Home » date » 2010 » Dec » 21 »

paper: standard deviation 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: Tue, 21 Dec 2010 13:34:54 +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/21/t1292938591nzbm14msm2ed12j.htm/, Retrieved Thu, 23 May 2013 10:38:40 +0000

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

System-generated keywords (parent):

t1292869493nqdzf3lao7biq7z (pk = 113053)

Estimated Impact

Dataseries X:

» Textfile « » CSV « » Stem and Leaf « » Histogram « » Kernel Density « » Harrell-Davis Quantiles « » Central Tendency « » Variability «

Output produced by software:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	557.4235	28.9928268427439	68.247
2	516.761	22.6630255261737	49.335
3	500.84475	19.3844696836583	43.1770000000001
4	459.42475	20.8225332012382	43.7
5	419.304	20.3720509358614	45.48
6	402.79	25.6678876809137	55.684
7	429.496	30.4463356196877	62.977
8	472.9065	34.8406707216341	70.944
9	549.7385	42.6800917563837	79.515
10	588.67625	24.185793204207	56.237
11	596.87225	29.0274963597736	63.3090000000001
12	588.251	23.0717899175595	50.933
13	570.04575	22.5363921894492	55.16
14	541.0475	24.1779538905452	54.5899999999999
15	507.63225	23.2730539089738	54.471
16	474.42675	23.7489296653554	57.501
17	469.7395	28.3565516180417	65.444
18	491.48075	30.9907850752984	64.471
19	538.1405	33.1517496018938	70.024
20	576.612	31.4403791643803	64.641
21	596.39725	23.6003649883499	56.089
22	588.26125	23.6080377184692	51.55
23	532.45875	21.0700082482977	41.997
24	504.865	19.5863059984946	47.578
25	554.52875	27.26852318914	55.781

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	22.3991917175778
beta	0.00729070510241743
S.D.	0.0199456201572606
T-STAT	0.365529125940135
p-value	0.718056692404911

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	2.29201354208930
beta	0.152675207330269
S.D.	0.357901713689886
T-STAT	0.426584175181007
p-value	0.67364853645006
Lambda	0.847324792669731

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292938591nzbm14msm2ed12j/1fdd01292938491.png (opens in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292938591nzbm14msm2ed12j/1fdd01292938491.ps (opens in new window)

Click here to open pdf file.

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292938591nzbm14msm2ed12j/2fdd01292938491.png (opens in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292938591nzbm14msm2ed12j/2fdd01292938491.ps (opens in new window)

Click here to open pdf file.

Parameters (Session):

par1 = 4 ;

Parameters (R input):

par1 = 4 ;

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')