[R] Looking for a test of standard normality

[Herschtal Alan]

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. I could just perform a KS test on the 2 samples, but
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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