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Standard Deviation - Mean Plot

*Unverified author*

R Software Module: /rwasp_smp.wasp (opens new window with default values)

Title produced by software: Standard Deviation-Mean Plot

Date of computation: Mon, 16 Aug 2010 12:59:21 +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/Aug/16/t128196357015isgukox3qn5wl.htm/, Retrieved Mon, 16 Aug 2010 14:59:32 +0200

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/Aug/16/t128196357015isgukox3qn5wl.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 «

244 243 242 240 260 259 244 234 235 235 236 238 240 233 233 233 247 251 233 226 233 233 227 225 223 212 206 202 223 221 212 205 204 200 195 193 196 180 174 164 192 189 181 167 166 164 167 164 161 141 134 111 147 144 142 140 143 137 140 130 129 112 101 74 104 103 100 98 99 91 92 94 93 76 64 32 62 69 69 68 68 59 66 73 70 57 48 22 64 74 67 61 61 52 54 69 69 53 50 22 69 78 74 63 67 59 60 80 77 58 54 32 78 86 84 78 72 64 62 72

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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	242.25	1.70782512765993	4
2	249.25	12.5266382827424	26
3	236	1.41421356237310	3
4	234.75	3.5	7
5	239.25	11.7295922066086	25
6	229.5	4.12310562561766	8
7	210.75	9.14239210126832	21
8	215.25	8.34166250416147	18
9	198	4.96655480858378	11
10	178.5	13.4039795085887	32
11	182.25	11.1766124861993	25
12	165.25	1.5	3
13	136.75	20.6296711882020	50
14	143.25	2.98607881119482	7
15	137.5	5.56776436283002	13
16	104	23.079572497485	55
17	101.25	2.75378527364305	6
18	94	3.55902608401044	8
19	66.25	25.7471681290713	61
20	67	3.36650164612069	7
21	66.5	5.8022983951764	14
22	49.25	20.2875166871979	48
23	66.5	5.56776436283002	13
24	59	7.7028133388609	17
25	48.5	19.5362910161235	47
26	71	6.48074069840786	15
27	66.5	9.67815409397198	21
28	55.25	18.4639287982452	45
29	81.5	4.12310562561766	8
30	67.5	5.25991127935317	10

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	13.0378963627019
beta	-0.0288030085855783
S.D.	0.0176026505504006
T-STAT	-1.63628815462242
p-value	0.112972132068010

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	4.18304937583329
beta	-0.478264612426929
S.D.	0.256356069732124
T-STAT	-1.8656262476121
p-value	0.0726032769100583
Lambda	1.47826461242693

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/16/t128196357015isgukox3qn5wl/1nwkg1281963560.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/16/t128196357015isgukox3qn5wl/1nwkg1281963560.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/16/t128196357015isgukox3qn5wl/2nwkg1281963560.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/16/t128196357015isgukox3qn5wl/2nwkg1281963560.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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