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paper

*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, 28 Dec 2010 19:27:52 +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/28/t1293564335nik3z8qyg1hlai7.htm/, Retrieved Tue, 28 Dec 2010 20:25:36 +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/28/t1293564335nik3z8qyg1hlai7.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 «

595.130 526.883 562.254 545.427 522.084 483.414 528.797 532.749 511.380 472.941 516.118 502.940 476.118 432.418 475.525 453.638 431.417 390.934 436.414 418.451 399.528 367.749 423.433 420.450 415.906 392.949 453.203 455.926 451.879 434.996 498.811 505.940 517.395 508.456 585.132 587.971 584.027 557.196 613.433 600.049 588.993 559.271 622.580 616.645 603.243 557.949 608.882 582.930 570.492 542.907 598.067 568.717 551.773 514.465 569.055 528.897 515.229 481.141 535.612 498.547 478.587 445.911 503.412 469.797 458.365 436.761 502.205 481.627 473.698 457.200 521.671 513.354 515.369 505.652 575.676 555.865 559.504 540.994 605.635 600.315 588.224 569.861 625.950 601.554 587.760 573.307 621.764 570.214 547.034 511.873 553.870 517.058 505.702 479.060 526.638 508.060 532.394 532.115 587.896 565.710 572.708 544.417 597.160

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

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	0.00729070510241742
S.D.	0.0199456201572606
T-STAT	0.365529125940135
p-value	0.718056692404912

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	2.2920135420893
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/28/t1293564335nik3z8qyg1hlai7/1d9ex1293564468.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293564335nik3z8qyg1hlai7/1d9ex1293564468.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293564335nik3z8qyg1hlai7/2d9ex1293564468.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293564335nik3z8qyg1hlai7/2d9ex1293564468.ps (open in new window)

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')

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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