James, Is the degree of the problem going to be proportional to the degree of correlation? Can he ignore a small amount of correlation?
Would we agree to avoid anything using a CV and all ANOVA procedures? There are lots of examples out there where these types of things have been done. Be wary, Andrew! Again, I suggest manufacturing a data set with known distributions in order to check that your statistic represents what you want to study. Correlation and non-normality are hard to avoid in plant measures. Soule (1971), who I referenced before, used a statistic much like Anderson's generalized variance, with some additional transformations. I was interested in population variability, but ultimately I became interested in within-plant variability as a way to weight characters. That is where plants, with their modular form, provide a way for us to recognize some kinds of environmental variation. Yrs, Patricia On 10/16/07, morphmet <[EMAIL PROTECTED]> wrote: > > The classical measure for this is the generalized variance which is > the determinant of the covariance matrix. This would probably work > well unless some of the variables were highly correlated. The problem > then is that a perfect correlation results in a generalized variance > equal to zero even there is lots of variability in each variable > studied. > > There are also some ad hoc measures that could be tried such as the > average or geometric mean of the variances. > > The variables should also be in the same units - perhaps > log-transformed morphological measurements. > > ========================= > F. James Rohlf > Distinguished Professor, Stony Brook University > http://life.bio.sunysb.edu/ee/rohlf > > > > -----Original Message----- > > From: morphmet [mailto:[EMAIL PROTECTED] > > Sent: Monday, October 15, 2007 3:46 PM > > To: morphmet > > Subject: Measure of variability > > > > Dear Morphometricians: I am a taxonomist working on a revision of a > > genus with about 80 species of plants (palms). I have a data matrix > > with > > measures of about 20 variables, taken from herbarium specimens. Some > > species are obviously much more variable than others. What I want is > > a > > single measure of variability of each species. What is this? > > > > Thanks. Andrew Henderson > > > > > > -- > > Replies will be sent to the list. > > For more information visit http://www.morphometrics.org > > > > > -- > Replies will be sent to the list. > For more information visit http://www.morphometrics.org > > -- Replies will be sent to the list. For more information visit http://www.morphometrics.orgJames, Is the degree of the problem going to be proportional to the degree of correlation? Can he ignore a small amount of correlation?
Would we agree to avoid anything using a CV and all ANOVA procedures? There are lots of examples out there where these types of things have been done. Be wary, Andrew! Again, I suggest manufacturing a data set with known distributions in order to check that your statistic represents what you want to study. Correlation and non-normality are hard to avoid in plant measures.
Soule (1971), who I referenced before, used a statistic much like Anderson's generalized variance, with some additional transformations.
I was interested in population variability, but ultimately I became interested in within-plant variability as a way to weight characters. That is where plants, with their modular form, provide a way for us to recognize some kinds of environmental variation.
Yrs,
Patricia
On 10/16/07, morphmet <[EMAIL PROTECTED]> wrote:
The classical measure for this is the generalized variance which is
the determinant of the covariance matrix. This would probably work
well unless some of the variables were highly correlated. The problem
then is that a perfect correlation results in a generalized variance
equal to zero even there is lots of variability in each variable
studied.
There are also some ad hoc measures that could be tried such as the
average or geometric mean of the variances.
The variables should also be in the same units - perhaps
log-transformed morphological measurements.
=========================
F. James Rohlf
Distinguished Professor, Stony Brook University
http://life.bio.sunysb.edu/ee/rohlf
> -----Original Message-----
> From: morphmet [mailto:[EMAIL PROTECTED]]
> Sent: Monday, October 15, 2007 3:46 PM
> To: morphmet
> Subject: Measure of variability
>
> Dear Morphometricians: I am a taxonomist working on a revision of a
> genus with about 80 species of plants (palms). I have a data matrix
> with
> measures of about 20 variables, taken from herbarium specimens. Some
> species are obviously much more variable than others. What I want is
> a
> single measure of variability of each species. What is this?
>
> Thanks. Andrew Henderson
>
>
> --
> Replies will be sent to the list.
> For more information visit http://www.morphometrics.org
--
Replies will be sent to the list.
For more information visit http://www.morphometrics.org
