ks.test {ctest}R Documentation

Kolmogorov-Smirnov Tests

Description

Performs one or two sample Kolmogorov-Smirnov tests.

Usage

ks.test(x, y, ..., alternative = c("two.sided", "less", "greater"),
        exact = NULL)

Arguments

x a numeric vector of data values.
y either a numeric vector of data values, or a character string naming a distribution function.
... parameters of the distribution specified by y.
alternative indicates the alternative hypothesis and must be one of "two.sided" (default), "less", or "greater". You can specify just the initial letter.
exact a logical indicating whether an exact p-value should be computed. Only used in the two-sided two-sample case.

Details

If y is numeric, a two sample test of the null that x and y were drawn from the same distribution is performed.

Alternatively, y can be a character string naming a distribution function. In this case, a one sample test of the null that the distribution function underlying x is y with parameters specified by ... is carried out.

The possible values "two.sided", "less" and "greater" of alternative specify the null hypothesis that the true distribution function of x is equal to, not less than or not greater than the hypothesized distribution function (one-sample case) or the distribution function of y (two-sample case), respectively.

Currently, exact p-value are only available for the two-sided two-sample test. In this case, by default (if exact is not specified), an exact p-value is computed if the product of the sample sizes is less than 10000. Otherwise, the asymptotic distributions are used. This approximation may be inaccurate in small samples.

Value

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

statistic the value of the test statistic.
p.value the p-value of the test.
alternative a character string describing the alternative hypothesis.
method a character string indicating what type of test was performed.
data.name a character string giving the name(s) of the data.

References

Conover, W. J. (1971), Practical nonparametric statistics. New York: John Wiley & Sons. Pages 295–301 (one-sample ``Kolmogorov'' test), 309–314 (two-sample ``Smirnov'' test).

See Also

shapiro.test which performs the Shapiro-Wilk test for normality.

Examples

x <- rnorm(50)
y <- runif(30)
# Do x and y come from the same distribution?
ks.test(x, y)
# Does x come from a shifted gamma distribution with shape 3 and scale 2?
ks.test(x+2, "pgamma", 3, 2) # two-sided
ks.test(x+2, "pgamma", 3, 2, alternative = "gr")