Independent and Dependent Variables, Bivariate Tables


Cross tabulation allows us to look at the relationship between two variables by organizing them in a table. This is called bivariate analysis. The easiest, most straightforward way of conducting bivariate analysis is by constructing a bivariate table. We generally refer to bivariate tables in terms of rows and columns. In other words, a table with two rows and two columns would be a 2 x 2 table. By convention, the independent variable is usually placed in the columns and the dependent variable is placed in the rows. Rows and columns intersect at cells. The row totals are found along the right side, and the column totals are found along the bottom.

Bivariate analysis allows us to answer two questions:

  1. Is there a relationship between the two variables?
  2. If so, what is the pattern or direction of the relationship?
  • The independent variable is the cause. Its value is independent of other variables in your study.
  • The dependent variable is the effect. Its value depends on changes in the independent variable.

An independent variable is the variable you manipulate or vary in an experimental study to explore its effects. It’s called “independent” because it’s not influenced by any other variables in the study.

You design a study to test whether changes in room temperature have an effect on math test scores.

Your independent variable is the temperature of the room. You vary the room temperature by making it cooler for half the participants, and warmer for the other half.

Your dependent variable is math test scores. You measure the math skills of all participants using a standardized test and check whether they differ based on room temperature.

Imagine that we want to make a graph of the amount of rainfall that occurs at different times of year. Rainfall depends on time of year, but time of year does not depend on rainfall. Therefore, rainfall is the dependent variable and time of year is the independent variable.

You want to see the effect of studying or sleeping on a test score. In the example, “test score” is the dependent variable. “Studying” or “sleeping” is the independent variable because these factors impact how much a student scores on the test.

An easy way to remember is to insert the names of the two variables you are using in this sentence in they way that makes the most sense. Then you can figure out which is the independent variable and which is the dependent variable:

(Independent variable) causes a change in (Dependent Variable) and it isn’t possible that (Dependent Variable) could cause a change in (Independent Variable).

In the example below, we are going to see if there is a relationship between the authoritarianism of bosses and the efficiency of the workers in 44 different offices. In other words, we’re going to see if there is a relationship between how big of a jerk a given boss is and how hard his or her employees work. We’ve broken the bosses into two categories: low authoritarianism (totally chill) and high authoritarianism (overbearing jerk). Similarly, we’ve broken down the workers according to efficiency (high and low).

Worker Efficiency and Workplace Authoritarianism

Low Authoritarianism High Authoritarianism Total
Low Efficiency 10 12 22
High Efficiency 17 5 22
Total 27 17 44


Since the bosses’ authoritarianism is our independent variable, we put that in the columns. Employee efficiency goes in the rows. The row and column totals are displayed. Displaying our data in terms of raw scores is all well and good, but the differences in the number of workers who fall into each group (there are 27 employees who work in low authoritarianism environments compared to 17 who work in high authoritarianism environments) makes direct comparison impossible. In order to make legitimate comparisons between the two groups, we need to calculate the relative frequency for each (also known as the column percentages). We always calculate percentages according to the variable in the column, as that is our independent variable. Let’s calculate column percentages for the low authoritarian employees first. There are a total of 27, with 10 falling into the low efficiency category, and 17 falling into the high efficiency category. In order to figure out percentages, we need to divide each (10 and 17) by the column total (27).

10/27 = 0.3704; 0.3704 * 100 = 37.04 percent
17/27 = 0.6296; 0.6296*100 = 62.96 percent

These numbers tell us that of the 27 employees who work in low authoritarian environments, more than 60 percent of them are highly efficient workers. Now let’s do the same thing for the employees in high authoritarian environments:

12/17 = 0.7059; 0.7059*100 = 70.59 percent
5/17 = 0.2941; 0.2941*100 = 29.41 percent

Worker Efficiency and Workplace Authoritarianism

Low Authoritarianism High Authoritarianism Total
Low Efficiency 10 (37.04%) 12 (70.59%) 22 (50%)
High Efficiency 17 (62.96%) 5 (29.41%) 22 (50%)
Total 27 (100%) 17 (100%) 44 (100%)


Notice that the percentages in our columns add up to 100 percent. If that’s not the case, we’ve done something wrong.


Put the independent variable in the column position
Put the dependent variable in the row position
Calculate the column percentages