Descriptive Statistics for one Categorical Variable

We’ll look at the mtcars dataset, which is included with the base distribution of R as a dataframe. First we’ll run a few standard commands to examine a new dataframe when we know nothing but the name of the dataframe.

str(mtcars)

## 'data.frame':    32 obs. of  11 variables:
##  $ mpg : num  21 21 22.8 21.4 18.7 18.1 14.3 24.4 22.8 19.2 ...
##  $ cyl : num  6 6 4 6 8 6 8 4 4 6 ...
##  $ disp: num  160 160 108 258 360 ...
##  $ hp  : num  110 110 93 110 175 105 245 62 95 123 ...
##  $ drat: num  3.9 3.9 3.85 3.08 3.15 2.76 3.21 3.69 3.92 3.92 ...
##  $ wt  : num  2.62 2.88 2.32 3.21 3.44 ...
##  $ qsec: num  16.5 17 18.6 19.4 17 ...
##  $ vs  : num  0 0 1 1 0 1 0 1 1 1 ...
##  $ am  : num  1 1 1 0 0 0 0 0 0 0 ...
##  $ gear: num  4 4 4 3 3 3 3 4 4 4 ...
##  $ carb: num  4 4 1 1 2 1 4 2 2 4 ...

summary(mtcars)

##       mpg             cyl             disp             hp       
##  Min.   :10.40   Min.   :4.000   Min.   : 71.1   Min.   : 52.0  
##  1st Qu.:15.43   1st Qu.:4.000   1st Qu.:120.8   1st Qu.: 96.5  
##  Median :19.20   Median :6.000   Median :196.3   Median :123.0  
##  Mean   :20.09   Mean   :6.188   Mean   :230.7   Mean   :146.7  
##  3rd Qu.:22.80   3rd Qu.:8.000   3rd Qu.:326.0   3rd Qu.:180.0  
##  Max.   :33.90   Max.   :8.000   Max.   :472.0   Max.   :335.0  
##       drat             wt             qsec             vs        
##  Min.   :2.760   Min.   :1.513   Min.   :14.50   Min.   :0.0000  
##  1st Qu.:3.080   1st Qu.:2.581   1st Qu.:16.89   1st Qu.:0.0000  
##  Median :3.695   Median :3.325   Median :17.71   Median :0.0000  
##  Mean   :3.597   Mean   :3.217   Mean   :17.85   Mean   :0.4375  
##  3rd Qu.:3.920   3rd Qu.:3.610   3rd Qu.:18.90   3rd Qu.:1.0000  
##  Max.   :4.930   Max.   :5.424   Max.   :22.90   Max.   :1.0000  
##        am              gear            carb      
##  Min.   :0.0000   Min.   :3.000   Min.   :1.000  
##  1st Qu.:0.0000   1st Qu.:3.000   1st Qu.:2.000  
##  Median :0.0000   Median :4.000   Median :2.000  
##  Mean   :0.4062   Mean   :3.688   Mean   :2.812  
##  3rd Qu.:1.0000   3rd Qu.:4.000   3rd Qu.:4.000  
##  Max.   :1.0000   Max.   :5.000   Max.   :8.000

Note that there are some numerical variables here, which are categorical in nature. One example is ‘am,’ which tells us whether the car has an automatic (am = 0) or manual transmission (am = 1). To create a variable that R will treat as categorical, we need to run a special command.

mtcars$TranType = as.factor(mtcars$am)

Now we can run the standard commands to exploare a categorical variable.

Simple Counts

# Get simple counts of each categorical value
table(mtcars$TranType)

## 
##  0  1 
## 19 13

Note that since TranType is within the dataframe mtcars, we must refer to it as mtcars$TranType

Proportions

table(mtcars$TranType)/length(mtcars$TranType)

## 
##       0       1 
## 0.59375 0.40625

Create a barplot of the values

barplot(table(mtcars$TranType))

Note that we must run the barplot command on a table, not the raw data.

Use the dataframe cdc loaded in Lab 1 for the following exercises.

Load the Data

load("cdc.Rdata")

Exercise

Show the counts of the values of the categorical variable genhlth.

Solution

table(cdc$genhlth)

## 
## excellent very good      good      fair      poor 
##      4657      6972      5675      2019       677

Show the Proportions

Solution

table(cdc$genhlth)/nrow(cdc)

## 
## excellent very good      good      fair      poor 
##   0.23285   0.34860   0.28375   0.10095   0.03385

Create a barplot

barplot(table(cdc$genhlth))

Question

Identify the most common and least common values of cdc$genhlth.

Solution

The most common value is “very good”. The least common value is “poor”.