Factor Variables and Visualization (mtcars)

PART 1 - Data Setup

1) Import the inbuilt mtcars data and view it

data(mtcars)
View(mtcars)

2) Display the data structures of all the columns in mtcars using str()

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 ...

3a) Display the data structure of a specific column (e.g. cyl) using class()

class(mtcars$cyl)

## [1] "numeric"

class(mtcars$am)

## [1] "numeric"

class(mtcars$vs)

## [1] "numeric"

class(mtcars$gear)

## [1] "numeric"

3b) Convert a numeric or character column into a factor variable, using as.factor()

mtcars$cyl <- as.factor(mtcars$cyl)
mtcars$am <- as.factor(mtcars$am)
mtcars$vs <- as.factor(mtcars$vs)
mtcars$gear <- as.factor(mtcars$gear)

# Verify that their data type has been changed
class(mtcars$cyl)

## [1] "factor"

class(mtcars$am)

## [1] "factor"

class(mtcars$vs)

## [1] "factor"

class(mtcars$gear)

## [1] "factor"

3c) Review the “levels” of a factor variable, using levels()

levels(mtcars$cyl)

## [1] "4" "6" "8"

levels(mtcars$am)

## [1] "0" "1"

levels(mtcars$vs)

## [1] "0" "1"

levels(mtcars$gear)

## [1] "3" "4" "5"

3d) Change the “levels” of a factor variable, using levels()

# Consider mtcars$vs. "vs" tracks whether a car has a V-shaped engine (vs=1) or not (vs=0)

# 1) Verify that column vs is a factor variable. Convert it to a factor variable, if necessary
class(mtcars$vs)

## [1] "factor"

mtcars$vs <- as.factor(mtcars$vs)

# 2) Display vs in a table
table(mtcars$vs)

## 
##  0  1 
## 18 14

# 3) Check the current levels of vs
levels(mtcars$vs)

## [1] "0" "1"

# 4) Modify the levels of mtcars$vs 
mtcars$vs <- factor(mtcars$vs, levels = c("1", "0"))

# 5) Check that the levels of vs have changed
levels(mtcars$vs)

## [1] "1" "0"

table(mtcars$vs)

## 
##  1  0 
## 14 18

PART 2 - Data Visualization

Create a pie chart showing the proportion of cars from the mtcars data set that have different transmission types.

# 1) Create the Contingency Table for which you want a Pie Chart
tab1 <- table(mtcars$am)
tab1

## 
##  0  1 
## 19 13

# 2) Calculate percentages %
tab2 = prop.table(tab1)
tab2

## 
##       0       1 
## 0.59375 0.40625

percent <- round(tab2*100,1)
percent

## 
##    0    1 
## 59.4 40.6

# 3a) Create labels for each pie in the chart
pielabels <- paste(percent, "%", sep="")
pielabels

## [1] "59.4%" "40.6%"

# 3b) Generate the Pie Chart
pie(tab2, 
    col = c("lightblue","red"), 
    labels = pielabels,
    main = '% of cars by Transmission (am)', 
    cex = 1.1)

# 3c) Legend for the pie chart
legend("topright", 
       c("1","0"), 
       cex=0.8, 
       fill=rainbow(length(tab2)))

Pie Chart using the plotly package

library(plotly)
# 1) Create the Contingency Table for which you want a Pie Chart
tab1 <- table(mtcars$am)
tab2 = prop.table(tab1)

# 2) Create a dataframe containing the percentages %
percent <- round(tab2*100,1)
df = data.frame(percent)
df

##   Var1 Freq
## 1    0 59.4
## 2    1 40.6

# 3) Generate the Pie Chart
fig <- plot_ly(df, 
               labels = ~Var1, 
               values = ~Freq, 
               type = 'pie'
               )
fig <- fig %>% layout(title = '% of cars by Transmission (am)')

fig # 4) Display the Pie Chart

Display a barplot showing the percentage of of cars having different cylinders

# 1) Generate the Contingency Table with Proportions
tab1 <- table(mtcars$cyl)
tab2 <- prop.table(tab1)
tab3 <- round(tab2*100, 2)
tab3

## 
##     4     6     8 
## 34.38 21.88 43.75

# 2) Generate the Bar Plot
bp <- barplot(tab3,
              xlab = "cyl", ylab = "Percent (%)",
              main = "% Cars by number of cylinders (cyl=4,6,8)",
              col = c("yellow"), 
              beside = TRUE,
              ylim = c(0, 60))

# 3) (Optional) Display the percentages on the Bar Plot
text(bp, 0, tab3, pos=3)

Creating the same Bar Chart using the plotly package

# 1) Create the Contingency Table 
tab1 <- table(mtcars$cyl)
tab2 <- prop.table(tab1)
tab3 <- round(tab2*100, 2)
tab4 <- data.frame(tab3)
tab4

##   Var1  Freq
## 1    4 34.38
## 2    6 21.88
## 3    8 43.75

# 2) Set the x axis and y axis for the Bar Chart
mtcars$cyl <- as.factor(mtcars$cyl) # Check that cyl is a factor
x <- levels(mtcars$cyl)
y <- tab4$Freq

# 3) (Optional) Set the labels for the bar chart
mytext <- c('4 cyl', '6 cyl', '8 cyl')

# 4) Create the dataframe for the bar chart
df <- data.frame(x, y, mytext)
#df

# 5) Generate the bar chart
fig <- plot_ly(df, 
               x = ~x, 
               y = ~y, 
               type = 'bar',
               text = mytext, 
               textposition = 'auto',
               marker = list(color = 'rgb(258,202,225)')
              )
fig # 6) Display the bar chart

Display a Grouped Barplot showing the % of cars having different Cylinders & Transmissions

# 1) 
tab1 <- table(mtcars$am, mtcars$cyl)
tab2 <- prop.table(tab1)
tab3 <- round(tab2*100, 2)

# 2) Grouped bar-plot
bp <- barplot(tab3,
        xlab = "cyl", ylab = "Percent (%)",
        main = "% Cars by number of cylinders (cyl=4,6,8) and transmission (am=0,1)",
        col = c("lightblue","orange"), 
        beside = TRUE,
        ylim = c(0, 50),
        legend = rownames(tab3))

# 3) (Optional) Display percentage on the bars
text(bp, 0, tab3, pos = 3)

Display a Stacked Barplot showing the counts of of cars having different Cylinders & Transmission

# 1) Create table of counts
counts <- table(mtcars$am, mtcars$cyl)

# 2) Generate a Stacked Bar plot
barplot(counts, 
        col = c("white","black"),
                xlab = "cyl", ylab = "Counts",
                main = "Count Cars by cylinders (cyl=4,6,8) and transmission (am=0,1)",
                legend = rownames(counts))

PART 3 - Statistical Testing

Comparing Proportions using Chi-Square Goodness of Fit

attach(mtcars)

## The following object is masked from package:ggplot2:
## 
##     mpg

table_am = table(am)
addmargins(table_am)

## am
##   0   1 Sum 
##  19  13  32

prop.table(table_am)*100

## am
##      0      1 
## 59.375 40.625

CHI-SQUARE TEST FOR GIVEN PROBABILITIES

Null Hypothesis H0a: True proportion of am=1 cars is 60%, am=0 cars is 40%

chisq6040 = chisq.test(table_am,
                       p = c(0.6, 0.4)
                      )
chisq6040

## 
##  Chi-squared test for given probabilities
## 
## data:  table_am
## X-squared = 0.0052083, df = 1, p-value = 0.9425

Since p value > 0.05 , we fail to reject the Null Hypothesis H0a

Null Hypothesis H0b: True proportion of am=1 cars is 80%, am=0 cars is 20%

chisq8020 = chisq.test(table_am, 
                       p=c(0.8, 0.2))
chisq8020

## 
##  Chi-squared test for given probabilities
## 
## data:  table_am
## X-squared = 8.5078, df = 1, p-value = 0.003536

Since p value < 0.05 , we reject the Null Hypothesis H0b

Null Hypothesis H0c: True proportion of am=1 cars is 50%, am=0 is 50%

chisq5050 = chisq.test(table_am, p=c(0.5,0.5))
chisq5050

## 
##  Chi-squared test for given probabilities
## 
## data:  table_am
## X-squared = 1.125, df = 1, p-value = 0.2888

Since p value > 0.05 , we fail to reject the Null Hypothesis H0c

Cylinders

tablecyl = table(cyl)
addmargins(tablecyl)

## cyl
##   4   6   8 Sum 
##  11   7  14  32

prop.table(tablecyl)*100

## cyl
##      4      6      8 
## 34.375 21.875 43.750

Null Hypothesis H0d: True proportion of car cylinders = {4,6,8} is {1/3, 1/3, 1/3}

chisq333 = chisq.test(tablecyl, 
                       p = c(1/3, 1/3, 1/3))
chisq333

## 
##  Chi-squared test for given probabilities
## 
## data:  tablecyl
## X-squared = 2.3125, df = 2, p-value = 0.3147

Since p value > 0.05, we fail to reject the Null Hypothesis H0d