chisq.test {stats}R Documentation

Pearson's Chi-squared Test for Count Data


chisq.test performs chi-squared contingency table tests and goodness-of-fit tests.


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


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. An error is given if any entry of p is negative.
rescale.p a logical scalar; if TRUE then p is rescaled (if necessary) to sum to 1. If rescale.p is FALSE, and p does not sum to 1, an error is given.
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.


If x is a matrix with one row or column, or if x is a vector and y is not given, then a “goodness-of-fit test” is performed (“x is treated as a one-dimensional contingency table”). The entries of x must be non-negative integers. 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. Again, the entries of x must be non-negative 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.

In the contingency table case 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.)

In the goodness-of-fit case this is done by random sampling from the discrete distribution specified by p, each sample being of size n = sum(x). This simulation is done in raw R and is slow.


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. 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).


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.


## 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(as.table(x))         # the same
x <- c(89,37,30,28,2)
p <- c(40,20,20,15,5)
chisq.test(x, p = p)            # gives an error
chisq.test(x, p = p, rescale.p = TRUE)
                                # works
p <- c(0.40,0.20,0.20,0.19,0.01)
                                # Expected count in category 5
                                # is 1.86 < 5 ==> chi square approx.
chisq.test(x, p = p)            #               maybe doubtful, but is ok!
chisq.test(x, p = p,simulate.p.value = TRUE)

## Case B. Raw data
x <- trunc(5 * runif(100))
chisq.test(table(x))            # NOT 'chisq.test(x)'!

[Package stats version 2.1.0 Index]