Thanks for your response, however it seems to me that the
Anderson-Darling Test and the Shapiro-Wilk test are both tests of
composite normality, at least as implemented in R. I.e. they test
whether it is reasonable to assume that the data came from any normal
distribution, not specifically the standard normal. Consider the
p-values that come from the following code.
> qq <- rnorm(100,3,4)
> ks.test(qq, "pnorm")
One-sample Kolmogorov-Smirnov test
data: qq
D = 0.5614, p-value < 2.2e-16
alternative hypothesis: two-sided
> shapiro.test(qq)
Shapiro-Wilk normality test
data: qq
W = 0.9831, p-value = 0.2286
Alan Herschtal
Senior Biostatistician
Peter MacCallum Cancer Centre
Phone +61 3 9656 3639
Fax +61 3 9656 1420
Email [email protected]
________________________________
From: Mark Lamias [mailto:[email protected]]
Sent: Friday, 9 November 2012 2:22 PM
To: Rolf Turner; Herschtal Alan
Cc: [email protected]
Subject: Re: [R] Looking for a test of standard normality
The Anderson-Darling Test and the Shapiro-Wilk test have considerably
more power.
I'd refer you to a non-R related discussion board for statistics related
questions. Perhaps the following might be more useful:
http://stats.stackexchange.com/questions/8184/most-powerful-gof-test-for
-normality
Sincerely yours,
Mark J. Lamias
________________________________
From: Rolf Turner <[email protected]>
To: Herschtal Alan <[email protected]>
Cc: [email protected]
Sent: Thursday, November 8, 2012 10:16 PM
Subject: Re: [R] Looking for a test of standard normality
Others may correct me, but I cannot imagine any test of standard
normality
giving appreciably more power than is given by the Kolmogorov-Smirnov
test.
I also wonder about the point of testing for (standard) normality in the
first place. There is a quote --- I think it refers to testing for
heteroscedasticity,
but I believe it applies equally to testing for normality --- about
such testing
being analogous to going out of the harbour in a rowing dinghy to see if
it's
safe for an ocean liner to put to sea.
cheers,
Rolf Turner
On 09/11/12 13:23, Herschtal Alan wrote:
> Dear list members,
>
> I am looking for a goodness of test that will tell me if a sample is
> likely to have come from a standard normal distribution. I can find
> plenty of omnibus tests for normality in the nor.test package, but
none
> of them appear to allow me to test against the specific alternative
that
> the data are not standard normal. My back up option is to use a
> Kolmogorov-Smirnov test, but my impression is that that is not a very
> powerful test. Any suggestions?
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