the covariation between two variables into a number ranging from –1.0 to +1.0 Covariation: is defined as the amount of change in one variable systematically associated with a change in another variable

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Correlation Coefficients and Covariation A correlation indicates the strength of association between two variables by its size. The sign indicates the direction of the association.

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Correlation Coefficients and Covariation Covariation can be examined with use of a scatter diagram.

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Correlation Coefficients and Covariation

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The Pearson Product Moment Correlation Coefficient Pearson product moment correlation: measures the degree of linear association between two variables

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The Pearson Product Moment Correlation Coefficient Special considerations in linear correlation procedures: Correlation takes into account only the relationship between TWO variables, not interaction with other variables. Correlation does not demonstrate cause and effect. Correlation will not detect non-linear relationships between variables.

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Concluding Comments on Associate Analyses Researchers will always test the null hypothesis of NO relationship or no correlation. When the null hypothesis is rejected, then the researcher may have a managerially important relationship to share with the manager.

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Case 18.3 The Hobbit’s Choice: Survey Associative Analysis Please read Case 18.3 on pp. 557. Analyze the case and answer Questions 1, 2, 3.

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