Whether the two variables have the same units does not matter. Moreover, even if there were some way of converting cm to kg the correlation would still be the same because the correlation is invariant under unit conversion as it is invariant under multiplication of its arguments by a constant. As for your second question, the correlation estimator is a continuous function of each of the individual data points, so perturbing the values of any of them by a sufficiently small amount will only perturb the correlation by a small amount.> -----Original Message----- > From: dechao wang [SMTP:dechwang at yahoo.co.uk] > Sent: Thursday, March 07, 2002 5:34 AM > To: r-help at stat.math.ethz.ch > Subject: [R] linear correlation? > > Hi, I have checked statistic textbooks about > correlations, but I am still not sure the correlation > analysis with different units, for example, > > x1<-c(1, 2, 3, 100, 200, 300) > x2<-c(1.1,2.8,3.3, 108, 209, 303) > the unit of the first 3 numbers is cm > the unit of the last 3 numbers is kg > > cor(x1,x2)=0.999655 > > Can I explain the correlation coefficient as normal in > which all numbers have the same unit? > > Secondly, if keep the three large numbers unchanged, > just change the three small numbers, the coefficient > changes little, this means that the variation of three > small numbers is hidden by the three larger numbers. > Is there any solution in R to solve this issue? > > Thanks, > > Dechao > > __________________________________________________ > > Everything you'll ever need on one web page > from News and Sport to Email and Music Charts > > -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-. > -.-.- > r-help mailing list -- Read > http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html > Send "info", "help", or "[un]subscribe" > (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch > _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._. > _._._-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._
Perhaps I've led a sheltered life, but my own experience leads me to
question the logic behind an analysis that leads me to want to compute
correlations between vectors in which the elements have different units;
cm and kg are not generally interconvertible!
R. Woodrow Setzer, Jr. Phone:
(919) 541-0128
Experimental Toxicology Division Fax: (919)
541-5394
Pharmacokinetics Branch
NHEERL MD-74; US EPA; RTP, NC 27711
dechao wang
<dechwang at yahoo.co.u To: r-help at
stat.math.ethz.ch
k> cc:
Sent by: Subject: [R] linear
correlation?
owner-r-help at stat.ma
th.ethz.ch
03/07/02 05:33 AM
Hi, I have checked statistic textbooks about
correlations, but I am still not sure the correlation
analysis with different units, for example,
x1<-c(1, 2, 3, 100, 200, 300)
x2<-c(1.1,2.8,3.3, 108, 209, 303)
the unit of the first 3 numbers is cm
the unit of the last 3 numbers is kg
cor(x1,x2)=0.999655
Can I explain the correlation coefficient as normal in
which all numbers have the same unit?
Secondly, if keep the three large numbers unchanged,
just change the three small numbers, the coefficient
changes little, this means that the variation of three
small numbers is hidden by the three larger numbers.
Is there any solution in R to solve this issue?
Thanks,
Dechao
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To follow up, consider the vector x3 <- c(3,2,1,108, 209, 303) with the same units as before.> cor(x1,x3)[1] 0.9995864 Now express the first three values as microns instead of cm: x4 <- x3 x4[1:3] <- 10000 * x4[1:3]> cor(x1,x4)[1] -0.7461934 Just changing the units changes the whole sense of the correlation. R. Woodrow Setzer, Jr. Phone: (919) 541-0128 Experimental Toxicology Division Fax: (919) 541-5394 Pharmacokinetics Branch NHEERL MD-74; US EPA; RTP, NC 27711 Andrew Perrin <andrew_perrin at unc.e To: Joerg Maeder <maeder at atmos.umnw.ethz.ch> du> cc: dechao wang <dechwang at yahoo.co.uk>, "'R-help at lists.R-project.org'" Sent by: <R-help at stat.math.ethz.ch> owner-r-help at stat.ma Subject: Re: [R] linear correlation? th.ethz.ch 03/07/02 09:45 AM Please respond to andrew_perrin On Thu, 7 Mar 2002, Joerg Maeder wrote:> Hello > > dechao wang wrote: > > > > Hi, I have checked statistic textbooks about > > correlations, but I am still not sure the correlation > > analysis with different units, for example, > > > > x1<-c(1, 2, 3, 100, 200, 300) > > x2<-c(1.1,2.8,3.3, 108, 209, 303) > > the unit of the first 3 numbers is cm > > the unit of the last 3 numbers is kg > > > > cor(x1,x2)=0.999655 > > > > Can I explain the correlation coefficient as normal in > > which all numbers have the same unit? > > No, that will give different results. The unit must be the same forall> values. Which unit isn't important, but it must be the sameOOPS - I apologize, I misread the question, I understood the OP to be saying that x1 was in cm and x2 was in kg. What on earth would a correlation mean between two vectors, each of which is made up of two entirely different measures? (These aren't just different units, they're measures of entirely different phenomena.) ---------------------------------------------------------------------- Andrew J Perrin - andrew_perrin at unc.edu - http://www.unc.edu/~aperrin Assistant Professor of Sociology, U of North Carolina, Chapel Hill 269 Hamilton Hall, CB#3210, Chapel Hill, NC 27599-3210 USA -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-. -.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._. _._._._ -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._
Sorry, I also misread your original question and thought x1 was in cm and x2 in kg. I don't think it makes any sense for some values of x1 (or x2) to be in cm and others in kg. How can they represent samples from the same population? It would be okay if, say, some were in cm and others in km as they are equivalent units, and you could simply convert to the same unit, but otherwise I don't see how some members of a population are in cm and others in kg.> -----Original Message----- > From: Scott, Uriel [SMTP:uriel.scott at mirant.com] > Sent: Thursday, March 07, 2002 10:12 AM > To: 'dechao wang'; r-help at stat.math.ethz.ch > Subject: RE: [R] linear correlation? > > > Whether the two variables have the same units does not matter. Moreover, > even if there were some way of converting cm to kg the correlation would > still be the same because the correlation is invariant under unit > conversion > as it is invariant under multiplication of its arguments by a constant. > > As for your second question, the correlation estimator is a continuous > function of each of the individual data points, so perturbing the values > of > any of them by a sufficiently small amount will only perturb the > correlation > by a small amount. > > > -----Original Message----- > > From: dechao wang [SMTP:dechwang at yahoo.co.uk] > > Sent: Thursday, March 07, 2002 5:34 AM > > To: r-help at stat.math.ethz.ch > > Subject: [R] linear correlation? > > > > Hi, I have checked statistic textbooks about > > correlations, but I am still not sure the correlation > > analysis with different units, for example, > > > > x1<-c(1, 2, 3, 100, 200, 300) > > x2<-c(1.1,2.8,3.3, 108, 209, 303) > > the unit of the first 3 numbers is cm > > the unit of the last 3 numbers is kg > > > > cor(x1,x2)=0.999655 > > > > Can I explain the correlation coefficient as normal in > > which all numbers have the same unit? > > > > Secondly, if keep the three large numbers unchanged, > > just change the three small numbers, the coefficient > > changes little, this means that the variation of three > > small numbers is hidden by the three larger numbers. > > Is there any solution in R to solve this issue? > > > > Thanks, > > > > Dechao > > > > __________________________________________________ > > > > Everything you'll ever need on one web page > > from News and Sport to Email and Music Charts > > > > > -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-. > > -.-.- > > r-help mailing list -- Read > > http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html > > Send "info", "help", or "[un]subscribe" > > (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch > > > _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._. > > _._._ > -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-. > -.-.- > r-help mailing list -- Read > http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html > Send "info", "help", or "[un]subscribe" > (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch > _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._. > _._._-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._
If you have 3 numbers a1, a2, a3 representing the lengths of 3 branches and
b1, b2, b3 representing their branching angles then this should be
represented as { (a1,b1), (a2,b2), (a3,b3) } rather than { a1, a2, a3, b1,
b2, b3 }. I.e., you have 3 samples from a bivariate random variable
(length, angle), not 6 samples from a univariate RV.
> -----Original Message-----
> From: dechao wang [SMTP:dechwang at yahoo.co.uk]
> Sent: Thursday, March 07, 2002 10:29 AM
> To: andrew_perrin at unc.edu
> Cc: r-help at stat.math.ethz.ch
> Subject: Re: [R] linear correlation?
>
> --- Andrew Perrin <andrew_perrin at unc.edu> wrote: > On
> Thu, 7 Mar 2002, [iso-8859-1] dechao wang wrote:
> >
> > > Thanks Andrew,
> > >
> > > Consider the following example:
> > > > x1<-c(1, 2, 3, 100, 200, 300)
> > > > x2<-c(1.1,2.8,3.3, 108, 209, 303)
> > > > x3<-c(2.8,3.8,5.3, 108, 209, 303)
> > > > cor(x1,x2)
> > > [1] 0.999655
> > > > cor(x1,x3)
> > > [1] 0.9997286
> > >
> > > You can see that as x2 changed to x3 with only
> > first
> > > three numbers changing, the coefficients (x1, x2)
> > and
> > > (x1,x3) changed little. I thought this may be
> > because
> > > the last three numbers were in different units.
> >
> > It's not because they're different units -- it's
> > because they're different
> > measures altogether! Can you state, in words (e.g.,
> > not in mathematical
> > terms) what you think a correlation would *mean*
> > between these two
> > vectors? R is happily telling you, as any
> > statistical package would, what
> > the correlation is between two vectors of numbers.
> > But that correlation
> > doesn't necessarily mean anything at all; its
> > meaning is based on what the
> > vectors measure.
> >
>
> There are lots of examples. Let us consider the first
> three numbers representing three branches of an apple
> tree, the last three numbers representing the
> corresponding branching angles of the branches. So x1,
> x2, x3 represents three different trees. Maybe we can
> ask which tree is similar to which tree?
>
> __________________________________________________
>
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What about if we measure the height (x1 in cm) and weight (x2 in kg) of
a sample of people from some population. It seems it makes sense to me
to get the correlation between x1 and x2.
Charlie Liu,
Intern at ECO/EPA.
"Scott, Uriel"
<uriel.scott at mirant. To: "Scott,
Uriel" <uriel.scott at mirant.com>, 'dechao
com> wang' <dechwang at
yahoo.co.uk>, r-help at stat.math.ethz.ch
Sent by: cc:
owner-r-help at stat.ma Subject: RE: [R] linear
correlation?
th.ethz.ch
03/07/02 12:28 PM
Sorry, I also misread your original question and thought x1 was in cm
and x2
in kg.
I don't think it makes any sense for some values of x1 (or x2) to be in
cm
and others in kg. How can they represent samples from the same
population?
It would be okay if, say, some were in cm and others in km as they are
equivalent units, and you could simply convert to the same unit, but
otherwise I don't see how some members of a population are in cm and
others
in kg.
> -----Original Message-----
> From: Scott, Uriel [SMTP:uriel.scott at mirant.com]
> Sent: Thursday, March 07, 2002 10:12 AM
> To: 'dechao wang'; r-help at stat.math.ethz.ch
> Subject: RE: [R] linear correlation?
>
>
> Whether the two variables have the same units does not matter.
Moreover,> even if there were some way of converting cm to kg the correlation
would> still be the same because the correlation is invariant under unit
> conversion
> as it is invariant under multiplication of its arguments by a
constant.>
> As for your second question, the correlation estimator is a continuous
> function of each of the individual data points, so perturbing the
values> of
> any of them by a sufficiently small amount will only perturb the
> correlation
> by a small amount.
>
> > -----Original Message-----
> > From: dechao wang [SMTP:dechwang at yahoo.co.uk]
> > Sent: Thursday, March 07, 2002 5:34 AM
> > To: r-help at stat.math.ethz.ch
> > Subject: [R] linear correlation?
> >
> > Hi, I have checked statistic textbooks about
> > correlations, but I am still not sure the correlation
> > analysis with different units, for example,
> >
> > x1<-c(1, 2, 3, 100, 200, 300)
> > x2<-c(1.1,2.8,3.3, 108, 209, 303)
> > the unit of the first 3 numbers is cm
> > the unit of the last 3 numbers is kg
> >
> > cor(x1,x2)=0.999655
> >
> > Can I explain the correlation coefficient as normal in
> > which all numbers have the same unit?
> >
> > Secondly, if keep the three large numbers unchanged,
> > just change the three small numbers, the coefficient
> > changes little, this means that the variation of three
> > small numbers is hidden by the three larger numbers.
> > Is there any solution in R to solve this issue?
> >
> > Thanks,
> >
> > Dechao
> >
> > __________________________________________________
> >
> > Everything you'll ever need on one web page
> > from News and Sport to Email and Music Charts
> >
> >
> -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.
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> > (in the "body", not the subject !) To:
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Evgenia Dimitriadou
2002-Mar-19 13:32 UTC
[R] assessing performance of a classfication method
if i understood right you want to match the class labels to the clustering labels. try matchClasses in library(e1071). best, -e On 19 Mar 2002, Allan Strand wrote:> Hi all, > > I have developed a routine to classify observations based upon > clustering. In my current case there are 5 classes, so the data at > the end of the classification look like this: > > obs class > 1 2 > 2 2 > 3 1 > 4 4 > 5 4 > 6 3 > 7 5 > 8 5 > . . > . . > > I always know the numbers of classes a priori. I wanted to see how > well my approach is performing so I wrote a simulation to generate > observations in a fairly realistic manner. I then run the simulated > observations through my scheme. The "known" simulated data have the > same form as the results of the classification, but the class > identifiers may differ. In other words, a class of observations may be > constructed correctly by my approach, but the "name" of the class may > change. > > I would like to compare the results of my scheme to the "known" > simulated classes and assess its error rate. AS I start, I would just > like to know the number of observations that were mis-classified. No > doubt this is a brain-dead question to those who work in this field, > but this is my first foray into such analyses. Ultimately I was > wondering of there is an R package that performs such analyses out of > the box or if anyone who does these kind of analyses routinely has a > code snippet I could use as an example. > > Cheers, > a. > -- > Allan Strand, Biology http://linum.cofc.edu > College of Charleston Ph. (843) 953-8085 > Charleston, SC 29424 Fax (843) 953-5453 > > -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- > r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html > Send "info", "help", or "[un]subscribe" > (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch > _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._ >************************************************************************ * Evgenia Dimitriadou * ************************************************************************ * Institut f?r Statistik * Tel: (+43 1) 58801 10773 * * Technische Universit?t Wien * Fax: (+43 1) 58801 10798 * * Wiedner Hauptstr. 8-10/1071 * Evgenia.Dimitriadou at ci.tuwien.ac.at * * A-1040 Wien, Austria * http://www.ci.tuwien.ac.at/~dimi* ************************************************************************ -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._
Allan Strand wrote: Apart from matchClasses(), you might look at classAgreement(), also in e1071. g. -d> > Hi all, > > I have developed a routine to classify observations based upon > clustering. In my current case there are 5 classes, so the data at > the end of the classification look like this: > > obs class > 1 2 > 2 2 > 3 1 > 4 4 > 5 4 > 6 3 > 7 5 > 8 5 > . . > . . > > I always know the numbers of classes a priori. I wanted to see how > well my approach is performing so I wrote a simulation to generate > observations in a fairly realistic manner. I then run the simulated > observations through my scheme. The "known" simulated data have the > same form as the results of the classification, but the class > identifiers may differ. In other words, a class of observations may be > constructed correctly by my approach, but the "name" of the class may > change. > > I would like to compare the results of my scheme to the "known" > simulated classes and assess its error rate. AS I start, I would just > like to know the number of observations that were mis-classified. No > doubt this is a brain-dead question to those who work in this field, > but this is my first foray into such analyses. Ultimately I was > wondering of there is an R package that performs such analyses out of > the box or if anyone who does these kind of analyses routinely has a > code snippet I could use as an example. > > Cheers, > a. > -- > Allan Strand, Biology http://linum.cofc.edu > College of Charleston Ph. (843) 953-8085 > Charleston, SC 29424 Fax (843) 953-5453 > > -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- > r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html > Send "info", "help", or "[un]subscribe" > (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch > _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._-- Mag. David Meyer Wiedner Hauptstrasse 8-10 Vienna University of Technology A-1040 Vienna/AUSTRIA Department for Tel.: (+431) 58801/10772 Statistics and Probability Theory mail: david.meyer at ci.tuwien.ac.at -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._
R-help comes through again. I had several responses to my question yesterday (all within an hour of posting). I have found two similar solutions to my problem. The first was suggested by Ron Wehrens and is found in his CompClus package (http://www-cac.sci.kun.nl/cac/). The other came from David Meyer and is found below. Thanks everyone, a. David Meyer <david.meyer at ci.tuwien.ac.at> writes:> Allan Strand wrote: > > Apart from matchClasses(), you might look at classAgreement(), also in > e1071. > > g. > -d > > > > > Hi all, > > > > I have developed a routine to classify observations based upon > > clustering. In my current case there are 5 classes, so the data at > > the end of the classification look like this:snip> > > > I would like to compare the results of my scheme to the "known" > > simulated classes and assess its error rate. AS I start, I would just > > like to know the number of observations that were mis-classified. No > > doubt this is a brain-dead question to those who work in this field, > > but this is my first foray into such analyses. Ultimately I was > > wondering of there is an R package that performs such analyses out of > > the box or if anyone who does these kind of analyses routinely has a > > code snippet I could use as an example.snip> > -- > Mag. David Meyer Wiedner Hauptstrasse 8-10 > Vienna University of Technology A-1040 Vienna/AUSTRIA > Department for Tel.: (+431) 58801/10772 > Statistics and Probability Theory mail: david.meyer at ci.tuwien.ac.at-- Allan Strand, Biology http://linum.cofc.edu College of Charleston Ph. (843) 953-8085 Charleston, SC 29424 Fax (843) 953-5453 -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._
