# 2.1.2 - Two Categorical Variables

2.1.2 - Two Categorical VariablesData concerning two categorical (i.e., nominal- or ordinal-level) variables can be displayed in a two-way contingency table, clustered bar chart, or stacked bar chart. Here, we'll look at an example of each. At the end of this lesson, you will learn how Minitab Express can be used to make two-way contingency tables and clustered bar charts. Minitab Express cannot be used to make stacked bar charts.

## Two-Way Contingency Table

A **two-way contingency table**, also know as a *two-way table* or just *contingency table*, displays data from two categorical variables. This is similar to the frequency tables we saw in the last lesson, but with two dimensions. One variable will be represented in the rows and a second variable will be represented in the columns. Later in this lesson we'll see how a two-way table can be used to compute a variety of different proportions.

The example below displays the counts of Penn State undergraduate and graduate students who are Pennsylvania residents and not Pennsylvania residents.

PA Resident | Non-PA Resident | Total | |
---|---|---|---|

Undergraduate | 54,239 | 26,841 | 81,080 |

Graduate | 5,596 | 9,732 | 15,328 |

Total | 59,835 | 36,573 | 96,408 |

## Stacked Bar Chart

A **stacked bar chart** is also known as a *segmented bar chart*. One categorical variable is represented on the x-axis and the second categorical variable is displayed as different parts (i.e., segments) of each bar. Minitab Express cannot be used to construct stacked bar charts, however many other software programs will. The stacked bar chart below was constructed using the statistical software program R.

On this stacked bar chart, the bar on the left represents the number of students who are Pennsylvania residents. The bar on the right represents the number of students who are not Pennsylvania residents. The bottom of each bar, which is light green, represents the number of students who are enrolled at the undergraduate-level. The top of each bar, which is blue, represents the number of students who are enrolled at the graduate-level.

From this bar chart, we can see that overall there are more students who are Pennsylvania residents than non-Pennsylvania residents because the bar on the left is higher than the bar on the right. In both bars, the light green section is much bigger than the blue section, which tells us that there are more undergraduate-students than there are graduate-students in both groups.

The light green section is bigger in the left bar compared to the right bar, which tells us that undergraduate-students are more likely to be Pennsylvania residents. The blue section is bigger in the right bar compared to the left bar, which tells us that graduate-students are more likely to be non-Pennsylvania residents.

## Clustered Bar Chart

In a **clustered bar chart** each bar represents one combination of the two categorical variables. If you compare this to the two-way contingency table above, each bar represents the value in one cell. This is also known as a *side-by-side bar chart*. The clustered bar chart below was made using Minitab Express.

## Choosing the Best Visual Display

The two-way contingency table, stacked bar chart, and clustered bar chart shown above were all made using the same data concerning Penn State enrollments by academic level and state residency. The best visual display depends on the scenario. For example, if our primary goal was to compare the number of students who are Pennsylvania residents and non-Pennsylvania residents, and academic level was a secondary variable of interest, the stacked bar chart may be preferred. If we wanted to compare the number of students in each combination of academic level and state residency to see which groups were largest and smallest, the clustered bar chart may be preferred. Often, more than one of these graphs may be appropriate.

# 2.1.2.1 - Minitab Express: Two-Way Table

2.1.2.1 - Minitab Express: Two-Way Table## MinitabExpress – Two-Way Table

This example will use data collected from a sample of students enrolled in online sections of STAT 200 during the Summer 2020 semester. These data can be downloaded as a Minitab Express Project or as a CSV file:

To create a two-way table of the *Work Status* and *Primary Campus* variables in Minitab Express:

- Open the data set in Minitab Express
- On a PC: Select
*STATISTICS > Cross Tabulation and Chi-square*

On a Mac: Select*Statistics > Tables > Cross Tabulation and Chi-Square* - We have a data file where each row represents one case, so we will keep the default data entry method of
*Raw data (categorical variables)*in the drop down menu - Double click the variable
*Work Status*in the box on the left to insert it into the*Rows*box on the right - Double click the variable
*Primary Campus*in the box on the left to insert it into the*Columns*box on the right - Click
*OK*

This should result in the two-way table below:

Commonwealth Campus | University Park | World Campus | All | |
---|---|---|---|---|

Full-time | 0 | 26 | 78 | 104 |

Not working | 1 | 99 | 25 | 125 |

Missing | 0 | 2 | 0 | |

All | 5 | 221 | 115 | 341 |

Cell Contents: Count |

Select your operating system below to see a step-by-step guide for this example.

# 2.1.2.2 - Minitab Express: Clustered Bar Chart

2.1.2.2 - Minitab Express: Clustered Bar Chart## MinitabExpress – Clustered Bar Chart

This example will use data collected from a sample of students enrolled in online sections of STAT 200 during the Summer 2020 semester. These data can be downloaded as a Minitab Express Project or as a CSV file:

To create a clustered bar chart of the *Work Status* and *Primary Campus* variables in Minitab Express:

- Open the data set in Minitab Express
- On a PC: Select
*GRAPHS> Bar Chart > Counts of Unique Values > Clustered*

On a Mac: Select*Graphs > Bar Chart > Counts of unique values in a categorical variable > Clustered* - Double click the variables
*Work Status*and*Primary Campus*in the box on the left to insert them both into the*Categorical variables*box on the right - Click
*OK*

This should result in the clustered bar chart below:

Select your operating system below to see a step-by-step guide for this example.

**Note**: The order in which the variables are entered into the *Categorical variables* box in Minitab Express determines how the bars will be clustered. For example, if we entered *Primary Campus* and then *Work Status*, the result would be the following clustered bar chart:

## Summarized Data

In the example above, raw data were used. In other words, our Minitab Express file contained one row for each case. It is also possible to use Minitab Express to construct a clustered bar chart with summarized data, for example, if you have data in a frequency table. To do this, on a PC select *GRAPHS > Bar Chart > Summarized Data > Data in a Two-Way Table > Clustered*. On a Mac, select *Graphs > Bar Chart > Summarized values for each category in a table >Two-way table > Clustered*. For an example, see the Minitab Express Support page.