Date: Fri, 7 Jul 2006 12:09:43 +0530
Reply-To: Madan Gopal Kundu <Madan.Kundu@RANBAXY.COM>
Sender: "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From: Madan Gopal Kundu <Madan.Kundu@RANBAXY.COM>
Subject: Re: Test of Normality
Content-Type: text/plain; charset="us-ascii"
Thanks for your so informative reply. I have one more question to you.
Suppose I have a data which can be divided based on different treatment
group. If the data within a or few treatment groups comes to be non
normal whereas the total data follows normal distribution then can we
apply ANOVA on that data?
Thanks and Regards,
From: SAS(r) Discussion [mailto:SAS-L@LISTSERV.UGA.EDU] On Behalf Of
David L Cassell
Sent: Friday, July 07, 2006 11:58 AM
Subject: Re: Test of Normality
>We know there is a number of statistical test to test the normality of
>distribution. some of these are:
>1. Kolmogorov Smirnov test
>2. Shapiro -Wilk's test
>3. D'Agostino-Pearson Omnibus test
>4. Cramer-vol Mises
>Now my questions are:
>which test I should use and in what situation?
>Which one is most powerful in what situation?
>Which one is most conservative in what situation?
>Any comments on this topic will be appreciated.
>Thanks and Reards,
Okay, first of all, you left out a bunch. And SAS does not do all known
normality tests. There's also Filliben, Durbin, studentized range,
binned chi-square, skewness test, kurtosis test, and half a dozen that
I'm not thinking of at the moment.
Then there's the question of what you want to *test*. Just saying
a 'test of normality' is not all that helpful. Some tests have
alternative hypotheses (like 'if non-normal the distribution is skewed
the right') and others do not. It turns out that matters.
The details of comparions of these critters are really extensive. Here
some papers you can look up for details:
Shapiro, Wilk, and Chen. 1968. A comparative study of various tests for
normality. Journal of the American Statistical Association. 63
Pearson, D'Agostino, and Bowman. 1977. Tests for departure from
normality: Comparison of powers. Biometrika 64 (August): pp. 231-246.
Here are more you can look up:
Gastwirth and Owens. 1977. Biometrika.
D'Agostino and Rosman. 1974. Biometrika.
Fama and Roll. 1971. JASA.
D'Agostino. 1973. Communications in Statistics.
Chen. 1971. JASA.
Dumonceaux, Antle, and Haas. 1973. Technometrics.
Uthoff. 1973. Annals of Statistics.
There are a million different combinations people have looked at.
One-sided alternative or not. Symmetric alternative or not. Long-
tailed or not. Contaminated distribution or not (and what *kind*
of contamination: scale? location?). You could write a master's thesis
just on a review of all these different options, and all the papers
written since these seminal ones.
My bottom line: use Shapiro-Wilk.
My 2nd line: the goodness-of-fit tests always lose to something else.
Now.. why are you obsessing about tests of normality?
David L. Cassell
3115 NW Norwood Pl.
Corvallis OR 97330
Express yourself instantly with MSN Messenger! Download today - it's
(i) The information contained in this e-mail message is intended only for the confidential use of the recipient(s) named above. This message is privileged and confidential. If the reader of this message is not the intended recipient or an agent responsible for delivering it to the intended recipient, you are hereby notified that you have received this document in error and that any review, dissemination, distribution, or copying of this message is strictly prohibited. If you have received this communication in error, please notify us immediately by e-mail, and delete the original message.
(ii) The sender confirms that Ranbaxy shall not be responsible if this email message is used for any indecent, unsolicited or illegal purposes, which are in violation of any existing laws and the same shall solely be the responsibility of the sender and that Ranbaxy shall at all times be indemnified of any civil and/ or criminal liabilities or consequences there.