Hi all,
I am trying to figure out the formula used by R's Spearman rho (using
cor(method="spearman")) because I can't seem to get the same value
as by
calculating "by hand". Perhaps I'm using "cor" wrong,
but I don't know
where. Basically, I am running these commands:
> y=read.table(file="tmp",header=TRUE,sep="\t")
> y
IQ Hours
1 106 7
2 86 0
3 97 20
4 113 12
5 120 12
6 110 17
> cor(y[1],y[2],method="spearman")
Hours
IQ 0.2319084
[it's an abbreviated example of one I took from Wikipedia]. I
calculated by hand (apologies if the table looks strange when pasted
into e-mail):
IQ Hours rank(IQ) rank(hours) diff diff^2
1 106 7 3 2 1 1
2 86 0 1 1 0 0
3 97 20 2 6 -4 16
4 113 12 5 3.5 1.5 2.25
5 120 12 6 3.5 2.5 6.25
6 110 17 4 5 -1 1
26.5
rho= 0.242857
where rho = (1 - ((6 * 26.5) / 6 * (6^2 - 1))). I kept modifying the
table and realized that the difference in result comes from ties. i.e.,
if I remove the tie in rows 4 and 5, I get the same result from both cor
and calculating by hand. Perhaps I'm handling ties wrong...does anyone
know how R does it or perhaps I need to change how I'm using it?
Thank you!
Ray
Hi, You can try with cor.test(rank(y[1]),rank(y[2])) On 5/29/07, Raymond Wan <rwan at kuicr.kyoto-u.ac.jp> wrote:> > Hi all, > > I am trying to figure out the formula used by R's Spearman rho (using > cor(method="spearman")) because I can't seem to get the same value as by > calculating "by hand". Perhaps I'm using "cor" wrong, but I don't know > where. Basically, I am running these commands: > > > y=read.table(file="tmp",header=TRUE,sep="\t") > > y > IQ Hours > 1 106 7 > 2 86 0 > 3 97 20 > 4 113 12 > 5 120 12 > 6 110 17 > > cor(y[1],y[2],method="spearman") > Hours > IQ 0.2319084 > > [it's an abbreviated example of one I took from Wikipedia]. I > calculated by hand (apologies if the table looks strange when pasted > into e-mail): > > IQ Hours rank(IQ) rank(hours) diff diff^2 > 1 106 7 3 2 1 1 > 2 86 0 1 1 0 0 > 3 97 20 2 6 -4 16 > 4 113 12 5 3.5 1.5 2.25 > 5 120 12 6 3.5 2.5 6.25 > 6 110 17 4 5 -1 1 > 26.5 > > rho= 0.242857 > > where rho = (1 - ((6 * 26.5) / 6 * (6^2 - 1))). I kept modifying the > table and realized that the difference in result comes from ties. i.e., > if I remove the tie in rows 4 and 5, I get the same result from both cor > and calculating by hand. Perhaps I'm handling ties wrong...does anyone > know how R does it or perhaps I need to change how I'm using it? > > Thank you! > > Ray > > ______________________________________________ > R-help at stat.math.ethz.ch mailing list > stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. >-- "The scientists of today think deeply instead of clearly. One must be sane to think clearly, but one can think deeply and be quite insane." Nikola Tesla macgrass.com
Dear Ray,
The R's Spearman calculated by R is correct for ties or nonties, which is
not correct is the probability for the case of ties. I send to you formulates it
for the correlation with ties, that is equal to R.
Regards,
Felipe de Mendiburu
Statistician
# Spearman correlation "rs" with ties or no ties
rs<-function(x,y) {
d<-rank(x)-rank(y)
tx<-as.numeric(table(x))
ty<-as.numeric(table(y))
Lx<-sum((tx^3-tx)/12)
Ly<-sum((ty^3-ty)/12)
N<-length(x)
SX2<- (N^3-N)/12 - Lx
SY2<- (N^3-N)/12 - Ly
rs<- (SX2+SY2-sum(d^2))/(2*sqrt(SX2*SY2))
return(rs)
}
# Aplicacion> cor(y[,1],y[,2],method="spearman")
[1] 0.2319084> rs(y[,1],y[,2])
[1] 0.2319084
-----Original Message-----
From: r-help-bounces at stat.math.ethz.ch
[mailto:r-help-bounces at stat.math.ethz.ch]On Behalf Of Raymond Wan
Sent: Monday, May 28, 2007 10:29 PM
To: r-help at stat.math.ethz.ch
Subject: [R] R's Spearman
Hi all,
I am trying to figure out the formula used by R's Spearman rho (using
cor(method="spearman")) because I can't seem to get the same value
as by
calculating "by hand". Perhaps I'm using "cor" wrong,
but I don't know
where. Basically, I am running these commands:
> y=read.table(file="tmp",header=TRUE,sep="\t")
> y
IQ Hours
1 106 7
2 86 0
3 97 20
4 113 12
5 120 12
6 110 17
> cor(y[1],y[2],method="spearman")
Hours
IQ 0.2319084
[it's an abbreviated example of one I took from Wikipedia]. I
calculated by hand (apologies if the table looks strange when pasted
into e-mail):
IQ Hours rank(IQ) rank(hours) diff diff^2
1 106 7 3 2 1 1
2 86 0 1 1 0 0
3 97 20 2 6 -4 16
4 113 12 5 3.5 1.5 2.25
5 120 12 6 3.5 2.5 6.25
6 110 17 4 5 -1 1
26.5
rho= 0.242857
where rho = (1 - ((6 * 26.5) / 6 * (6^2 - 1))). I kept modifying the
table and realized that the difference in result comes from ties. i.e.,
if I remove the tie in rows 4 and 5, I get the same result from both cor
and calculating by hand. Perhaps I'm handling ties wrong...does anyone
know how R does it or perhaps I need to change how I'm using it?
Thank you!
Ray
______________________________________________
R-help at stat.math.ethz.ch mailing list
stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.