From: Douglas Bates <bates_at_stat.wisc.edu>

Date: Fri, 29 Feb 2008 10:51:04 -0600

R-help_at_r-project.org mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. Received on Fri 29 Feb 2008 - 16:53:28 GMT

Date: Fri, 29 Feb 2008 10:51:04 -0600

On Fri, Feb 29, 2008 at 10:32 AM, Nauta, A.L. <A.L.Nauta_at_students.uu.nl> wrote:

*> I tried a 6-way anova, and indeed found out that changing the order of
**> factors influences the SS, F-ratio's and p-values. So what should I do if I
**> want to know which factor most strongly rejects H0? (H0 is the hypothese of
**> "no difference" in the population means) Should I better do 6 one-way
**> anova's (on each factor) and then compare the p-values?
*

No.

If you are going to try to perform a 6-way anova on an unbalanced data set you should read more about the analysis of variance so that you can understand the model and the hypotheses involved or ask a statistical consultant. This is not a topic that can be explained in a couple of email messages.

You may find Bill Venables paper "Exegeses on Linear Models" (do an internet search on the title to find a copy) a good starting point.

> ________________________________

*>
**> From: dmbates_at_gmail.com on behalf of Douglas Bates
**> Sent: Fri 29-2-2008 15:38
**> To: Nauta, A.L.
**> Cc: R Help
**>
**>
**> Subject: Re: [R] unbalanced one-way ANOVA
**>
**>
**>
**>
**>
**> On Fri, Feb 29, 2008 at 4:47 AM, Nauta, A.L. <A.L.Nauta_at_students.uu.nl>
**> wrote:
**>
**> > Thank you for your reply,
**> > is your answer (that the approach does not depend on balance in the data)
**> > only valid for one-way anova, or also for two-way or more-way anova?
**>
**> Any kind.
**>
**> You should be aware that for unbalanced data sets the sum of squares
**> attributed to a term depends on the order in which the terms occur in
**> the model. That is, the sum of squares and the F-ratios and the
**> p-values for, say, factor A will be different if you fit a model
**>
**> y ~ A + B
**>
**> versus the model
**>
**> y ~ B + A
**>
**> to a data set where factors A and B are unbalanced.
**>
**> This is because the sums of squares displayed by R's anova methods are
**> the sequential sums of squares. Although other statistical software
**> may calculate other, more exotic, types of sums of squares, many of us
**> would argue that these are the only ones that make sense.
**>
**> If in doubt about which sum of squares to use, the general rule is
**> that you should only pay attention to the F ratio and p-value for the
**> last term in the model.
**>
**> > ________________________________
**> > From: dmbates_at_gmail.com on behalf of Douglas Bates
**> > Sent: Fri 29-2-2008 0:39
**> > To: Nauta, A.L.
**> > Cc: r-help_at_r-project.org
**> > Subject: Re: [R] unbalanced one-way ANOVA
**> >
**> >
**> >
**> >
**> >
**> > On Thu, Feb 28, 2008 at 7:52 AM, Nauta, A.L. <A.L.Nauta_at_students.uu.nl>
**> > wrote:
**> > > Hi,
**> >
**> > > I have an unbalanced dataset on which I would like to perform a one-way
**> > anova test using R (aov). According to Wannacott and Wannacott (1990) p.
**> > 333, one-way anova with unbalanced data is possible with a few
**> modifications
**> > in the anova-calculations. The modified anova calculations should take
**> into
**> > account different sample sizes and a modified definition of the average. I
**> > was wondering if the aov-function in R is suitable for one-way anova on
**> > unbalanced data.
**> >
**> > Yes.
**> >
**> > The analysis of variance is performed in R by fitting a linear model
**> > created from indicator variables for the levels of the factor. This
**> > validity of this approach does not depend on balance in the data.
**> >
**> > The formulas given in an introductory textbook are almost never the
**> > way that results are computed in practice. I think we would all be
**> > better off if they didn't even give these misleading formulas.
**> >
**>
*

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