# Relationships Among Variables

Let's take a step back and look at what this class is all about. Basically, we are trying to either build theories or test theories. Theories are explanations for why certain variables are related to each other.

What do we mean by variables being related to each other? Fundamentally, it means that the values of variable correspond to the values of another variable, for each case in the dataset. In other words, knowing the value of one variable, for a given case, helps you to predict the value of the other one. If the variables are perfectly related, then knowing the value of one variable tells you exactly what the value of the other variable is.

To actually measure relationships among variables, you have to know what level of measurement the variable is. The level of measurement determines what kinds of mathematical operations can meaningfully be performed on the values of a variable. In this course, we basically deal with just three kinds of relationships:

Variables Test for Relationship Example
Both variables are nominal level Chi-square test See which divisions have the most female employees
Independent variable is nominal,

Dependent variable is interval or ratio

T-test (if indep has 2 categories only);

ANOVA

Test hypothesis that male employees are more satisfied than female employees
Both variables are interval level Correlation; Regression Look at relationship between job satisfaction and salary level

As you know, many social science variables, such as attitude scales, are really ordinal level measurements. But there are not many measures of ordinal relationship, and all are beyond the scope of this class. So what do you do? There are two choices: one, treat them as nominal and use chi-square tests, or two, treat them as interval and use correlation and regression. People normally do the latter (treat them as interval).