[18957] in s-news-athena
RE: [S] Shapiro-Wilks' test
daemon@ATHENA.MIT.EDU (Ranjan Maitra)
Tue Aug 17 23:28:23 1999
Date: Tue, 17 Aug 1999 23:23:43 -0400 (EDT)
From: Ranjan Maitra <maitra@math.umbc.edu>
To: Tom Gatliffe <TomGofBoulder@email.msn.com>
Cc: S-news <s-news@wubios.wustl.edu>
In-Reply-To: <LOBBLBJANBJEJGBDPLPCEEBDCBAA.TomGofBoulder@email.msn.com>
Message-Id: <Pine.LNX.4.04.9908172323070.5930-100000@param.math.umbc.edu>
Mime-Version: 1.0
Content-Type: TEXT/PLAIN; charset=US-ASCII
Thanks a lot for your effort, Tom. I think this will be very helpful.
Thanks again,
Ranjan
On Tue, 17 Aug 1999, Tom Gatliffe wrote:
> The following is a function I pulled off the StatLib Library. It seems to
> agree
> with the Shapiro Wilk tests performed by a couple of other programs I have
> used.
>
> > shapiro.wilk.test
> function(x)
> {
> # "shapiro.wilk.test"
> #
> # This function is an S version of the procedure described by
> # J. P. Royston (1982) in "An Extension of Shapiro and Wilk's
> # W Test for Normality to Large Samples", Applied Statistics,
> # Vol. 31, No. 2, pp 115-124.
> #
> n <- length(x)
> index <- 1:n
> m <- qnorm((index - 0.375)/(n + 0.25))
> y <- sort(x)
> mu <- mean(y)
> SSq <- sum((y - mu)^2)
> astar <- 2 * m
> ends <- c(1, n)
> astar.p <- astar[ - ends]
> if(n <= 20)
> m <- n - 1
> else m <- n
> if(m < 20)
> aa <- gamma(0.5 * (m + 1))/(sqrt(2) *
> gamma(0.5 * m + 1))
> else {
> f1 <- (6 * m + 7)/(6 * m + 13)
> f2 <- exp(1)/(m + 2)
> f3 <- (m + 1)/(m + 2)
> f3 <- f3^(m - 2)
> aa <- f1 * sqrt(f2 * f3)
> }
> astar.1 <- (aa * sum(astar.p^2))/(1 - 2 * aa)
> astar.1 <- sqrt(astar.1)
> astar[1] <- - astar.1
> astar[n] <- astar.1
> A <- astar/sqrt(sum(astar^2))
> W <- (sum(A * y)^2)/SSq
> if(n <= 20) {
> u <- log(n) - 3
> lambda <- 0.118898 + 0.133414 * u +
> 0.327907 * u^2
> logmu <- -0.37542 - 0.492145 * u -
> 1.124332 * u^2 - 0.199422 * u^3
> logsigma <- -3.155805 + 0.729399 * u +
> 3.01855 * u^2 + 1.5558776 * u^3
> }
> if(n > 20) {
> u <- log(n) - 5
> lambda <- 0.480385 + 0.318828 * u +
> 0.0241665 * u^3 + 0.00879701 *
> u^4 + 0.002989646 * u^5
> logmu <- -1.91487 - 1.37888 * u -
> 0.04189209 * u^2 + 0.1066339 *
> u^3 - 0.03513666 * u^4 -
> 0.01504614 * u^5
> logsigma <- -3.83538 - 1.015807 * u - 0.331885 *
> u^2 + 0.1773538 * u^3 - 0.01638782 * u^4 -
> 0.03215018 * u^5 + 0.003852646 * u^6
> }
> mu <- exp(logmu)
> sigma <- exp(logsigma)
> y <- (1 - W)^lambda
> z <- (y - mu)/sigma
> p <- 1 - pnorm(z)
> if(n < 7) {
> warning("n is to small for this program
> to correctly estimate p"
> )
> p <- NA
> }
> if(n > 2000) {
> warning("n is too large for this program
> to correctly estimate p"
> )
> p <- NA
> }
> out <- list(W = W, n = n, p = p)
> out
> }
> >
>
>
> Tom Gatliffe
> Rocky Flats Environmental Tech Site
>
> -----Original Message-----
> From: owner-s-news@wubios.wustl.edu
> [mailto:owner-s-news@wubios.wustl.edu]On Behalf Of Ranjan Maitra
> Sent: Tuesday, August 17, 1999 1:25 PM
> To: S-news
> Subject: [S] Shapiro-Wilks' test
>
>
>
> Dear all,
>
> Does anyone know if there is a way to perform the Shapiro-Wilks' test in
> Splus?
>
> Please post as a follow-up or I will summarize and post the responses.
>
> Thanks,
> Ranjan
>
> ***************************************************************************
> Ranjan Maitra, Department of Mathematics and Statistics,
> University of Maryland, Baltimore County, Baltimore, MD 21250, USA.
> ***************************************************************************
>
> \|/ satyamevajayate | tamasomaajyotirgamaya \|/
> -*- | -*-
> /|\ TRUTH SHALL PREVAIL | FROM DARKNESS TO LIGHT /|\
>
> ***************************************************************************
> Ph: 410-455-2436 FAX: 410-455-1066 http://www.math.umbc.edu/~maitra
> ***************************************************************************
>
> -----------------------------------------------------------------------
> This message was distributed by s-news@wubios.wustl.edu. To unsubscribe
> send e-mail to s-news-request@wubios.wustl.edu with the BODY of the
> message: unsubscribe s-news
>
>
***************************************************************************
Ranjan Maitra, Department of Mathematics and Statistics,
University of Maryland, Baltimore County, Baltimore, MD 21250, USA.
***************************************************************************
\|/ satyamevajayate | tamasomaajyotirgamaya \|/
-*- | -*-
/|\ TRUTH SHALL PREVAIL | FROM DARKNESS TO LIGHT /|\
***************************************************************************
Ph: 410-455-2436 FAX: 410-455-1066 http://www.math.umbc.edu/~maitra
***************************************************************************
-----------------------------------------------------------------------
This message was distributed by s-news@wubios.wustl.edu. To unsubscribe
send e-mail to s-news-request@wubios.wustl.edu with the BODY of the
message: unsubscribe s-news
