4A: Examining Categorical Variables

Data Sets

load(url('https://github.com/hungtong/DS-01-101/raw/refs/heads/main/dataset/l4a_data.rdata'))
load(url('https://github.com/hungtong/DS-01-101/raw/refs/heads/main/dataset/cdc.rdata'))

Topics

Basic variable types
Frequency distribution, mode, and bar plot
Stacked and side-by-side bar plot

Basic variable types

Data are commonly organized into a data matrix. In this format, each row is an observation and each column is a variable or feature.

Roughly speaking, a variable can be numerical or categorical.

A numerical variable represents numbers that are meaningful to add, subtract, or take averages.
A categorical variable refers to specific categories that describe a characteristic.

Examining a categorical variable

A frequency distribution is a tabular summary of data showing the number (frequency) of observations in each categories.

The mode is the category that appears the most. There can be multiple modes.
A bar plot visualizes the frequency distribution of a categorical variable using bars of different heights.

Examining two categorical variables

A contingency table is a tabular summary of data for two categorical variables showing the frequency of their shared characteristics.

Stacked bar plot can be used to visualize the contingency table.

Side-by-side bar plot is also a good option.

Obtaining frequency distribution and bar plot in R

Frequency distribution for a categorical variable can be obtained using the table() function.
Bar plot can be generated using the barplot() function. Horizontal or vertical bars can be made by adjusting horiz = TRUE.
Common graphical parameters in base R plotting include:
- col - add color to the plot
- main - main title label
- xlab - label for x-axis
- ylab - label for y-axis
- xlim - x-axis range
- ylim - y-axis range
- cex.main - size of main title
- cex.lab - size of axis labels
- cex.axis - size of tick labels
For predefined and hex-value colors, check out the following websites:

💻 Hands-On

Obtain the frequency distribution and bar plot of the soft_drink data set.

Answer

To obtain the frequency distribution and bar plot of the soft_drink data set, we use the table() and barplot() functions.

freq <- table(soft_drink)
freq

soft_drink
 Coca-Cola  Diet Coke Dr. Pepper      Pepsi     Sprite 
        19          8          5         13          5

barplot(
  freq,
  col       = "#FFCC00",       # add color
  main      = "Bar Plot",      # main title
  xlab      = "Soft Drink",    # label for x-axis
  ylab      = "Frequency",     # label for y-axis
  cex.main  = 1.5,             # size of title
  cex.lab   = 1.2,             # size of axis labels 
  cex.axis  = 1.2,             # size of tick labels
  cex.names = 1.2,             # size of categories
  ylim      = c(0, 20)         # y-axis range
)

💻 Hands-On

Try the following code and describe the difference between the two methods of generating a bar plot for the activity data set.

freq <- table(activity)

# Method 1
barplot(freq)

# Method 2
barplot(
  c(2183, 757, 1520), 
  names.arg = c('Sedentary', 'Active', 'Very Active')
)

Answer

Note the frequency distribution of the activity data set.

freq <- table(activity)
freq

activity
     Active   Sedentary Very Active 
        757        2183        1520

Using method 1, we obtain

# Method 1
barplot(freq)

By default, table() and barplot() will arrange categories in the alphabetical order, which is not necessarily the natural order of ordinal categories. For ordinal categories, it is better than to manually rearrange the categories as in method 2.

# Method 2
barplot(
  c(2183, 757, 1520), 
  names.arg = c('Sedentary', 'Active', 'Very Active')
)

Stacked and side-by-side bar plot in R

For two categorical variables, the table() function produces a contingency table.
By default, stacked bar plot will be made. However, side-by-side bar plot can be made by setting beside = TRUE.
Setting legend = TRUE and giving a vector of colors to col will help differentiate the categories.

💻 Hands-On

Obtain the contingency table and bar plot of the pet and vacation data set.

Answer

To obtain the contingency table and bar plot of the pet and vacation data set, we use the table() and barplot() functions.

conti_tab <- table(pet, vacation)
conti_tab

           vacation
pet         Beach City Mountain
  No Pet       20   25       15
  Pet Owner    30   22       25

barplot(
  conti_tab, 
  beside    = TRUE, 
  legend    = TRUE, 
  col       = c("steelblue4", "steelblue1"),
  xlab      = "Preferred Vacation Type",    
  ylab      = "Frequency",                     
  cex.lab   = 1.2,                        
  cex.axis  = 1.2,                       
  cex.names = 1.2,                      
  ylim      = c(0, 50)                     
)

Behavioral survey from the Centers for Disease Control and Prevention (CDC)

The data set is slightly modified from OpenIntro,

The Behavioral Risk Factor Surveillance System (BRFSS) is an annual telephone survey of 350,000 people in the United States collected by the Centers for Disease Control and Prevention (CDC). As its name implies, the BRFSS is designed to identify risk factors in the adult population and report emerging health trends. For example, respondents are asked about their diet and weekly physical activity, their HIV/AIDS status, possible tobacco use, and even their level of healthcare coverage. The BRFSS Web site contains a complete description of the survey, the questions that were asked and even research results that have been derived from the data.

This data set is a random sample of 20,000 people from the BRFSS survey conducted in 2000. While there are over 200 questions or variables in this dataset, this data set only includes 9 variables.

The data set has the following variables:

genhlth - General health, with categories Excellent, Very Good, Good, Fair, and Poor
exerany - Whether the respondent exercised in the past month
hlthplan - Whether respondent has some form of health coverage
smoke100 - Whether respondent has smoked at least 100 cigarettes in their entire life
height - Respondent’s height in inches
weight - Respondent’s weight in pounds
wtdesire - Respondent’s desired weight in pounds
age - Respondent’s age in years
gender - Respondent’s gender

💻 Hands-On

Retrieve the first few respondents, a vector of variable names, and the structure of the cdc data set.

Answer

The first few respondents are

head(cdc)

    genhlth exerany hlthplan smoke100 height weight wtdesire age gender
1      Good      No      Yes       No     70    175      175  77   Male
2      Good      No      Yes      Yes     64    125      115  33 Female
3      Good     Yes      Yes      Yes     60    105      105  49 Female
4      Good     Yes      Yes       No     66    132      124  42 Female
5 Very Good      No      Yes       No     61    150      130  55 Female
6 Very Good     Yes      Yes       No     64    114      114  55 Female

A vector of variable names is

colnames(cdc)    # names(cdc)

[1] "genhlth"  "exerany"  "hlthplan" "smoke100" "height"   "weight"   "wtdesire"
[8] "age"      "gender"

The structure of the cdc data set is described as follows:

str(cdc)

'data.frame':   20000 obs. of  9 variables:
 $ genhlth : Factor w/ 5 levels "Excellent","Very Good",..: 3 3 3 3 2 2 2 2 3 3 ...
 $ exerany : Factor w/ 2 levels "Yes","No": 2 2 1 1 2 1 1 2 2 1 ...
 $ hlthplan: Factor w/ 2 levels "Yes","No": 1 1 1 1 1 1 1 1 1 1 ...
 $ smoke100: Factor w/ 2 levels "Yes","No": 2 1 1 2 2 2 2 2 1 2 ...
 $ height  : num  70 64 60 66 61 64 71 67 65 70 ...
 $ weight  : int  175 125 105 132 150 114 194 170 150 180 ...
 $ wtdesire: int  175 115 105 124 130 114 185 160 130 170 ...
 $ age     : int  77 33 49 42 55 55 31 45 27 44 ...
 $ gender  : Factor w/ 2 levels "Male","Female": 1 2 2 2 2 2 1 1 2 1 ...

💻 Hands-On

How many respondents are there? How many variables? Identify the type of each variable.

Answer

The number of respondents is

nrow(cdc)

[1] 20000

The number of variables is

ncol(cdc)

[1] 9

A different way to explore the number of respondents and variables is

dim(cdc)

[1] 20000     9

In the data set, height, weight, wtdesire, and age are numerical, while the rest are categorical.

💻 Hands-On

Are there any missing values in the data set?

Answer

There are no missing values in the data set. Recall that the complete.cases() function gives a logical vector indicating which observations have no missing values.

sum(!complete.cases(cdc))

[1] 0

💻 Hands-On

Examine the general health of respondents using appropriate summary statistics and graphical displays.

Answer

genhlth represents the general health of respondents. This is an ordinal categorical variable with 5 levels. To summarize this variable, we can look at its frequency distribution and bar plot.

freq <- table(cdc$genhlth)
freq


Excellent Very Good      Good      Fair      Poor 
     4657      6972      5675      2019       677

barplot(freq, col = 'tomato', main = 'General Health')

Most respondents have Very Good and Good health, which is a positive thing. Fair and Poor are much less common.

💻 Hands-On

Examine the number of respondents who have smoked 100 cigarettes in their lifetime using appropriate summary statistics and graphical displays.

Answer

smoke100 indicates respondents who respondents who have smoked 100 cigarettes in their lifetime. This is a nomial categorical variable with two levels.

freq <- table(cdc$smoke100)
freq


  Yes    No 
 9441 10559

barplot(freq, col = 'chartreuse3', main = 'Smoking Status')

There are more non-smokers but the number of smokers is close to half of the data set.

💻 Hands-On

What is the relationship between smoking habits and general health?

Answer

To explore the relationship between two categorical variables, smoking habit smoke100 and general health genhlth, we can use contingency table and side-by-side bar plots.

conti_tab <- table(cdc$smoke100, cdc$genhlth)
conti_tab

     
      Excellent Very Good Good Fair Poor
  Yes      1778      3214 2893 1108  448
  No       2879      3758 2782  911  229

barplot(conti_tab, beside = TRUE, legend = TRUE,
        col = c("aquamarine1", "cadetblue4"))

Respondents with Excellent and Very Good health tend to be non-smokers (especially Excellent), whereas respondents with Fair and Poor health tend to be smokers.