Contingency Tables & Visualization

1. Reading the data

# reading the data
data(mtcars)
colnames(mtcars)

##  [1] "mpg"  "cyl"  "disp" "hp"   "drat" "wt"   "qsec" "vs"   "am"   "gear"
## [11] "carb"

attach(mtcars)
View(mtcars)

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)

2. Proportions and Percentages

prop.table()

1) Rows and Columns add up to 100%

t0 = table(cyl, gear)
t0

##    gear
## cyl  3  4  5
##   4  1  8  2
##   6  2  4  1
##   8 12  0  2

t1 = 100*prop.table(t0)
t1

##    gear
## cyl      3      4      5
##   4  3.125 25.000  6.250
##   6  6.250 12.500  3.125
##   8 37.500  0.000  6.250

t2 = addmargins(t1)
t2

##      gear
## cyl         3       4       5     Sum
##   4     3.125  25.000   6.250  34.375
##   6     6.250  12.500   3.125  21.875
##   8    37.500   0.000   6.250  43.750
##   Sum  46.875  37.500  15.625 100.000

2) Rows add up to 100%

u0 = table(cyl, gear)
u0

##    gear
## cyl  3  4  5
##   4  1  8  2
##   6  2  4  1
##   8 12  0  2

u1 = 100*prop.table(u0,1)
u1

##    gear
## cyl         3         4         5
##   4  9.090909 72.727273 18.181818
##   6 28.571429 57.142857 14.285714
##   8 85.714286  0.000000 14.285714

u2 = addmargins(u1,2)
u2

##    gear
## cyl          3          4          5        Sum
##   4   9.090909  72.727273  18.181818 100.000000
##   6  28.571429  57.142857  14.285714 100.000000
##   8  85.714286   0.000000  14.285714 100.000000

3) Columns add up to 100%

v0 = table(cyl, gear)
v1 = 100*prop.table(v0,2)
v1

##    gear
## cyl         3         4         5
##   4  6.666667 66.666667 40.000000
##   6 13.333333 33.333333 20.000000
##   8 80.000000  0.000000 40.000000

addmargins()

v2 = addmargins(v1,1)
v2

##      gear
## cyl            3          4          5
##   4     6.666667  66.666667  40.000000
##   6    13.333333  33.333333  20.000000
##   8    80.000000   0.000000  40.000000
##   Sum 100.000000 100.000000 100.000000

round()

t1

##    gear
## cyl      3      4      5
##   4  3.125 25.000  6.250
##   6  6.250 12.500  3.125
##   8 37.500  0.000  6.250

t2 = addmargins(t1)
t3 = round(t2,2)
t3

##      gear
## cyl        3      4      5    Sum
##   4     3.12  25.00   6.25  34.38
##   6     6.25  12.50   3.12  21.88
##   8    37.50   0.00   6.25  43.75
##   Sum  46.88  37.50  15.62 100.00

3. Visualization

Create a Pie Chart, Showing the proportion of {am = 1 & am = 0} cars.

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

# 2) Calculate percentages %
tab2 = prop.table(tab1)
percent <- round(tab2*100,1)

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


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

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

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

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


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

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

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)",
                beside = FALSE,
                legend = rownames(counts))