# Creating and manipulating frequency tables

#### 2022-04-21

R provides many methods for creating frequency and contingency tables. Several are described below. In the examples below, we use some real examples and some anonymous ones, where the variables A, B, and C represent categorical variables, and X represents an arbitrary R data object.

## Forms of frequency data

The first thing you need to know is that categorical data can be represented in three different forms in R, and it is sometimes necessary to convert from one form to another, for carrying out statistical tests, fitting models or visualizing the results. Once a data object exists in R, you can examine its complete structure with the str() function, or view the names of its components with the names() function.

### Case form

Categorical data in case form are simply data frames containing individual observations, with one or more factors, used as the classifying variables. In case form, there may also be numeric covariates. The total number of observations is nrow(X), and the number of variables is ncol(X).

Example:

The Arthritis data is available in case form in the vcd package. There are two explanatory factors: Treatment and Sex. Age is a numeric covariate, and Improved is the response— an ordered factor, with levels None < Some < Marked. Excluding Age, this represents a $$2 \times 2 \times 3$$ contingency table for Treatment, Sex and Improved, but in case form.

names(Arthritis)      # show the variables
## [1] "ID"        "Treatment" "Sex"       "Age"       "Improved"

str(Arthritis)        # show the structure
## '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 ...
##  $Improved : Ord.factor w/ 3 levels "None"<"Some"<..: 2 1 1 3 3 3 1 3 1 1 ... head(Arthritis,5) # first 5 observations, same as Arthritis[1:5,] ## ID Treatment Sex Age Improved ## 1 57 Treated Male 27 Some ## 2 46 Treated Male 29 None ## 3 77 Treated Male 30 None ## 4 17 Treated Male 32 Marked ## 5 36 Treated Male 46 Marked ### Frequency form Data in frequency form is also a data frame containing one or more factors, and a frequency variable, often called Freq or count. The total number of observations is: sum(X$Freq), sum(X[,"Freq"]) or some equivalent form.

The number of cells in the table is given by nrow(X).

Example: For small frequency tables, it is often convenient to enter them in frequency form using expand.grid() for the factors and c() to list the counts in a vector. The example below, from (Agresti, 2002) gives results for the 1991 General Social Survey, with respondents classified by sex and party identification.

# Agresti (2002), table 3.11, p. 106
GSS <- data.frame(
expand.grid(sex = c("female", "male"),
party = c("dem", "indep", "rep")),
count = c(279,165,73,47,225,191))

GSS
##      sex party count
## 1 female   dem   279
## 2   male   dem   165
## 3 female indep    73
## 4   male indep    47
## 5 female   rep   225
## 6   male   rep   191
names(GSS)
## [1] "sex"   "party" "count"
str(GSS)
## 'data.frame':    6 obs. of  3 variables:
##  $sex : Factor w/ 2 levels "female","male": 1 2 1 2 1 2 ##$ party: Factor w/ 3 levels "dem","indep",..: 1 1 2 2 3 3
##  $count: num 279 165 73 47 225 191 sum(GSS$count)
## [1] 980

### Table form

Table form data is represented by a matrix, array or table object, whose elements are the frequencies in an $$n$$-way table. The variable names (factors) and their levels are given by dimnames(X). The total number of observations is sum(X). The number of dimensions of the table is length(dimnames(X)), and the table sizes are given by sapply(dimnames(X), length).

Example: The HairEyeColor is stored in table form in vcd.

str(HairEyeColor)                      # show the structure
##  'table' num [1:4, 1:4, 1:2] 32 53 10 3 11 50 10 30 10 25 ...
##  - attr(*, "dimnames")=List of 3
##   ..$Hair: chr [1:4] "Black" "Brown" "Red" "Blond" ## ..$ Eye : chr [1:4] "Brown" "Blue" "Hazel" "Green"
##   ..$Sex : chr [1:2] "Male" "Female" sum(HairEyeColor) # number of cases ## [1] 592 sapply(dimnames(HairEyeColor), length) # table dimension sizes ## Hair Eye Sex ## 4 4 2 Example: Enter frequencies in a matrix, and assign dimnames, giving the variable names and category labels. Note that, by default, matrix() uses the elements supplied by columns in the result, unless you specify byrow=TRUE. # A 4 x 4 table Agresti (2002, Table 2.8, p. 57) Job Satisfaction JobSat <- matrix(c( 1, 2, 1, 0, 3, 3, 6, 1, 10,10,14, 9, 6, 7,12,11), 4, 4) dimnames(JobSat) = list( income = c("< 15k", "15-25k", "25-40k", "> 40k"), satisfaction = c("VeryD", "LittleD", "ModerateS", "VeryS") ) JobSat ## satisfaction ## income VeryD LittleD ModerateS VeryS ## < 15k 1 3 10 6 ## 15-25k 2 3 10 7 ## 25-40k 1 6 14 12 ## > 40k 0 1 9 11 JobSat is a matrix, not an object of class("table"), and some functions are happier with tables than matrices. You can coerce it to a table with as.table(), JobSat <- as.table(JobSat) str(JobSat) ## 'table' num [1:4, 1:4] 1 2 1 0 3 3 6 1 10 10 ... ## - attr(*, "dimnames")=List of 2 ## ..$ income      : chr [1:4] "< 15k" "15-25k" "25-40k" "> 40k"
##   ..$satisfaction: chr [1:4] "VeryD" "LittleD" "ModerateS" "VeryS" ## Ordered factors and reordered tables In table form, the values of the table factors are ordered by their position in the table. Thus in the JobSat data, both income and satisfaction represent ordered factors, and the positions of the values in the rows and columns reflects their ordered nature. Yet, for analysis, there are time when you need numeric values for the levels of ordered factors in a table, e.g., to treat a factor as a quantitative variable. In such cases, you can simply re-assign the dimnames attribute of the table variables. For example, here, we assign numeric values to income as the middle of their ranges, and treat satisfaction as equally spaced with integer scores. dimnames(JobSat)$income <- c(7.5,20,32.5,60)
dimnames(JobSat)$satisfaction <- 1:4 For the HairEyeColor data, hair color and eye color are ordered arbitrarily. For visualizing the data using mosaic plots and other methods described below, it turns out to be more useful to assure that both hair color and eye color are ordered from dark to light. Hair colors are actually ordered this way already, and it is easiest to re-order eye colors by indexing. Again str() is your friend. HairEyeColor <- HairEyeColor[, c(1,3,4,2), ] str(HairEyeColor) ## 'table' num [1:4, 1:4, 1:2] 32 53 10 3 10 25 7 5 3 15 ... ## - attr(*, "dimnames")=List of 3 ## ..$ Hair: chr [1:4] "Black" "Brown" "Red" "Blond"
##   ..$Eye : chr [1:4] "Brown" "Hazel" "Green" "Blue" ## ..$ Sex : chr [1:2] "Male" "Female"

This is also the order for both hair color and eye color shown in the result of a correspondence analysis () below.

With data in case form or frequency form, when you have ordered factors represented with character values, you must ensure that they are treated as ordered in R.

Imagine that the Arthritis data was read from a text file.
By default the Improved will be ordered alphabetically: Marked, None, Some — not what we want. In this case, the function ordered() (and others) can be useful.

Arthritis <- read.csv("arthritis.txt",header=TRUE)
Arthritis$Improved <- ordered(Arthritis$Improved,
levels=c("None", "Some", "Marked")
)

The dataset Arthritis in the vcd package is a data.frame in this form With this order of Improved, the response in this data, a mosaic display of Treatment and Improved () shows a clearly interpretable pattern.

The original version of mosaic in the vcd package required the input to be a contingency table in array form, so we convert using xtabs().

data(Arthritis, package="vcd")
art <- xtabs(~Treatment + Improved, data = Arthritis)
mosaic(art, gp = shading_max, split_vertical = TRUE, main="Arthritis: [Treatment] [Improved]")

Finally, there are situations where, particularly for display purposes, you want to re-order the dimensions of an $$n$$-way table, or change the labels for the variables or levels. This is easy when the data are in table form: aperm() permutes the dimensions, and assigning to names and dimnames changes variable names and level labels respectively. We will use the following version of UCBAdmissions in @(sec:mantel) below.1

UCB <- aperm(UCBAdmissions, c(2, 1, 3))
dimnames(UCB)[[2]] <- c("Yes", "No")

# display as a flattened table
stats::ftable(UCB)
##               Department   A   B   C   D   E   F
## Male   Yes               512 353 120 138  53  22
##        No                313 207 205 279 138 351
## Female Yes                89  17 202 131  94  24
##        No                 19   8 391 244 299 317

## structable()

For 3-way and larger tables the structable() function in vcd provides a convenient and flexible tabular display. The variables assigned to the rows and columns of a two-way display can be specified by a model formula.

structable(HairEyeColor)                   # show the table: default
##              Eye Brown Hazel Green Blue
## Hair  Sex
## Black Male          32    10     3   11
##       Female        36     5     2    9
## Brown Male          53    25    15   50
##       Female        66    29    14   34
## Red   Male          10     7     7   10
##       Female        16     7     7    7
## Blond Male           3     5     8   30
##       Female         4     5     8   64

structable(Hair+Sex ~ Eye, HairEyeColor)   # specify col ~ row variables
##       Hair Black        Brown         Red        Blond
##       Sex   Male Female  Male Female Male Female  Male Female
## Eye
## Brown         32     36    53     66   10     16     3      4
## Hazel         10      5    25     29    7      7     5      5
## Green          3      2    15     14    7      7     8      8
## Blue          11      9    50     34   10      7    30     64

It also returns an object of class "structable" which may be plotted with mosaic() (not shown here).

HSE < - structable(Hair+Sex ~ Eye, HairEyeColor)   # save structable object
mosaic(HSE)                                        # plot it

## table() and friends

You can generate frequency tables from factor variables using the table() function, tables of proportions using the prop.table() function, and marginal frequencies using margin.table().

For these examples, create some categorical vectors:

 n=500
A <- factor(sample(c("a1","a2"), n, rep=TRUE))
B <- factor(sample(c("b1","b2"), n, rep=TRUE))
C <- factor(sample(c("c1","c2"), n, rep=TRUE))
mydata <- data.frame(A,B,C)

These lines illustrate table-related functions:

# 2-Way Frequency Table
attach(mydata)
## The following objects are masked _by_ .GlobalEnv:
##
##     A, B, C
mytable <- table(A,B)   # A will be rows, B will be columns
mytable                 # print table
##     B
## A     b1  b2
##   a1 116 114
##   a2 138 132

margin.table(mytable, 1) # A frequencies (summed over B)
## A
##  a1  a2
## 230 270
margin.table(mytable, 2) # B frequencies (summed over A)
## B
##  b1  b2
## 254 246

prop.table(mytable)    # cell percentages
##     B
## A       b1    b2
##   a1 0.232 0.228
##   a2 0.276 0.264
prop.table(mytable, 1) # row percentages
##     B
## A           b1        b2
##   a1 0.5043478 0.4956522
##   a2 0.5111111 0.4888889
prop.table(mytable, 2) # column percentages
##     B
## A           b1        b2
##   a1 0.4566929 0.4634146
##   a2 0.5433071 0.5365854

table() can also generate multidimensional tables based on 3 or more categorical variables. In this case, you can use the ftable() or structable() function to print the results more attractively.

# 3-Way Frequency Table
mytable <- table(A, B, C)
ftable(mytable)
##       C c1 c2
## A  B
## a1 b1   45 71
##    b2   59 55
## a2 b1   62 76
##    b2   76 56

table() ignores missing values by default. To include NA as a category in counts, include the table option exclude=NULL if the variable is a vector. If the variable is a factor you have to create a new factor using .

## xtabs()

The xtabs() function allows you to create cross-tabulations of data using formula style input. This typically works with case-form data supplied in a data frame or a matrix. The result is a contingency table in array format, whose dimensions are determined by the terms on the right side of the formula.

# 3-Way Frequency Table
mytable <- xtabs(~A+B+C, data=mydata)

ftable(mytable)    # print table
##       C c1 c2
## A  B
## a1 b1   45 71
##    b2   59 55
## a2 b1   62 76
##    b2   76 56

summary(mytable)   # chi-square test of indepedence
## Call: xtabs(formula = ~A + B + C, data = mydata)
## Number of cases in table: 500
## Number of factors: 3
## Test for independence of all factors:
##  Chisq = 9.888, df = 4, p-value = 0.04235

If a variable is included on the left side of the formula, it is assumed to be a vector of frequencies (useful if the data have already been tabulated in frequency form).

(GSStab <- xtabs(count ~ sex + party, data=GSS))
##         party
## sex      dem indep rep
##   female 279    73 225
##   male   165    47 191

summary(GSStab)
## Call: xtabs(formula = count ~ sex + party, data = GSS)
## Number of cases in table: 980
## Number of factors: 2
## Test for independence of all factors:
##  Chisq = 7.01, df = 2, p-value = 0.03005

## Collapsing over table factors: aggregate(), margin.table() and apply()}

It sometimes happens that we have a data set with more variables or factors than we want to analyse, or else, having done some initial analyses, we decide that certain factors are not important, and so should be excluded from graphic displays by collapsing (summing) over them. For example, mosaic plots and fourfold displays are often simpler to construct from versions of the data collapsed over the factors which are not shown in the plots.

The appropriate tools to use again depend on the form in which the data are represented— a case-form data frame, a frequency-form data frame (aggregate()), or a table-form array or table object (margin.table() or apply()).

When the data are in frequency form, and we want to produce another frequency data frame, aggregate() is a handy tool, using the argument FUN=sum to sum the frequency variable over the factors not mentioned in the formula.

Example: The data frame DaytonSurvey in the vcdExtra package represents a $$2^5$$ table giving the frequencies of reported use (ever used?’’) of alcohol, cigarettes and marijuana in a sample of high school seniors, also classified by sex and race.

str(DaytonSurvey)
## 'data.frame':    32 obs. of  6 variables:
##  $cigarette: Factor w/ 2 levels "Yes","No": 1 2 1 2 1 2 1 2 1 2 ... ##$ alcohol  : Factor w/ 2 levels "Yes","No": 1 1 2 2 1 1 2 2 1 1 ...
##  $marijuana: Factor w/ 2 levels "Yes","No": 1 1 1 1 2 2 2 2 1 1 ... ##$ sex      : Factor w/ 2 levels "female","male": 1 1 1 1 1 1 1 1 2 2 ...
##  $race : Factor w/ 2 levels "white","other": 1 1 1 1 1 1 1 1 1 1 ... ##$ Freq     : num  405 13 1 1 268 218 17 117 453 28 ...
##   cigarette alcohol marijuana    sex  race Freq
## 1       Yes     Yes       Yes female white  405
## 2        No     Yes       Yes female white   13
## 3       Yes      No       Yes female white    1
## 4        No      No       Yes female white    1
## 5       Yes     Yes        No female white  268
## 6        No     Yes        No female white  218

To focus on the associations among the substances, we want to collapse over sex and race. The right-hand side of the formula used in the call to aggregate() gives the factors to be retained in the new frequency data frame, Dayton.ACM.df.

# data in frequency form
# collapse over sex and race
Dayton.ACM.df <- aggregate(Freq ~ cigarette+alcohol+marijuana,
data=DaytonSurvey,
FUN=sum)
Dayton.ACM.df
##   cigarette alcohol marijuana Freq
## 1       Yes     Yes       Yes  911
## 2        No     Yes       Yes   44
## 3       Yes      No       Yes    3
## 4        No      No       Yes    2
## 5       Yes     Yes        No  538
## 6        No     Yes        No  456
## 7       Yes      No        No   43
## 8        No      No        No  279

When the data are in table form, and we want to produce another table, apply() with FUN=sum can be used in a similar way to sum the table over dimensions not mentioned in the MARGIN argument. margin.table() is just a wrapper for apply() using the sum() function.

Example: To illustrate, we first convert the DaytonSurvey to a 5-way table using xtabs(), giving Dayton.tab.

# in table form
Dayton.tab <- xtabs(Freq ~ cigarette+alcohol+marijuana+sex+race,
data=DaytonSurvey)
structable(cigarette+alcohol+marijuana ~ sex+race,
data=Dayton.tab)
##              cigarette Yes              No
##              alcohol   Yes      No     Yes      No
##              marijuana Yes  No Yes  No Yes  No Yes  No
## sex    race
## female white           405 268   1  17  13 218   1 117
##        other            23  23   0   1   2  19   0  12
## male   white           453 228   1  17  28 201   1 133
##        other            30  19   1   8   1  18   0  17

Then, use apply() on Dayton.tab to give the 3-way table Dayton.ACM.tab summed over sex and race. The elements in this new table are the column sums for Dayton.tab shown by structable() just above.

# collapse over sex and race
Dayton.ACM.tab <- apply(Dayton.tab, MARGIN=1:3, FUN=sum)
Dayton.ACM.tab <- margin.table(Dayton.tab, 1:3)   # same result

structable(cigarette+alcohol ~ marijuana, data=Dayton.ACM.tab)
##           cigarette Yes      No
##           alcohol   Yes  No Yes  No
## marijuana
## Yes                 911   3  44   2
## No                  538  43 456 279

Many of these operations can be performed using the **ply() functions in the plyr package. For example, with the data in a frequency form data frame, use ddply() to collapse over unmentioned factors, and plyr::summarise() as the function to be applied to each piece.

library(plyr)
Dayton.ACM.df <- plyr::ddply(DaytonSurvey,
.(cigarette, alcohol, marijuana),
plyr::summarise, Freq=sum(Freq))

Dayton.ACM.df

## Collapsing table levels: collapse.table()

A related problem arises when we have a table or array and for some purpose we want to reduce the number of levels of some factors by summing subsets of the frequencies. For example, we may have initially coded Age in 10-year intervals, and decide that, either for analysis or display purposes, we want to reduce Age to 20-year intervals. The collapse.table() function in vcdExtra was designed for this purpose.

Example: Create a 3-way table, and collapse Age from 10-year to 20-year intervals. First, we generate a $$2 \times 6 \times 3$$ table of random counts from a Poisson distribution with mean of 100.

# create some sample data in frequency form
sex <- c("Male", "Female")
age <- c("10-19", "20-29",  "30-39", "40-49", "50-59", "60-69")
education <- c("low", 'med', 'high')
data <- expand.grid(sex=sex, age=age, education=education)
counts <- rpois(36, 100)   # random Possion cell frequencies
data <- cbind(data, counts)

# make it into a 3-way table
t1 <- xtabs(counts ~ sex + age + education, data=data)
structable(t1)
##                  age 10-19 20-29 30-39 40-49 50-59 60-69
## sex    education
## Male   low              98   105   104    90    90   101
##        med              97   105   101    88    97   107
##        high             99   101   109    88    99    96
## Female low             102   117   101   105    85    88
##        med             106    84    92   116   110    96
##        high            106    96   121    91   107   102

Now collapse age to 20-year intervals, and education to 2 levels. In the arguments, levels of age and education given the same label are summed in the resulting smaller table.

# collapse age to 3 levels, education to 2 levels
t2 <- collapse.table(t1,
age=c("10-29", "10-29",  "30-49", "30-49", "50-69", "50-69"),
education=c("<high", "<high", "high"))
structable(t2)
##                  age 10-29 30-49 50-69
## sex    education
## Male   <high           405   383   395
##        high            200   197   195
## Female <high           409   414   379
##        high            202   212   209

## Converting among frequency tables and data frames

As we’ve seen, a given contingency table can be represented equivalently in different forms, but some R functions were designed for one particular representation.

The table below shows some handy tools for converting from one form to another.

From this To this
Case form Frequency form Table form
Case form noop xtabs(~A+B) table(A,B)
Frequency form expand.dft(X) noop xtabs(count~A+B)
Table form expand.dft(X) as.data.frame(X) noop

For example, a contingency table in table form (an object of class(table)) can be converted to a data.frame with as.data.frame().2 The resulting data.frame contains columns representing the classifying factors and the table entries (as a column named by the responseName argument, defaulting to Freq. This is the inverse of xtabs().

Example: Convert the GSStab in table form to a data.frame in frequency form.

as.data.frame(GSStab)
##      sex party Freq
## 1 female   dem  279
## 2   male   dem  165
## 3 female indep   73
## 4   male indep   47
## 5 female   rep  225
## 6   male   rep  191

Example: Convert the Arthritis data in case form to a 3-way table of Treatment $$\times$$ Sex $$\times$$ Improved. Note the use of with() to avoid having to use Arthritis\$Treatment etc. within the call to table().%3 Art.tab <- with(Arthritis, table(Treatment, Sex, Improved)) str(Art.tab) ## 'table' int [1:2, 1:2, 1:3] 19 6 10 7 7 5 0 2 6 16 ... ## - attr(*, "dimnames")=List of 3 ## ..$ Treatment: chr [1:2] "Placebo" "Treated"
##   ..$Sex : chr [1:2] "Female" "Male" ## ..$ Improved : chr [1:3] "None" "Some" "Marked"

ftable(Art.tab)
##                  Improved None Some Marked
## Treatment Sex
## Placebo   Female            19    7      6
##           Male              10    0      1
## Treated   Female             6    5     16
##           Male               7    2      5

There may also be times that you will need an equivalent case form data.frame with factors representing the table variables rather than the frequency table. For example, the mca() function in package MASS only operates on data in this format. Marc Schwartz initially provided code for expand.dft() on the Rhelp mailing list for converting a table back into a case form data.frame. This function is included in vcdExtra.

Example: Convert the Arthritis data in table form (Art.tab) back to a data.frame in case form, with factors Treatment, Sex and Improved.

Art.df <- expand.dft(Art.tab)
str(Art.df)
## 'data.frame':    84 obs. of  3 variables:
##  $Treatment: chr "Placebo" "Placebo" "Placebo" "Placebo" ... ##$ Sex      : chr  "Female" "Female" "Female" "Female" ...
##  $Improved : chr "None" "None" "None" "None" ... ## A complex example If you’ve followed so far, you’re ready for a more complicated example. The data file, tv.dat represents a 4-way table of size $$5 \times 11 \times 5 \times 3$$ where the table variables (unnamed in the file) are read as V1V4, and the cell frequency is read as V5. The file, stored in the doc/extdata directory of vcdExtra, can be read as follows: tv.data<-read.table(system.file("extdata","tv.dat", package="vcdExtra")) head(tv.data,5) ## V1 V2 V3 V4 V5 ## 1 1 1 1 1 6 ## 2 2 1 1 1 18 ## 3 3 1 1 1 6 ## 4 4 1 1 1 2 ## 5 5 1 1 1 11 For a local file, just use read.table() in this form: tv.data<-read.table("C:/R/data/tv.dat") The data tv.dat came from the initial implementation of mosaic displays in R by Jay Emerson. In turn, they came from the initial development of mosaic displays (Hartigan & Kleiner, 1984) that illustrated the method with data on a large sample of TV viewers whose behavior had been recorded for the Neilson ratings. This data set contains sample television audience data from Neilsen Media Research for the week starting November 6, 1995. The table variables are: • V1– values 1:5 correspond to the days Monday–Friday; • V2– values 1:11 correspond to the quarter hour times 8:00PM through 10:30PM; • V3– values 1:5 correspond to ABC, CBS, NBC, Fox, and non-network choices; • V4– values 1:3 correspond to transition states: turn the television Off, Switch channels, or Persist in viewing the current channel. We are interested just the cell frequencies, and rely on the facts that the 1. the table is complete— there are no missing cells, so nrow(tv.data) = 825; 2. the observations are ordered so that V1 varies most rapidly and V4 most slowly. From this, we can just extract the frequency column and reshape it into an array. [That would be dangerous if any observations were out of order.] TV <- array(tv.data[,5], dim=c(5,11,5,3)) dimnames(TV) <- list(c("Monday","Tuesday","Wednesday","Thursday","Friday"), c("8:00","8:15","8:30","8:45","9:00","9:15","9:30", "9:45","10:00","10:15","10:30"), c("ABC","CBS","NBC","Fox","Other"), c("Off","Switch","Persist")) names(dimnames(TV))<-c("Day", "Time", "Network", "State") More generally (even if there are missing cells), we can use xtabs() (or plyr::daply()) to do the cross-tabulation, using V5 as the frequency variable. Here’s how to do this same operation with xtabs(): TV <- xtabs(V5 ~ ., data=tv.data) dimnames(TV) <- list(Day = c("Monday","Tuesday","Wednesday","Thursday","Friday"), Time = c("8:00","8:15","8:30","8:45","9:00","9:15","9:30", "9:45","10:00","10:15","10:30"), Network = c("ABC","CBS","NBC","Fox","Other"), State = c("Off","Switch","Persist")) # table dimensions dim(TV) But this 4-way table is too large and awkward to work with. Among the networks, Fox and Other occur infrequently. We can also cut it down to a 3-way table by considering only viewers who persist with the current station.4 TV2 <- TV[,,1:3,] # keep only ABC, CBS, NBC TV2 <- TV2[,,,3] # keep only Persist -- now a 3 way table structable(TV2) ## Time 8:00 8:15 8:30 8:45 9:00 9:15 9:30 9:45 10:00 10:15 10:30 ## Day Network ## Monday ABC 146 151 156 83 325 350 386 340 352 280 278 ## CBS 337 293 304 233 311 251 241 164 252 265 272 ## NBC 263 219 236 140 226 235 239 246 279 263 283 ## Tuesday ABC 244 181 231 205 385 283 345 192 329 351 364 ## CBS 173 180 184 109 218 235 256 250 274 263 261 ## NBC 315 254 280 241 370 214 195 111 188 190 210 ## Wednesday ABC 233 161 194 156 339 264 279 140 237 228 203 ## CBS 158 126 207 59 98 103 122 86 109 105 110 ## NBC 134 146 166 66 194 230 264 143 274 289 306 ## Thursday ABC 174 183 197 181 187 198 211 86 110 122 117 ## CBS 196 185 195 104 106 116 116 47 102 84 84 ## NBC 515 463 472 477 590 473 446 349 649 705 747 ## Friday ABC 294 281 305 239 278 246 245 138 246 232 233 ## CBS 130 144 154 81 129 153 136 126 138 136 152 ## NBC 195 220 248 160 172 164 169 85 183 198 204 Finally, for some purposes, we might want to collapse the 11 times into a smaller number. Half-hour time slots make more sense. Here, we use as.data.frame.table() to convert the table back to a data frame, levels() to re-assign the values of Time, and finally, xtabs() to give a new, collapsed frequency table. TV.df <- as.data.frame.table(TV2) levels(TV.df$Time) <- c(rep("8:00", 2),
rep("8:30", 2),
rep("9:00", 2),
rep("9:30", 2),
rep("10:00",2),
"10:30"
)

TV3 <- xtabs(Freq ~ Day + Time + Network, TV.df)

structable(Day ~ Time+Network, TV3)
##               Day Monday Tuesday Wednesday Thursday Friday
## Time  Network
## 8:00  ABC            297     425       394      357    575
##       CBS            630     353       284      381    274
##       NBC            482     569       280      978    415
## 8:30  ABC            239     436       350      378    544
##       CBS            537     293       266      299    235
##       NBC            376     521       232      949    408
## 9:00  ABC            675     668       603      385    524
##       CBS            562     453       201      222    282
##       NBC            461     584       424     1063    336
## 9:30  ABC            726     537       419      297    383
##       CBS            405     506       208      163    262
##       NBC            485     306       407      795    254
## 10:00 ABC            632     680       465      232    478
##       CBS            517     537       214      186    274
##       NBC            542     378       563     1354    381
## 10:30 ABC            278     364       203      117    233
##       CBS            272     261       110       84    152
##       NBC            283     210       306      747    204

We’ve come this far, so we might as well show a mosaic display. This is analogous to that used by Hartigan & Kleiner (1984).

mosaic(TV3, shade = TRUE,
labeling = labeling_border(rot_labels = c(0, 0, 0, 90)))

This mosaic displays can be read at several levels, corresponding to the successive splits of the tiles and the residual shading. Several trends are clear for viewers who persist:

• Overall, there are about the same number of viewers on each weekday, with slightly more on Thursday.
• Looking at time slots, viewership is slightly greater from 9:00 - 10:00 overall and also 8:00 - 9:00 on Thursday and Friday

From the residual shading of the tiles:

• Monday: CBS dominates in all time slots.
• Tuesday” ABC and CBS dominate after 9:00
• Thursday: is a largely NBC day
• Friday: ABC dominates in the early evening

# References

Agresti, A. (2002). Categorical data analysis (2nd ed.). Hoboken, New Jersey: John Wiley & Sons.
Hartigan, J. A., & Kleiner, B. (1984). A mosaic of television ratings. The American Statistician, 38, 32–35.

1. Changing Admit to Admit? might be useful for display purposes, but is dangerous— because it is then difficult to use that variable name in a model formula. See @(sec:tips) for options labeling_args and set_labelsto change variable and level names for displays in the strucplot framework.↩︎

2. Because R is object-oriented, this is actually a short-hand for the function as.data.frame.table().↩︎

3. table() does not allow a data argument to provide an environment in which the table variables are to be found. In the examples in @(sec:table) I used attach(mydata) for this purpose, but attach() leaves the variables in the global environment, while with() just evaluates the table() expression in a temporary environment of the data.↩︎

4. This relies on the fact that that indexing an array drops dimensions of length 1 by default, using the argument drop=TRUE; the result is coerced to the lowest possible dimension.↩︎