7.2Frequency and contingency tables

graphically displaying results. We’ll be using functions in the basic installation, along with functions from the vcd and gmodels packages. In the following examples, assume that A, B, and C represent categorical variables.

The data for this section come from the Arthritis dataset included with the vcd package. The data are from Kock & Edward (1988) and represent a double-blind clinical trial of new treatments for rheumatoid arthritis. Here are the first few observations:

>library(vcd)

>head(Arthritis)

Treatment (Placebo, Treated), Sex (Male, Female), and Improved (None, Some, Marked) are all categorical factors. In the next section, you’ll create frequency and contingency tables (cross-classifications) from the data.

7.2.1Generating frequency tables

R provides several methods for creating frequency and contingency tables. The most important functions are listed in table 7.1.

Table 7.1 Functions for creating and manipulating contingency tables

In the following sections, we’ll use each of these functions to explore categorical variables. We’ll begin with simple frequencies, followed by two-way contingency tables, and end with multiway contingency tables. The first step is to create a table using either the table() or xtabs() function and then manipulate it using the other functions.

ONE-WAY TABLES

You can generate simple frequency counts using the table() function. Here’s an example:

>mytable <- with(Arthritis, table(Improved))

>mytable

Improved

None Some Marked

42 14 28

You can turn these frequencies into proportions with prop.table()

> prop.table(mytable) Improved

None Some Marked 0.500 0.167 0.333

or into percentages using prop.table()*100:

> prop.table(mytable)*100 Improved

None Some Marked

50.016.7 33.3

Here you can see that 50% of study participants had some or marked improvement (16.7 + 33.3).

TWO-WAY TABLES

For two-way tables, the format for the table() function is

mytable <- table(A, B)

where A is the row variable and B is the column variable. Alternatively, the xtabs() function allows you to create a contingency table using formula-style input. The format is

mytable <- xtabs(~ A + B, data=mydata)

where mydata is a matrix or data frame. In general, the variables to be cross-classified appear on the right of the formula (that is, to the right of the ~) separated by + signs. If a variable is included on the left side of the formula, it’s assumed to be a vector of frequencies (useful if the data have already been tabulated).

For the Arthritis data, you have

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

>mytable

You can generate marginal frequencies and proportions using the margin.table() and prop.table() functions, respectively. For row sums and row proportions, you have

> margin.table(mytable, 1) Treatment

Placebo Treated 3 41

> prop.table(mytable, 1)

Improved

Treatment None Some Marked

Placebo 0.674 0.163 0.163

Treated 0.317 0.171 0.512

The index (1) refers to the first variable in the table() statement. Looking at the table, you can see that 51% of treated individuals had marked improvement, compared to 16% of those receiving a placebo.

For column sums and column proportions, you have

> margin.table(mytable, 2)

Here, the index (2) refers to the second variable in the table() statement. Cell proportions are obtained with this statement:

> prop.table(mytable)

Improved

Treatment None Some Marked

Placebo 0.3452 0.0833 0.0833

Treated 0.1548 0.0833 0.2500

You can use the addmargins() function to add marginal sums to these tables. For example, the following code adds a Sum row and column:

When using addmargins(), the default is to create sum margins for all variables in a table. In contrast, the following code adds a Sum column alone:

> addmargins(prop.table(mytable, 1), 2)

Improved

Treatment None Some Marked Sum

Placebo 0.674 0.163 0.163 1.000

Treated 0.317 0.171 0.512 1.000

Similarly, this code adds a Sum row:

> addmargins(prop.table(mytable, 2), 1)

In the table, you see that 25% of those patients with marked improvement received a placebo.

NOTE The table() function ignores missing values (NAs) by default. To include NA as a valid category in the frequency counts, include the table option useNA="ifany".

A third method for creating two-way tables is the CrossTable() function in the gmodels package. The CrossTable() function produces two-way tables modeled after PROC FREQ in SAS or CROSSTABS in SPSS. The following listing shows an example.

Listing 7.10 Two-way table using CrossTable

>library(gmodels)

>CrossTable(Arthritis$Treatment, Arthritis$Improved)