Contingency Table

What is a contingency table or cross tab?

Contingency tables are used in descriptive statistics to get an overview of two categorical variables. In the crosstab you can read how often the combination of the values of two characteristics occurs.

Frequencies can be reported as absolute counts or relative percentages. Therefore, a cross-tab in statistics shows how two variables are related.

Crosstabs in Statistics

If two categorical variables are present, a crosstab is obtained by entering the values of the variables in the table. For the first variable, the values are placed from left to right (columns), and the values of the second variable from top to bottom (rows). The individual cells are then filled with either the absolute or the relative frequency.

Interpreting Crosstabs

How do you interpret a crosstab? A crosstab shows the frequencies of two variables.

In each cell of a crosstab, the frequencies of the characteristic combinations are plotted; in the example above, female and without a degree occur exactly 6 times.

Rows and Columns for the Crosstab

In this way, the values of one variable are plotted in the rows and the values of the other variable are plotted in the columns. There is no required arrangement. If one variable is considered independent, it is often placed in the columns and the dependent variable in the rows.

Absolute and Relative Frequencies for Crosstabs

When creating a crosstab, either the absolute or the relative frequencies can be output:

Absolute frequencies

Absolute frequencies are those values that indicate how often the respective combination of two characteristic values occurs.

Relative frequencies

Relative frequencies, on the other hand, indicate how often the respective combination of categories occurs in relation to all cases, a row total, or a column total. They are usually expressed as percentages. The chosen denominator should always be stated because it determines how the percentages are interpreted.

Example Contingency Table

The creation of crosstabs will now be examined in more detail using an example. In the example it is assumed that on a rainy day a student counts how many people "with" and how many "without" umbrellas come to the statistics lecture. In addition, the student makes a note of the gender of the students.

That's how it works with numiqo: Open the Online Statistics Software, copy the table below to the Calculator and select the variables Gender and With umbrella in the Descriptive Statistics area. numiqo will automatically create a contingency table for you.

The result can now easily be displayed in a contingency table. The cross-classified table now contains the absolute frequencies of the respective characteristic combinations:

Testing a Crosstab for Significance

A crosstab can be used to examine whether there is a relationship between the two variables. However, since a crosstab is a descriptive statistic, a statement can only be made about the sample. To test whether the variables are associated in the population, you can use a chi-square test of independence. Valid conclusions about the population also depend on how the sample was selected and on the assumptions of the test.