ks.test                package: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: `NULL' or a logical indicating whether an exact p-value
          should be computed.  See Details for the meaning of `NULL'.
          Only used in the two-sided two-sample case.

Details:

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

     Alternatively, `y' can be a character string naming a continuous
     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 presence of ties generates a warning, since continuous
     distributions do not generate them.

     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.

     Exact p-values are only available for the two-sided two-sample
     test with no ties.  In that case, if `exact = NULL' (the default)
     an exact p-value is computed if the product of the sample sizes is
     less than 10000.  Otherwise, asymptotic distributions are used
     whose approximations 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")

