| chisq.test {stats} | R Documentation |
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. |
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). |
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(x)
chisq.test(as.table(x)) # the same
x <- c(89,37,30,28,2)
p <- c(40,20,20,15,5)
try(
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)'!