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*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: Mon, 29 Nov 2010 11:05:08 +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/Nov/29/t1291028610pxa3dnub8abje3c.htm/, Retrieved Mon, 29 Nov 2010 12:03:35 +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/Nov/29/t1291028610pxa3dnub8abje3c.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 «

1483509 8036554 4623093 5528662 4221032 8061847 7640066 2935533 8161548 2543967 13163450 3348436 3997440 2322911 2019457 3047748 5728767 2605173 5646743 13121544 3453409 1878333 4247362 23022552 7646203 9016602 3606568 3173510 17568772 10805045 31056269 15623385 6663443 35435745 2823250 5197089 4120632 8832767 3695374 8385805 3777904 5199532 5297275 14847382 5900158 4416718 3926429 4876884 2795297 3385527 3877941 3556729 4982836 2976325 2295026 2218752 4146062 3302091 3864505 5454794 1749836 6684048 2809918 4092664 5070470 9814477 6665318 3912554 6188129 3627991 3308767 3820332 4932979 5567917 5020814 3803273 3999984 4883104 13731747 47531824 8415570 22178158 61211654 18223748 17678085 49299580 25899948 34121754 9859231 29740892 21085212 43003866 59549247 18026465 4680597 5564728 11792347 10371624 3728446 5732978 4067638 2395508 5018801 22068888 7678580 15510095 6471239 14349204 35151574 8210488 50226 etc...

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	'George Udny Yule' @ 72.249.76.132

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	5812308.08333333	3312517.75370574	11679941
2	5924286.58333333	6184840.94408869	21144219
3	12384656.75	10834927.0152040	32612495
4	6106405	3231244.9339519	11152008
5	3571323.75	980350.933519507	3236042
6	4812042	2200852.84038537	8064641
7	16625064.3333333	18847811.7939311	57408381
8	26542467.0833333	17382379.1838339	54868650
9	9098779	5891083.96310983	19673380
10	20094789.3333333	11870449.4527863	40810385
11	23672538.4166667	14609789.9415415	51943585
12	8787287.66666667	4887133.55454458	17544823
13	4918554.33333333	3388000.01761839	12156008
14	4895496.58333333	2561647.46441811	8059748
15	5320338.58333333	2463647.83273069	8788873
16	6336601.33333333	3694116.50194329	15118601
17	5091366.41666667	2608189.13367847	9068850
18	6306279.91666667	11503251.9517503	41219222
19	3272701.91666667	1153992.96872267	3804818
20	3059517	1435915.27671606	5009403
21	2769857.08333333	1647415.17246534	5894877
22	3642657.66666667	2725124.51965531	10365089
23	4946865.83333333	5606467.52230558	19378318
24	9430565.58333333	9900871.27270352	28747415
25	9529346.25	6490908.59977652	21176391
26	11859047.6666667	7876457.69555935	24905305
27	22178387.0833333	10338022.8159808	41874289
28	18241501.5	10513921.1230792	37777994
29	9347184.5	5632078.73279563	19861596

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	578809.483589033
beta	0.630013325969396
S.D.	0.0713535529034484
T-STAT	8.82945978628274
p-value	1.91156346858981e-09

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-2.45856607560088
beta	1.12654669229298
S.D.	0.109403356853796
T-STAT	10.2971857965791
p-value	7.54675276333026e-11
Lambda	-0.126546692292975

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/29/t1291028610pxa3dnub8abje3c/1h4hi1291028706.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/29/t1291028610pxa3dnub8abje3c/1h4hi1291028706.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/29/t1291028610pxa3dnub8abje3c/2h4hi1291028706.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/29/t1291028610pxa3dnub8abje3c/2h4hi1291028706.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = 0 ; par3 = 0 ; par4 = 12 ;

Parameters (R input):

par1 = 12 ; par2 = 0 ; par3 = 0 ; par4 = 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')

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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