Chapter 3: Displaying and Describing Categorical Data

Question 1

Define ‘Frequency table’.

Answer 1

A table that lists the categories in a categorical variable and gives the count (or percentage) of observations for each category.

Question 2

Define ‘Relative frequency table’.

Answer 2

A table that displays the proportions or percentages, rather than the counts, of values in each category.

Question 3

Define ‘Distribution’.

Answer 3

The distribution of a variable gives:

1. the possible values of the variable, and
2. the relative frequency of each value.

Question 4

Define ‘Area principle’.

Answer 4

In a statistical display, each data value should be represented by the same amount of area.

Question 5

Define ‘Bar chart’.

Answer 5

A chart that shows bars whose heights represent the count (or percentage) of observations for each category of a categorical variable.

Question 6

Define ‘Relative frequency chart’.

Answer 6

A chart that shows bars whose heights represent the percentages, instead of the counts, of observations for each category of a categorical variable.

Question 7

Define ‘Pie chart’.

Answer 7

A chart that shows how a “whole” divides into categories by showing a wedge of a circle whose area corresponds to the proportion in each category.

Question 8

Define ‘Categorical data condition’.

Answer 8

The methods in this chapter (chapter 2) are appropriate for displaying and describing categorical data. Be careful not to use them with quantitative data.

Question 9

Define ‘Contingency table’.

Answer 9

A table that displays counts and, sometimes, percentages of individuals falling into named categories on two or more variables. The table categorizes the individuals on all variables at once to reveal possible patterns in one variable that may be contingent on the category of the other.

Question 10

Define ‘Marginal distribution’.

Answer 10

In a contingency table, the distribution of either variable alone. The counts or percentages are the totals found in the margins (last row or column) of the table.

Question 11

Define ‘Joint distribution’.

Answer 11

The distribution of both variables in a contingency table, expressed as a percentage or a count.

Question 12

Define ‘Conditional distribution’.

Answer 12

The distribution of a variable restricting the WHO to consider only a smaller group of individuals.

Question 13

Define ‘Independent’.

Answer 13

Variables are said to be independent of the conditional distribution of one variable is the same for each category of the other.

Question 14

Define ‘Segmented bar chart’.

Answer 14

A chart that displays the conditional distribution of a categorical variable within each category of another variable.

Question 15

Define ‘Simpson’s paradox’.

Answer 15

Relationships among proportions taken within different groups or subsets can appear to contradict relationships among the overall proportions.

Question 16

How can we summarize categorical data?

Answer 16

1. Make and interpret a frequency table for a categorical variable. We can summarize categorical data by counting the number of cases in each category, sometimes expressing the resulting distribution as percentages.
2. Make and interpret a bar chart or a pie chart (using area principle).
3. Make and interpret a contingency table. When we want to see how two categorical variables are related, we put the counts (and/or %) in a two-way table.
4. Make and interpret bar charts and pie charts of marginal distributions. Along with marginal distribution, we also look at conditional distribution of a variable within each category of the other variable. This tells us the association between them and if there is dependence.