R: Pearson's Chi-square Test for Count Data

chisq.test {ctest}

R Documentation

Pearson's Chi-square Test for Count Data

Description

chisq.test performs chi-square 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-square 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-square 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.

Value

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

statistic

the value the chi-square test statistic.

parameter

the degrees of freedom of the approximate chi-square 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.

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$spray)$obs
                                # 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
x <- trunc(5 * runif(100))
chisq.test(table(x))            # NOT `chisq.test(x)'!