One-way and Two-way Contingency Tables

We are using here the Arthritis dataset from the package vcd.
The data represent a double-blind clinical trial of new treatments for rheumatoid arthritis.

library(vcd)
head(Arthritis)   # top few observations from the data

  ID Treatment  Sex Age Improved
1 57   Treated Male  27     Some
2 46   Treated Male  29     None
3 77   Treated Male  30     None
4 17   Treated Male  32   Marked
5 36   Treated Male  46   Marked
6 23   Treated Male  58   Marked

str(Arthritis)  # structure of the data frame

'data.frame':   84 obs. of  5 variables:
 $ ID       : int  57 46 77 17 36 23 75 39 33 55 ...
 $ Treatment: Factor w/ 2 levels "Placebo","Treated": 2 2 2 2 2 2 2 2 2 2 ...
 $ Sex      : Factor w/ 2 levels "Female","Male": 2 2 2 2 2 2 2 2 2 2 ...
 $ Age      : int  27 29 30 32 46 58 59 59 63 63 ...
 $ Improved : Ord.factor w/ 3 levels "None"<"Some"<..: 2 1 1 3 3 3 1 3 1 1 ...

Treatment(Placebo, Treated), Sex(Male, Female), and Improved (None, Some, Marked) are all categorical factors.

Simple frequrency counts using the table() function.

mytable <- with(Arthritis, table(Improved))
mytable  # frequencies

Improved
  None   Some Marked 
    42     14     28 

Frequencies into proportions and percentages with prop.table() function.

prop.table(mytable) # proportions

Improved
     None      Some    Marked 
0.5000000 0.1666667 0.3333333 

prop.table(mytable)*100 # percentages

Improved
    None     Some   Marked 
50.00000 16.66667 33.33333 

mytable <- xtabs(~ Treatment+Improved, data=Arthritis)
mytable # frequencies

         Improved
Treatment None Some Marked
  Placebo   29    7      7
  Treated   13    7     21

Generate marginal frequencies and proportions using the margin.table() and prop.table() functions.

margin.table(mytable,1) #row sums

Treatment
Placebo Treated 
     43      41 

prop.table(mytable, 1) # row proportions

         Improved
Treatment      None      Some    Marked
  Placebo 0.6744186 0.1627907 0.1627907
  Treated 0.3170732 0.1707317 0.5121951

The index (1) refers to the first variable in the table() statement.

Generate marginal frequencies and proportions using the margin.table() and prop.table() functions.

margin.table(mytable, 2) # column sums

Improved
  None   Some Marked 
    42     14     28 

prop.table(mytable, 2) # column proportions

         Improved
Treatment      None      Some    Marked
  Placebo 0.6904762 0.5000000 0.2500000
  Treated 0.3095238 0.5000000 0.7500000

The index (2) refers to the second variable in the table() statement.

We can obtained the cell proportions using the prop.table() statement.

prop.table(mytable) # cell proportions

         Improved
Treatment       None       Some     Marked
  Placebo 0.34523810 0.08333333 0.08333333
  Treated 0.15476190 0.08333333 0.25000000

Row and column sums using the funtion addmargins().

addmargins(mytable) # add row and column sums to table

         Improved
Treatment None Some Marked Sum
  Placebo   29    7      7  43
  Treated   13    7     21  41
  Sum       42   14     28  84

Sum margins for all the variable.

addmargins(prop.table(mytable))

         Improved
Treatment       None       Some     Marked        Sum
  Placebo 0.34523810 0.08333333 0.08333333 0.51190476
  Treated 0.15476190 0.08333333 0.25000000 0.48809524
  Sum     0.50000000 0.16666667 0.33333333 1.00000000

Column sum.

addmargins(prop.table(mytable, 1), 2) # column sum

         Improved
Treatment      None      Some    Marked       Sum
  Placebo 0.6744186 0.1627907 0.1627907 1.0000000
  Treated 0.3170732 0.1707317 0.5121951 1.0000000

Row sum.

addmargins(prop.table(mytable, 2), 1) # row sum

         Improved
Treatment      None      Some    Marked
  Placebo 0.6904762 0.5000000 0.2500000
  Treated 0.3095238 0.5000000 0.7500000
  Sum     1.0000000 1.0000000 1.0000000

Creating two way tables using CrossTable() function in the gmodels() package.

library(gmodels)
CrossTable(Arthritis$Treatment, Arthritis$Improved)