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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 computationTue, 24 Nov 2009 10:13:49 -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/2009/Nov/24/t1259082907dm8scpwvskef6cv.htm/, Retrieved Fri, 15 Aug 2025 01:29:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=59172, Retrieved Fri, 15 Aug 2025 01:29:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsws8mb1
Estimated Impact363

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Standard Deviation-Mean Plot] [Identifying Integ...] [2009-11-22 12:50:05] [b98453cac15ba1066b407e146608df68]
-    D          [Standard Deviation-Mean Plot] [] [2009-11-24 17:13:49] [9ea4b07b6662a0f40f92decdf1e3b5d5] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2756.76
2849.27
2921.44
2981.85
3080.58
3106.22
3119.31
3061.26
3097.31
3161.69
3257.16
3277.01
3295.32
3363.99
3494.17
3667.03
3813.06
3917.96
3895.51
3801.06
3570.12
3701.61
3862.27
3970.1
4138.52
4199.75
4290.89
4443.91
4502.64
4356.98
4591.27
4696.96
4621.4
4562.84
4202.52
4296.49
4435.23
4105.18
4116.68
3844.49
3720.98
3674.4
3857.62
3801.06
3504.37
3032.6
3047.03
2962.34
2197.82
2014.45
1862.83
1905.41
1810.99
1670.07
1864.44
2052.02
2029.6
2070.83
2293.41
2443.27

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59172&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59172&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59172&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
13055.82166666667155.281507230832520.25
23696.01666666667222.550220535964674.78
34408.68083333333186.791884993011558.44
43675.165465.3630941045341472.89
52017.92833333333216.874341322902773.2

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 3055.82166666667 & 155.281507230832 & 520.25 \tabularnewline
2 & 3696.01666666667 & 222.550220535964 & 674.78 \tabularnewline
3 & 4408.68083333333 & 186.791884993011 & 558.44 \tabularnewline
4 & 3675.165 & 465.363094104534 & 1472.89 \tabularnewline
5 & 2017.92833333333 & 216.874341322902 & 773.2 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59172&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]3055.82166666667[/C][C]155.281507230832[/C][C]520.25[/C][/ROW]
[ROW][C]2[/C][C]3696.01666666667[/C][C]222.550220535964[/C][C]674.78[/C][/ROW]
[ROW][C]3[/C][C]4408.68083333333[/C][C]186.791884993011[/C][C]558.44[/C][/ROW]
[ROW][C]4[/C][C]3675.165[/C][C]465.363094104534[/C][C]1472.89[/C][/ROW]
[ROW][C]5[/C][C]2017.92833333333[/C][C]216.874341322902[/C][C]773.2[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59172&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59172&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
13055.82166666667155.281507230832520.25
23696.01666666667222.550220535964674.78
34408.68083333333186.791884993011558.44
43675.165465.3630941045341472.89
52017.92833333333216.874341322902773.2






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha180.310094124248
beta0.0204888167190271
S.D.0.078896518615104
T-STAT0.259692278932884
p-value0.811903161559404

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 180.310094124248 \tabularnewline
beta & 0.0204888167190271 \tabularnewline
S.D. & 0.078896518615104 \tabularnewline
T-STAT & 0.259692278932884 \tabularnewline
p-value & 0.811903161559404 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59172&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]180.310094124248[/C][/ROW]
[ROW][C]beta[/C][C]0.0204888167190271[/C][/ROW]
[ROW][C]S.D.[/C][C]0.078896518615104[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.259692278932884[/C][/ROW]
[ROW][C]p-value[/C][C]0.811903161559404[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59172&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59172&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)
alpha180.310094124248
beta0.0204888167190271
S.D.0.078896518615104
T-STAT0.259692278932884
p-value0.811903161559404






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha3.82196995460562
beta0.200064491412243
S.D.0.801180825211442
T-STAT0.249712031437401
p-value0.818932367035057
Lambda0.799935508587757

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 3.82196995460562 \tabularnewline
beta & 0.200064491412243 \tabularnewline
S.D. & 0.801180825211442 \tabularnewline
T-STAT & 0.249712031437401 \tabularnewline
p-value & 0.818932367035057 \tabularnewline
Lambda & 0.799935508587757 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59172&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.82196995460562[/C][/ROW]
[ROW][C]beta[/C][C]0.200064491412243[/C][/ROW]
[ROW][C]S.D.[/C][C]0.801180825211442[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.249712031437401[/C][/ROW]
[ROW][C]p-value[/C][C]0.818932367035057[/C][/ROW]
[ROW][C]Lambda[/C][C]0.799935508587757[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59172&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59172&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)
alpha3.82196995460562
beta0.200064491412243
S.D.0.801180825211442
T-STAT0.249712031437401
p-value0.818932367035057
Lambda0.799935508587757


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 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')