R: Cross Tabulation

xtabs {stats} | R Documentation

## Cross Tabulation

### Description

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

### Usage

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

### Arguments

`formula` | 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.
`data` | 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)`.
`subset` | an optional vector specifying a subset of observations to be used.
`sparse` | 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).
`na.action` | a function which indicates what should happen when the data contain `NA`s.
`exclude` | a vector of values to be excluded when forming the set of levels of the classifying factors.
`drop.unused.levels` | 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.

### Details

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.

### Value

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.

### Examples

    ## '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'.
    DF
    ## 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 = paste("T", rep(1:4, 9*4), sep=""),
                          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 2.15.1 Index]