[R] Lilliefors Test

[Martina Pavlicova]

> Is it not true that the Shapiro Wilks test implemented in the package
> ctest requires the assumption that the population variance of the
> variable is known?

I am not sure about this one...

> Is it also not true that the Lilliefors is not a test of normality
> as such, but is rather a correction of the p-value for the
> Kolmogorov Smirnov test?

Yes, that is right. Here is the code:

null.hyp <- function(x) {
	## one observation from the null distribution
  mu <- mean(x)
  sigma <- sd(x)
  foo <- ks.test(x=x, y="pnorm", mean = mu, sd = sigma)
  sim <- foo$statistic
  sim
}

create.null <- function(n=n, rep=100000){
	## creates a sample of length 'rep' from null distribution
  null <- numeric(rep)
  for(i in 1:rep){
    null[i] <- null.hyp(rnorm(n))
  }
  null
}

Lilliefors.test <- function(sample=data, rep){
  n <- length(sample)
  null.dist <- create.null(n, rep)
  res <- list()
  res$statistic <- null.hyp(sample)
  res$p.value <- sum(null.dist>res$statistic)/rep
  res
}


Thanks,

Martina Pavlicova

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> | -----Original Message-----
> | From: kjetil at entelnet.bo [mailto:kjetil at entelnet.bo]
> | Sent: Friday, October 17, 2003 3:33 PM
> | To: R HELP; Martina Pavlicova
> | Subject: Re: [R] Lilliefors Test
> |
> |
> | On 17 Oct 2003 at 13:59, Martina Pavlicova wrote:
> |
> | There is shapiro.test in package ctest, which have much better power
> | properties than Lillefors test. So there is no need to have
> | Lilliefors test in R, except for archeological interest.
> |
> | Kjetil Halvorsen
> |
> | >
> | > Hello everybody,
> | >
> | > I would like to perform a test for normality (without specifying the
> | > mean a variance) on the sample data (80 observations). I found that
> | > Lilliefors test is appropriate. Does anybody have it
> | programmed already,
> | > or is there a function for this test in R?
> | >
> | > Thank you very much,
> | >
> | > Martina Pavlicova
> | >