Date: Wed, 24 Aug 2005 16:34:13 -0300
Reply-To: Hector Maletta <firstname.lastname@example.org>
Sender: "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
From: Hector Maletta <email@example.com>
Subject: Re: Nonparametric vs. Parametric
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Without addressing the full scope of the questions, let me recall once again
that normality is not required of the variables themselves, but of the
residuals. A variable can have a skewed or pointed or flattened distribution
(relative to normal) and still be analyzable by parametric methods, provided
the sample is a random sample and residuals are distributed normally. In
fact what is theoretically needed is that the SAMPLING DISTRIBUTION is
normal, i.e. that different results (e.g. different averages) obtained from
many similar samples show a normal distribution; the Law of Large Numbers
states that under such conditions the average of all those averages will
tend to equal the population average if sample size is large. This does not
require all variables to have a normal distribution either at population or
sample levels. However, an extremely skewed distribution in a sample makes
the resulting average more unstable (and the standard error larger)because
of outliers, but this is quite a different problem.
> -----Original Message-----
> From: SPSSX(r) Discussion [mailto:SPSSX-L@LISTSERV.UGA.EDU]
> On Behalf Of Nate Wojcik
> Sent: Wednesday, August 24, 2005 4:23 PM
> To: SPSSX-L@LISTSERV.UGA.EDU
> Subject: Nonparametric vs. Parametric
> i am currently analyzing data and i have come across a few
> ideas that i need clarification on. my design consists of a
> single DV and multiple IV's (with one IV containing greater
> than two levels). my hypotheses have been structured such
> that a multi-way ANOVA
> (three-way) should be sufficient. however, i am unable to
> satisfy the assumption of a normally distributed population.
> first of all, when determining the distribution and variances
> for a multi-way ANOVA, should the sample distribution be
> analyzed by grouping factors?
> second, since there are not any nonparametric equivalents for
> designs with more than two IV's (to the best of my knowledge,
> unless a SRH extension works, but how?), how important is it
> to meet all of the assumptions of a three-way ANOVA.
> furthermore, if i can transform my data (log and
> log+constant) to allow both the skewness and the kurtosis to
> approach zero, will this suffice a normally distributed
> population. are there any helpful cutoffs or limits?
> finally, if i am working with pre- and post-burn treatments,
> can these be viewed as repeated measures DVs? also, are
> there any statistical techniques that allow you to compare
> the variance explained with treatment response ratios
> (standardized data)?
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