# Chapter Main Points and Learning Objectives

Chapter main points

• A bivariate table displays the distribution of one variable across the categories of another variable. It is obtained by classifying cases based on their joint scores for two variables. Percentaging bivariate tables are used to examine the relationship between two variables that have been organized in a bivariate table. The percentages are always calculated within each category of the independent variable.
• A relationship is said to exist when certain values of one variable are associated with certain values of the other variable. Bivariate tables are interpreted by comparing percentages across different categories of the independent variable. A relationship is said to exist if the percentage distributions vary across the categories of the independent variable. Variables measured at the ordinal or interval-ratio levels may be positively or negatively associated. With a positive association, higher values of one variable correspond to higher values of the other variable. When there is a negative association between variables, higher values of one variable correspond to lower values of the other variable.
• Elaboration is a technique designed to clarify bivariate associations. It involves the introduction of control variables to interpret the links between the independent and dependent variables. In a spurious relationship,both the independent and dependent variables are influenced by a causally prior control variable, and there is no causal link between them. In an intervening relationship, the control variable follows the independent variable but precedes the dependent variable in the causal sequence. In a conditional relationship, the bivariate relationship between the independent and dependent variables is different in each of the partial tables.

Learning objectives

1. Create and analyze a bivariate table
2. Identify the properties of a bivariate relationship: existence, strength, and direction
3. Explain how to elaborate the relationship between variables: nonspuriousness, intervening, and conditional relationships