 # Chapter18 Determining and Interpreting Associations Among Variables.

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Chapter18 Determining and Interpreting Associations Among Variables

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

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

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

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

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

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

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

Chi-Square Analysis Computed chi-square values:

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

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.

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

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.

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

Correlation Coefficients and Covariation

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

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.

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.

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.