Transforming contingency tables into frequency tables in R

Problem

We want to tranform a contingency table into a frequency table in R.

# Contingency table
tbl <- table (mtcars[, c("am", "gear")])

   gear
am   3  4  5
  0 15  4  0
  1  0  8  5

Frequency tables

We transform the contingency table into a data frame.

df <- as.data.frame(tbl)
df

  am gear Freq
1  0    3   15
2  1    3    0
3  0    4    4
4  1    4    8
5  0    5    0
6  1    5    5

Transforming frequency tables in contingency tables

To transform a frequency table back to a contingency table.

ftable(xtabs(Freq ~ am + gear, data = df)) 

   gear  3  4  5
am              
0       15  4  0
1        0  8  5

It is the equivalent of:

ftable(mtcars[, c("am", "gear")])

References

• Contingency tables in R
• Proportion tables in R

Proportion tables in R

Problem

We want to create proportion tables for one or multiple variables.

Solution

• One variable

tabla <- table(mtcars$am)
prop.table(tabla)

      0       1 
0.59375 0.40625

• Two variables

tabla <- table(mtcars[, c("am", "gear")])
prop.table(tabla)

   gear
am        3       4       5
  0 0.46875 0.12500 0.00000
  1 0.00000 0.25000 0.15625

The prop.table function has two arguments:
• x, table created with the function table
• margin, with three possible values:
  Null - x/sum(x) default like in the previous example.
  1 - proportion calculated by rows.
  2 - proportion calculated by columns.


# By row
prop.table(tabla, 1)

   gear
am          3         4         5
  0 0.7894737 0.2105263 0.0000000
  1 0.0000000 0.6153846 0.3846154

# By column
prop.table(tabla, 2)

   gear
am          3         4         5
  0 1.0000000 0.3333333 0.0000000
  1 0.0000000 0.6666667 1.0000000

• Three variables

tabla <- table(mtcars[, c("am", "gear", "cyl")])
prop.table(tabla)

, , cyl = 4

   gear
am        3       4       5
  0 0.03125 0.06250 0.00000
  1 0.00000 0.18750 0.06250

, , cyl = 6

   gear
am        3       4       5
  0 0.06250 0.06250 0.00000
  1 0.00000 0.06250 0.03125

, , cyl = 8

   gear
am        3       4       5
  0 0.37500 0.00000 0.00000
  1 0.00000 0.00000 0.06250

• Flat Contingency Table

In the previous example, a better approach would be to create a flat contingency table..

tabla <- ftable(mtcars[, c("am", "gear", "cyl")])
prop.table(tabla)

        cyl       4       6       8
am gear                            
0  3        0.03125 0.06250 0.37500
   4        0.06250 0.06250 0.00000
   5        0.00000 0.00000 0.00000
1  3        0.00000 0.00000 0.00000
   4        0.18750 0.06250 0.00000
   5        0.06250 0.03125 0.06250

• Percentage table

We can use the function round.

round(prop.table(tabla)*100, 2)

         cyl     4     6     8
am gear                      
0  3         3.12  6.25 37.50
   4         6.25  6.25  0.00
   5         0.00  0.00  0.00
1  3         0.00  0.00  0.00
   4        18.75  6.25  0.00
   5         6.25  3.12  6.25

round(prop.table(tabla, 1)*100, 2) # By row, am y gear.

        cyl     4     6     8
am gear                      
0  3         6.67 13.33 80.00
   4        50.00 50.00  0.00
   5          NaN   NaN   NaN
1  3          NaN   NaN   NaN
   4        75.00 25.00  0.00
   5        40.00 20.00 40.00

round(prop.table(tabla, 2)*100, 2) # By column, cyl

        cyl     4     6     8
am gear                      
0  3         9.09 28.57 85.71
   4        18.18 28.57  0.00
   5         0.00  0.00  0.00
1  3         0.00  0.00  0.00
   4        54.55 28.57  0.00
   5        18.18 14.29 14.29

References

• Contingency tables in R

Contingency tables in R

Problem

We want to create a contingency table for one or multiple variables.

Solution

• One variable

table(mtcars$am)

 0  1 
19 13 

• Two variables

table(mtcars$am, mtcars$gear)

     3  4  5
  0 15  4  0
  1  0  8  5

If we want to include the names of the variables:

table(mtcars[, c("am", "gear")]) 
tabla <- table(mtcars[, 9:10])
# or the argument dnn:
table(mtcars$am, mtcars$gear, dnn = c("am", "gear"))

   gear
am   3  4  5
  0 15  4  0
  1  0  8  5

• Three variables

table(mtcars[, c("am", "gear", "cyl")])

, , cyl = 4

   gear
am   3  4  5
  0  1  2  0
  1  0  6  2

, , cyl = 6

   gear
am   3  4  5
  0  2  2  0
  1  0  2  1

, , cyl = 8

   gear
am   3  4  5
  0 12  0  0
  1  0  0  2

• Flat contingency tables

In the previous example, a better approach would be to create a flat contingency table.

ftable(mtcars[, c("am", "gear", "cyl")])

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

We use the arguments row.vars and col.vars to provide the numbers or names of the variables to be used for the rows and columns of the flat contingency table. If neither of these two is given, the last variable is used for the columns. In our example the variable cyl.

ftable(mtcars[, c("am", "gear", "cyl")], col.vars = c(1, 2))

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

Alternative

The function xtabs creates contingency tables using a formula interface, each variable separated by +.

# One variable
xtabs(~ am, mtcars)
# Two variables
xtabs(~ am + gear, mtcars)
# Three variables
xtabs(~ am + gear + cyl, mtcars)
# Flat contingency table
ftable(xtabs(~ am + gear + cyl, mtcars))

Related posts

• Spanish version
• Proportion tables in R

Tablas de contingencia en R

Problema

Deseamos crear una tabla de contingencia para uno o varios factores.

Solución

• Una dimensión

table(mtcars$am)

 0  1 
19 13 

• Dos dimensiones

table(mtcars$am, mtcars$gear)

Como hemos especificado dos vectores, no aparece el nombre de las dimensiones: am y gear.

     3  4  5
  0 15  4  0
  1  0  8  5

table(mtcars[, c("am", "gear")]) 
tabla <- table(mtcars[, 9:10])
# O usando el argumento dnn:
table(mtcars$am, mtcars$gear, dnn = c("am", "gear"))

   gear
am   3  4  5
  0 15  4  0
  1  0  8  5

• Tres dimensiones

table(mtcars[, c("am", "gear", "cyl")])

, , cyl = 4

   gear
am   3  4  5
  0  1  2  0
  1  0  6  2

, , cyl = 6

   gear
am   3  4  5
  0  2  2  0
  1  0  2  1

, , cyl = 8

   gear
am   3  4  5
  0 12  0  0
  1  0  0  2

• Tabla de contingencia plana

En el caso anterior sería más claro crear una tabla de contingencia plana (Flat Contingency Table).

ftable(mtcars[, c("am", "gear", "cyl")])

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

Podemos usar los argumentos row.vars y col.vars para especificar las filas y columnas que deseamos en la tabla de contingencia. Si ninguno es especificado, la última variable es usada para las columnas. Como en nuestro caso cyl.

ftable(mtcars[, c("am", "gear", "cyl")], col.vars = c(1, 2))

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

Alternativa

La función xtabs crea tablas de contingencia mediante el formato de fórmula, con cada variable separada por un +.

# Una dimensión
xtabs(~ am, mtcars)
# Dos dimensiones
xtabs(~ am + gear, mtcars)
# Tres dimensiones
xtabs(~ am + gear + cyl, mtcars)
# Tabla de contingencia plana
ftable(xtabs(~ am + gear + cyl, mtcars))

Referencias

• Tablas de proporciones en R
• Transformar tabla de contigencia en tabla de de frecuencias