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Determining and Interpreting Associations Among Variables Associative Analyses • Associative analyses: determine where stable relationships exist between two variables • Examples Ch 18 – What methods of doing business are associated with level of customer satisfaction? – What demographic variables are associated with repeat buying of Brand A? – Is type of sales training associated with sales performance of sales representatives? – Are purchase intention scores of a new product associated with actual sales of the product? 2 Relationships Between Two Variables • Relationship: a consistent, systematic linkage between the levels or labels for two variables • “Levels” refers to the characteristics of description for interval or ratio scales…the level of temperature, etc. • “Labels” refers to the characteristics of description for nominal or ordinal scales, buyers v. non-buyers, etc. • As we shall see, this concept is important in understanding the type of relationship… Ch 18 3 Relationships Between Two Variables • Nonmonotonic: two variables are associated, but only in a very general sense; don’t know “direction” of relationship, but we do know that the presence (or absence) of one variable is associated with the presence (or absence) of another. • At the presence of breakfast, we shall have the presence of orders for coffee. • At the presence of lunch, we shall have Ch 18 the absence of orders for coffee. 4 Nonmonotonic Relationship Ch 18 5 Relationships Between Two Variables • Monotonic: the general direction of a relationship between two variables is known – Increasing – Decreasing • Shoe store managers know that there is an association between the age of a child and shoe size. The older a child, the larger the shoe size. The direction is increasing, though we only know general Ch 18 6 direction, not actual size. Monotonic Increasing Relationship Ch 18 7 Relationships Between Two Variables • Linear: “straight-line” association between two variables • Here knowledge of one variable will yield knowledge of another variable • “100 customers produce $500 in Ch 18 revenue at Jack-in-the-Box” (p. 525) 8 Relationships Between Two Variables • Curvilinear: some smooth curve pattern describes the association • Example: Research shows that job satisfaction is high when one first starts to work for a company but goes down after a few years and then back up after workers have been with the same company for many years. This would be a U-shaped relationship. Ch 18 9 Characterizing Relationships Between Variables 1. Presence: whether any systematic relationship exists between two variables of interest 2. Direction: whether the relationship is positive or negative 3. Strength of association: how strong the relationship is: strong? moderate? weak? • Assess relationships in the order shown above. Ch 18 10