chisq.test {stats} | R Documentation

## Pearson's Chi-squared Test for Count Data

### Description

`chisq.test` performs chi-squared tests on contingency tables.

### Usage

    chisq.test(x, y = NULL, correct = TRUE,
               p = rep(1/length(x), length(x)),
               simulate.p.value = FALSE, B = 2000)

### Arguments

`x` | a vector or matrix.
`y` | a vector; ignored if `x` is a matrix.
`correct` | a logical indicating whether to apply continuity correction when computing the test statistic.
`p` | a vector of probabilities of the same length of `x`.
`simulate.p.value` | a logical indicating whether to compute p-values by Monte Carlo simulation.
`B` | an integer specifying the number of replicates used in the Monte Carlo simulation.

### Details

If `x` is a matrix with one row or column, or if `x` is a vector and `y` is not given, `x` is treated as a one-dimensional contingency table. In this case, the hypothesis tested is whether the population probabilities equal those in `p`, or are all equal if `p` is not given.

If `x` is a matrix with at least two rows and columns, it is taken as a two-dimensional contingency table, and hence its entries should be nonnegative integers. Otherwise, `x` and `y` must be vectors or factors of the same length; incomplete cases are removed, the objects are coerced into factor objects, and the contingency table is computed from these. Then, Pearson's chi-squared test of the null that the joint distribution of the cell counts in a 2-dimensional contingency table is the product of the row and column marginals is performed. If `simulate.p.value` is `FALSE`, the p-value is computed from the asymptotic chi-squared distribution of the test statistic; continuity correction is only used in the 2-by-2 case if `correct` is `TRUE`. Otherwise, if `simulate.p.value` is `TRUE`, the p-value is computed by Monte Carlo simulation with `B` replicates. This is done by random sampling from the set of all contingency tables with given marginals, and works only if the marginals are positive. (A C translation of the algorithm of Patefield (1981) is used.)

### Value

A list with class `"htest"` containing the following components:

`statistic` | the value the chi-squared test statistic.
`parameter` | the degrees of freedom of the approximate chi-squared distribution of the test statistic, `NA` if the p-value is computed by Monte Carlo simulation.
`p.value` | the p-value for the test.
`method` | a character string indicating the type of test performed, and whether Monte Carlo simulation or continuity correction was used.
`data.name` | a character string giving the name(s) of the data.
`observed` | the observed counts.
`expected` | the expected counts under the null hypothesis.
`residuals` | the Pearson residuals, `(observed - expected) / sqrt(expected)`.

### References

Patefield, W. M. (1981) Algorithm AS159. An efficient method of generating r x c tables with given row and column totals. Applied Statistics 30, 91–97.

### Examples

    data(InsectSprays)              # Not really a good example
    chisq.test(InsectSprays$count > 7, InsectSprays$spray)
                                    # Prints test summary
    chisq.test(InsectSprays$count > 7, InsectSprays$spray)$obs
                                    # Counts observed
    chisq.test(InsectSprays$count > 7, InsectSprays$spray)$exp
                                    # Counts expected under the null

    ## Effect of simulating p-values
    x <- matrix(c(12, 5, 7, 7), nc = 2)
    chisq.test(x)$p.value           # 0.4233
    chisq.test(x, simulate.p.value = TRUE, B = 10000)$p.value
                                    # around 0.29!

    ## Testing for population probabilities
    ## Case A. Tabulated data
    x <- c(A = 20, B = 15, C = 25)
    chisq.test(x)
    chisq.test(as.table(x))         # the same
    ## Case B. Raw data
    x <- trunc(5 * runif(100))
    chisq.test(table(x))            # NOT 'chisq.test(x)'!

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