Date:         Mon, 20 Sep 2010 05:20:34 -0700
Reply-To:     Bruce Weaver <bruce.weaver@hotmail.com>
Sender:       "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
From:         Bruce Weaver <bruce.weaver@hotmail.com>
Subject:      Re: Normality Issues
In-Reply-To:  <COL117-W3365910A8E893A9BE32FCED97E0@phx.gbl>
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DorraJ Oet wrote:
>
>
> Hi,
>
> There are these issues that are bothering me about normality. As we know,
> means comparison of means require normailty.
>
> Suppose if I am going to use an ANOVA testing, and my scale variable is
> not normal even after I do a LN or sqrt, what should I do?
>
> It will be nice also if there is a way for me to know which normalisation
> method to use as in sqrt, LN, or something else based on some Statistics.
>
> Thank you for any advice.
>
> Dorraj Oet
>
>


What do the distributions look like?  Note that you need to plot the two
groups separately.  And what are your sample sizes?


Here are some comments that might give some insight into why I asked those
questions.

1. Remember that the normality assumption applies to the errors, which means
it is normality within groups, not normality for all of the groups combined.

2. Independence of observations is the far more important assumption.

3. ANOVA and the t-test are quite robust to violations of normality,
especially as the sample size increases.

All t-tests have the same basic format:

   t = (statistic - parameter|H0) / SE of the statistic

If the statistic in the numerator has a sampling distribution that is
approximately normal, the test will be pretty good.

For the independent groups t-test, the statistic is the difference between
the two sample means.  The central limit theorem tells us that:

1. If the populations are normal, the sampling distribution will be normal,
regardless of sample size.

2. If the populations are not normal, the sampling distribution will
converge on the normal distribution as sample size increases.  (E.g., see
the sampling distribution demo here:
http://onlinestatbook.com/stat_sim/index.html.)

So if your population distributions are similar in shape and your sample
sizes are large enough, the t-test is probably better than you think.

HTH.



-----
--
Bruce Weaver
bweaver@lakeheadu.ca
http://sites.google.com/a/lakeheadu.ca/bweaver/

"When all else fails, RTFM."

NOTE: My Hotmail account is not monitored regularly.
To send me an e-mail, please use the address shown above.

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