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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationSat, 29 Nov 2008 04:37:20 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Nov/29/t1227958692aiffiq1c70ptqzh.htm/, Retrieved Sat, 18 May 2024 22:54:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26220, Retrieved Sat, 18 May 2024 22:54:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact205

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Box-Cox Normality Plot] [Lambda 60] [2007-12-13 15:24:10] [ede03b06b9ae6a59763c2cc70a5f12fe]
-   PD  [Box-Cox Normality Plot] [Box-Cox Normality...] [2008-11-29 10:58:38] [8545382734d98368249ce527c6558129]
-    D    [Box-Cox Normality Plot] [Box-Cox Normality...] [2008-11-29 11:00:30] [8545382734d98368249ce527c6558129]
- RMPD        [Standard Deviation-Mean Plot] [SDMP (okt02-sept08)] [2008-11-29 11:37:20] [1b288879226ab9a3cab0c803857233cc] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
95.4
101.2
101.5
101.9
101.7
100.1
97.4
96.5
99.2
102.2
105.3
111.1
114.9
124.5
142.2
159.7
165.2
198.6
207.8
219.6
239.6
235.3
218.5
213.8
205.5
198.4
198.5
190.2
180.7
193.6
192.8
195.5
197.2
196.9
178.9
172.4
156.4
143.7
153.6
168.8
185.8
199.9
205.4
197.5
199.6
200.5
193.7
179.6
169.1
169.8
195.5
194.8
204.5
203.8
204.8
204.9
240
248.3
258.4
254.9
288.3
333.6
346.3
357.5
490.7
468.2
471.2
517.1
609.2
682
614
554.2

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26220&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26220&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26220&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
11003.080043289739076.5
298.9252.400520776831565.2
3104.455.0849450996708511.9
4135.32519.797032605923544.8
5197.823.37120735720254.4
6226.812.569539901417825.8
7198.156.2559305196482715.3
8190.656.7292892145703914.8
9186.3512.637642185154624.8
10155.62510.335819593368825.1
11197.158.2577236572798919.6
12193.359.6500431777963220.9
13182.314.843404820548026.4
14204.50.4966554808583761.09999999999999
15250.48.0997942360696118.4000000000000
16331.42530.362627795806369.2
17486.822.528648428168148.9
18614.8552.3456142702837127.8

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 100 & 3.08004328973907 & 6.5 \tabularnewline
2 & 98.925 & 2.40052077683156 & 5.2 \tabularnewline
3 & 104.45 & 5.08494509967085 & 11.9 \tabularnewline
4 & 135.325 & 19.7970326059235 & 44.8 \tabularnewline
5 & 197.8 & 23.371207357202 & 54.4 \tabularnewline
6 & 226.8 & 12.5695399014178 & 25.8 \tabularnewline
7 & 198.15 & 6.25593051964827 & 15.3 \tabularnewline
8 & 190.65 & 6.72928921457039 & 14.8 \tabularnewline
9 & 186.35 & 12.6376421851546 & 24.8 \tabularnewline
10 & 155.625 & 10.3358195933688 & 25.1 \tabularnewline
11 & 197.15 & 8.25772365727989 & 19.6 \tabularnewline
12 & 193.35 & 9.65004317779632 & 20.9 \tabularnewline
13 & 182.3 & 14.8434048205480 & 26.4 \tabularnewline
14 & 204.5 & 0.496655480858376 & 1.09999999999999 \tabularnewline
15 & 250.4 & 8.09979423606961 & 18.4000000000000 \tabularnewline
16 & 331.425 & 30.3626277958063 & 69.2 \tabularnewline
17 & 486.8 & 22.5286484281681 & 48.9 \tabularnewline
18 & 614.85 & 52.3456142702837 & 127.8 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26220&T=1

[TABLE]
[ROW][C]Standard Deviation-Mean Plot[/C][/ROW]
[ROW][C]Section[/C][C]Mean[/C][C]Standard Deviation[/C][C]Range[/C][/ROW]
[ROW][C]1[/C][C]100[/C][C]3.08004328973907[/C][C]6.5[/C][/ROW]
[ROW][C]2[/C][C]98.925[/C][C]2.40052077683156[/C][C]5.2[/C][/ROW]
[ROW][C]3[/C][C]104.45[/C][C]5.08494509967085[/C][C]11.9[/C][/ROW]
[ROW][C]4[/C][C]135.325[/C][C]19.7970326059235[/C][C]44.8[/C][/ROW]
[ROW][C]5[/C][C]197.8[/C][C]23.371207357202[/C][C]54.4[/C][/ROW]
[ROW][C]6[/C][C]226.8[/C][C]12.5695399014178[/C][C]25.8[/C][/ROW]
[ROW][C]7[/C][C]198.15[/C][C]6.25593051964827[/C][C]15.3[/C][/ROW]
[ROW][C]8[/C][C]190.65[/C][C]6.72928921457039[/C][C]14.8[/C][/ROW]
[ROW][C]9[/C][C]186.35[/C][C]12.6376421851546[/C][C]24.8[/C][/ROW]
[ROW][C]10[/C][C]155.625[/C][C]10.3358195933688[/C][C]25.1[/C][/ROW]
[ROW][C]11[/C][C]197.15[/C][C]8.25772365727989[/C][C]19.6[/C][/ROW]
[ROW][C]12[/C][C]193.35[/C][C]9.65004317779632[/C][C]20.9[/C][/ROW]
[ROW][C]13[/C][C]182.3[/C][C]14.8434048205480[/C][C]26.4[/C][/ROW]
[ROW][C]14[/C][C]204.5[/C][C]0.496655480858376[/C][C]1.09999999999999[/C][/ROW]
[ROW][C]15[/C][C]250.4[/C][C]8.09979423606961[/C][C]18.4000000000000[/C][/ROW]
[ROW][C]16[/C][C]331.425[/C][C]30.3626277958063[/C][C]69.2[/C][/ROW]
[ROW][C]17[/C][C]486.8[/C][C]22.5286484281681[/C][C]48.9[/C][/ROW]
[ROW][C]18[/C][C]614.85[/C][C]52.3456142702837[/C][C]127.8[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26220&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26220&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
11003.080043289739076.5
298.9252.400520776831565.2
3104.455.0849450996708511.9
4135.32519.797032605923544.8
5197.823.37120735720254.4
6226.812.569539901417825.8
7198.156.2559305196482715.3
8190.656.7292892145703914.8
9186.3512.637642185154624.8
10155.62510.335819593368825.1
11197.158.2577236572798919.6
12193.359.6500431777963220.9
13182.314.843404820548026.4
14204.50.4966554808583761.09999999999999
15250.48.0997942360696118.4000000000000
16331.42530.362627795806369.2
17486.822.528648428168148.9
18614.8552.3456142702837127.8






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-3.62321280209625
beta0.0774539903690814
S.D.0.0134561348937579
T-STAT5.75603551693072
p-value2.94901863327410e-05

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -3.62321280209625 \tabularnewline
beta & 0.0774539903690814 \tabularnewline
S.D. & 0.0134561348937579 \tabularnewline
T-STAT & 5.75603551693072 \tabularnewline
p-value & 2.94901863327410e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26220&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.62321280209625[/C][/ROW]
[ROW][C]beta[/C][C]0.0774539903690814[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0134561348937579[/C][/ROW]
[ROW][C]T-STAT[/C][C]5.75603551693072[/C][/ROW]
[ROW][C]p-value[/C][C]2.94901863327410e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26220&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26220&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-3.62321280209625
beta0.0774539903690814
S.D.0.0134561348937579
T-STAT5.75603551693072
p-value2.94901863327410e-05






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-4.39450072440126
beta1.24839276121481
S.D.0.451394100778298
T-STAT2.76563818415509
p-value0.0137835018852611
Lambda-0.248392761214812

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -4.39450072440126 \tabularnewline
beta & 1.24839276121481 \tabularnewline
S.D. & 0.451394100778298 \tabularnewline
T-STAT & 2.76563818415509 \tabularnewline
p-value & 0.0137835018852611 \tabularnewline
Lambda & -0.248392761214812 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26220&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.39450072440126[/C][/ROW]
[ROW][C]beta[/C][C]1.24839276121481[/C][/ROW]
[ROW][C]S.D.[/C][C]0.451394100778298[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.76563818415509[/C][/ROW]
[ROW][C]p-value[/C][C]0.0137835018852611[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.248392761214812[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26220&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26220&T=3

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-4.39450072440126
beta1.24839276121481
S.D.0.451394100778298
T-STAT2.76563818415509
p-value0.0137835018852611
Lambda-0.248392761214812


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ;
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')