xtabs {stats}R Documentation

Cross Tabulation


Create a contingency table (optionally a sparse matrix) from cross-classifying factors, usually contained in a data frame, using a formula interface.


xtabs(formula = ~., data = parent.frame(), subset, sparse = FALSE,
      na.action, exclude = c(NA, NaN), drop.unused.levels = FALSE)



a formula object with the cross-classifying variables (separated by +) on the right hand side (or an object which can be coerced to a formula). Interactions are not allowed. On the left hand side, one may optionally give a vector or a matrix of counts; in the latter case, the columns are interpreted as corresponding to the levels of a variable. This is useful if the data have already been tabulated, see the examples below.


an optional matrix or data frame (or similar: see model.frame) containing the variables in the formula formula. By default the variables are taken from environment(formula).


an optional vector specifying a subset of observations to be used.


logical specifying if the result should be a sparse matrix, i.e., inheriting from sparseMatrix Only works for two factors (since there are no higher-order sparse array classes yet).


a function which indicates what should happen when the data contain NAs.


a vector of values to be excluded when forming the set of levels of the classifying factors.


a logical indicating whether to drop unused levels in the classifying factors. If this is FALSE and there are unused levels, the table will contain zero marginals, and a subsequent chi-squared test for independence of the factors will not work.


There is a summary method for contingency table objects created by table or xtabs(*, sparse = FALSE), which gives basic information and performs a chi-squared test for independence of factors (note that the function chisq.test currently only handles 2-d tables).

If a left hand side is given in formula, its entries are simply summed over the cells corresponding to the right hand side; this also works if the lhs does not give counts.

For variables in formula which are factors, exclude must be specified explicitly; the default exclusions will not be used.


By default, when sparse = FALSE, a contingency table in array representation of S3 class c("xtabs", "table"), with a "call" attribute storing the matched call.

When sparse = TRUE, a sparse numeric matrix, specifically an object of S4 class dgTMatrix from package Matrix.

See Also

table for traditional cross-tabulation, and as.data.frame.table which is the inverse operation of xtabs (see the DF example below).

sparseMatrix on sparse matrices in package Matrix.


## 'esoph' has the frequencies of cases and controls for all levels of
## the variables 'agegp', 'alcgp', and 'tobgp'.
xtabs(cbind(ncases, ncontrols) ~ ., data = esoph)
## Output is not really helpful ... flat tables are better:
ftable(xtabs(cbind(ncases, ncontrols) ~ ., data = esoph))
## In particular if we have fewer factors ...
ftable(xtabs(cbind(ncases, ncontrols) ~ agegp, data = esoph))

## This is already a contingency table in array form.
DF <- as.data.frame(UCBAdmissions)
## Now 'DF' is a data frame with a grid of the factors and the counts
## in variable 'Freq'.
## Nice for taking margins ...
xtabs(Freq ~ Gender + Admit, DF)
## And for testing independence ...
summary(xtabs(Freq ~ ., DF))

## Create a nice display for the warp break data.
warpbreaks$replicate <- rep(1:9, len = 54)
ftable(xtabs(breaks ~ wool + tension + replicate, data = warpbreaks))

### ---- Sparse Examples ----

if(require("Matrix")) {
 ## similar to "nlme"s  'ergoStool' :
 d.ergo <- data.frame(Type = paste0("T", rep(1:4, 9*4)),
                      Subj = gl(9, 4, 36*4))
 print(xtabs(~ Type + Subj, data = d.ergo)) # 4 replicates each
 set.seed(15) # a subset of cases:
 print(xtabs(~ Type + Subj, data = d.ergo[sample(36, 10), ], sparse = TRUE))

 ## Hypothetical two-level setup:
 inner <- factor(sample(letters[1:25], 100, replace = TRUE))
 inout <- factor(sample(LETTERS[1:5], 25, replace = TRUE))
 fr <- data.frame(inner = inner, outer = inout[as.integer(inner)])
 print(xtabs(~ inner + outer, fr, sparse = TRUE))

[Package stats version 3.3.2 Index]