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paper - SD Mean Plot

*The author of this computation has been verified*
R Software Module: /rwasp_smp.wasp (opens new window with default values)
Title produced by software: Standard Deviation-Mean Plot
Date of computation: Wed, 29 Dec 2010 04:08:05 +0000
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/29/t1293595747lceya7l5mtgs25a.htm/, Retrieved Wed, 29 Dec 2010 05:09:07 +0100
 
BibTeX entries for LaTeX users:
@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/29/t1293595747lceya7l5mtgs25a.htm/},
    year = {2010},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2010},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}
 
Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
11974 10106 12069 11412 11180 10508 11288 10928 10199 11030 11234 13747 13912 12376 12264 11675 11271 10672 10933 10379 10187 10747 10970 12175 14200 11676 11258 10872 11148 10690 10684 11658 10178 10981 10773 11665 11359 10716 12928 12317 11641 10459 10953 10703 10703 11101 11334 13268 13145 12334 13153 11289 11374 10914 11299 11284 10694 11077 11104 12820 14915 11773 11608 11468 11511 11200 11164 10960 10667 11556 11372 12333 13102 11115 12572 11557 12059 11420 11185 11113 10706 11523 11391 12634 13469 11735 13281 11968 11623 11084 11509 11134 10438 11530 11491 13093 13106 11305 13113 12203 11309 11088 11234 11619 10942 11445 11291 13281 13726 11300 11983 11092 11093 10692 10786 11166 10553 11103 10969 12090 12544 12264 13783 11214 11453 10883 10381 10348 10024 10805 10796 11907 12261 11377 12689 11474 10992 10764 12164 10409 10398 10349 10865 11630 12221 10884 12 etc...
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24


Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
111306.25978.9050585405943641
211463.41666666671067.155902245303725
311315.251018.374651991194022
411456.8333333333919.714366067812809
511707.25896.3151966904172459
611710.58333333331092.087780215944248
711698.0833333333731.9274005644072396
811862.9166666667940.5687310764633031
911828865.6791343427212339
1011379.4166666667870.9811038899373173
1111366.83333333331088.775194538533759
1211281787.5959970349362340
1311085.1666666667790.9469391849622579
1411261.3333333333821.4514131964372712
1511186.251147.998188547834132


Regression: S.E.(k) = alpha + beta * Mean(k)
alpha1277.19404038628
beta-0.0298963172635848
S.D.0.145337057236038
T-STAT-0.205703334250334
p-value0.840208905821725


Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha9.32521585709698
beta-0.266822697846112
S.D.1.79594808555766
T-STAT-0.148569271011673
p-value0.88417336779935
Lambda1.26682269784611
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293595747lceya7l5mtgs25a/1qzsk1293595681.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293595747lceya7l5mtgs25a/1qzsk1293595681.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293595747lceya7l5mtgs25a/2qzsk1293595681.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293595747lceya7l5mtgs25a/2qzsk1293595681.ps (open in new window)


 
Parameters (Session):
par1 = 12 ;
 
Parameters (R input):
par1 = 12 ;
 
R code (references can be found in the software module):
par1 <- as.numeric(par1)
(n <- length(x))
(np <- floor(n / par1))
arr <- array(NA,dim=c(par1,np))
j <- 0
k <- 1
for (i in 1:(np*par1))
{
j = j + 1
arr[j,k] <- x[i]
if (j == par1) {
j = 0
k=k+1
}
}
arr
arr.mean <- array(NA,dim=np)
arr.sd <- array(NA,dim=np)
arr.range <- array(NA,dim=np)
for (j in 1:np)
{
arr.mean[j] <- mean(arr[,j],na.rm=TRUE)
arr.sd[j] <- sd(arr[,j],na.rm=TRUE)
arr.range[j] <- max(arr[,j],na.rm=TRUE) - min(arr[,j],na.rm=TRUE)
}
arr.mean
arr.sd
arr.range
(lm1 <- lm(arr.sd~arr.mean))
(lnlm1 <- lm(log(arr.sd)~log(arr.mean)))
(lm2 <- lm(arr.range~arr.mean))
bitmap(file='test1.png')
plot(arr.mean,arr.sd,main='Standard Deviation-Mean Plot',xlab='mean',ylab='standard deviation')
dev.off()
bitmap(file='test2.png')
plot(arr.mean,arr.range,main='Range-Mean Plot',xlab='mean',ylab='range')
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Standard Deviation-Mean Plot',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Section',header=TRUE)
a<-table.element(a,'Mean',header=TRUE)
a<-table.element(a,'Standard Deviation',header=TRUE)
a<-table.element(a,'Range',header=TRUE)
a<-table.row.end(a)
for (j in 1:np) {
a<-table.row.start(a)
a<-table.element(a,j,header=TRUE)
a<-table.element(a,arr.mean[j])
a<-table.element(a,arr.sd[j] )
a<-table.element(a,arr.range[j] )
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Regression: S.E.(k) = alpha + beta * Mean(k)',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,lm1$coefficients[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,lm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,4])
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Regression: ln S.E.(k) = alpha + beta * ln Mean(k)',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,lnlm1$coefficients[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,lnlm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,4])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Lambda',header=TRUE)
a<-table.element(a,1-lnlm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable2.tab')
 




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Software written by Ed van Stee & Patrick Wessa


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