```Date: Wed, 24 Aug 2005 16:00:53 -0600 Reply-To: Nate Wojcik Sender: "SPSSX(r) Discussion" From: Nate Wojcik Subject: Re: Nonparametric vs. Parametric Comments: To: Hector Maletta In-Reply-To: Content-Type: text/plain; charset=ISO-8859-1 well, i am not ignoring what you are trying to teach me, i am just confused probably because we may misuse some of the statistical jargon in our field of ecology. your input and insight are highly valuable. i guess what i am trying to understand is how do i interpret a significant result of a kolmogorov-smirnov test of normality? is this not testing the sample residuals and errors? is this test important in trying to understand the distribution of my residuals and/or errors? nate On 8/24/05, Hector Maletta wrote: > Nate, > You seem to have ignored my previous remark that the normality of your > variable itself is not really that important. Parametric analysis applies > whenever you may assume your sample is a random sample, and therefore the > distribution of the differences between measures taken from many similar > samples and the population measure is a normal distribution. Errors should > be distributed normally, not the variables themselves. Otherwise, non > normally distributed variables (such as income, for example) would be > impossible tu analyze by means of samples. > In the case of a linear model, you assume that a linear relationship exists > in the population, but individuals in any sample may differ from it by an > error term, and the normality of distribution of these errors or residuals > is what you are concerned about, not the normality of the variable you are > analyzing. > > Hector > > > -----Original Message----- > > From: Nate Wojcik [mailto:nate.wojcik@gmail.com] > > Sent: Wednesday, August 24, 2005 6:06 PM > > To: Hector Maletta > > Cc: SPSSX-L@listserv.uga.edu > > Subject: Re: Nonparametric vs. Parametric > > > > hector, > > i am looking at the distribution of the enitre sample > > population, but it is still significantly non-normal. > > although i have transformed this data, i am unable to reject > > this null hypothesis. however, i have been able to reduce > > the levels of kurtosis and skewness of the entire sample > > populations to levels below 1.00 by log transforming the > > data, which visually appears to be normally distributed. is > > there a statistically ethical dilemma by continuing with a > > parametric analysis if you know that you are failing to > > satisfy the assumption of normality. my total sample size of > > the sample population is 500 samples and contains very little > > outlier samples. > > > > nate > > > > On 8/24/05, Hector Maletta wrote: > > > 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. > > > > > > Hector > > > > > > > -----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)? > > > > > > > > thanks > > > > > > > > nate > > > > > > > > __________ Informacisn de NOD32 1.1200 (20050823) __________ > > > > > > > > Este mensaje ha sido analizado con NOD32 Antivirus System > > > > http://www.nod32.com > > > > > > > > > > > > > > > > > > __________ Información de NOD32 1.1200 (20050823) __________ > > > > Este mensaje ha sido analizado con NOD32 Antivirus System > > http://www.nod32.com > > > > > > ```

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