Graphical and Numerical Summaries of Categorical Data

Graphical summaries

Help researchers visualize the data, detect outliers, assess model validity, and communicate findings.

Numerical summaries

Reduce data into frequencies and proportions (percentages).

Common graphical summaries for categorical data

Pie charts and bar charts.

Types of data for counts and percentages

Nominal and ordinal data.

Numerical summaries for one-sample categorical data

Frequencies and proportions/percentages.

Graphical summaries for one-sample categorical data

Pie charts or bar charts.

Real-life example for categorical statistics

Out-of-hospital cardiac arrest cases attended by the Scottish Ambulance Service (1991-1995).

Main variable of interest in the cardiac arrest study

Whether patients were discharged 'dead' or 'alive' from the hospital.

Dataset used in the cardiac arrest example

Ambulance Heart Attacks.sav.

Total participants in the cardiac arrest study

7,208 participants.

Patients discharged alive in the cardiac arrest study

636 patients (9%).

Patients who died in the hospital in the cardiac arrest study

6,572 patients (91%).

Graphical tools used to show discharge outcomes

Pie charts and bar charts.

Two-sample categorical data summarized numerically

Using frequencies and proportions by group.

Two-sample categorical data summarized graphically

Using grouped pie charts or bar charts.

Comparison made in the cardiac arrest study using two-sample data

Survival rates between patients who received CPR and those who did not.

Patients who received CPR from a bystander

3,309 patients.

Patients who did not receive CPR

3,899 patients.

Percentage of patients who received CPR and survived

13% were discharged alive.

Percentage of patients who did not receive CPR and survived

6% were discharged alive.

Overall survival rate in the cardiac arrest study

9% of all patients were discharged alive.

Conclusion drawn from the cardiac arrest data

Bystander CPR was associated with a higher hospital discharge rate (13% vs. 6%).