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 Markedstr(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 28Frequencies into proportions and percentages with prop.table() function.
prop.table(mytable) # proportions## Improved
## None Some Marked
## 0.5000000 0.1666667 0.3333333prop.table(mytable)*100 # percentages## Improved
## None Some Marked
## 50.00000 16.66667 33.33333mytable <- 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 41prop.table(mytable, 1) # row proportions## Improved
## Treatment None Some Marked
## Placebo 0.6744186 0.1627907 0.1627907
## Treated 0.3170732 0.1707317 0.5121951The 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 28prop.table(mytable, 2) # column proportions## Improved
## Treatment None Some Marked
## Placebo 0.6904762 0.5000000 0.2500000
## Treated 0.3095238 0.5000000 0.7500000The 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 0.25000000Row 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 84Sum 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 1.00000000Column 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 1.0000000Row 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 1.0000000Creating two way tables using CrossTable() function in the gmodels() package.
library(gmodels)
CrossTable(Arthritis$Treatment, Arthritis$Improved)##
##
## Cell Contents
## |-------------------------|
## | N |
## | Chi-square contribution |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 84
##
##
## | Arthritis$Improved
## Arthritis$Treatment | None | Some | Marked | Row Total |
## --------------------|-----------|-----------|-----------|-----------|
## Placebo | 29 | 7 | 7 | 43 |
## | 2.616 | 0.004 | 3.752 | |
## | 0.674 | 0.163 | 0.163 | 0.512 |
## | 0.690 | 0.500 | 0.250 | |
## | 0.345 | 0.083 | 0.083 | |
## --------------------|-----------|-----------|-----------|-----------|
## Treated | 13 | 7 | 21 | 41 |
## | 2.744 | 0.004 | 3.935 | |
## | 0.317 | 0.171 | 0.512 | 0.488 |
## | 0.310 | 0.500 | 0.750 | |
## | 0.155 | 0.083 | 0.250 | |
## --------------------|-----------|-----------|-----------|-----------|
## Column Total | 42 | 14 | 28 | 84 |
## | 0.500 | 0.167 | 0.333 | |
## --------------------|-----------|-----------|-----------|-----------|
##
##