Looking for a test of standard normality

Thanks for your response. The background is that I am trying to test
whether a small sample and a much larger sample actually came from the
same distribution.

as I said, ideally I'd like a test that is more powerful than that. So I
look at the percentile ranks of the small sample within the large
sample, which should be uniformly distributed if the 2 samples are from
the same population, and then transform using "qnorm". The result should
be standard normal. Perhaps the next best alternative is to do
chi-square test on the percentiles, checking for equal numbers in each
decile bin. This would certainly work, and the only disadvantage that I
can see is that the selection of the bin boundaries is somewhat
arbitrary.

Alan Herschtal
Senior Biostatistician
Peter MacCallum Cancer Centre

Phone +61 3 9656 3639
Fax +61 3 9656 1420
Email alan.herschtal at petermac.org


-----Original Message-----
From: Rolf Turner [mailto:rolf.turner at xtra.co.nz]
Sent: Friday, 9 November 2012 2:17 PM
To: Herschtal Alan
Cc: r-help at r-project.org
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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