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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationSat, 16 May 2009 05:08:39 -0600
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/May/16/t1242472156qp3gsb96naj3bbz.htm/, Retrieved Thu, 27 Aug 2026 17:08:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=40165, Retrieved Thu, 27 Aug 2026 17:08:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact481

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Standard Deviation-Mean Plot] [Opgave 8, oefenin...] [2009-05-16 11:08:39] [564a720da86171cdf215ca3dfe587c26] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1,54
1,55
1,53
1,55
1,55
1,53
1,54
1,54
1,54
1,53
1,53
1,53
1,54
1,53
1,53
1,54
1,55
1,53
1,53
1,53
1,53
1,52
1,54
1,53
1,52
1,54
1,53
1,54
1,54
1,53
1,54
1,54
1,52
1,52
1,57
1,6
1,59
1,6
1,6
1,62
1,61
1,61
1,62
1,61
1,62
1,61
1,62
1,61
1,61
1,58
1,57
1,57
1,66
1,66
1,67
1,68
1,66
1,66
1,64
1,61
1,58
1,57
1,54
1,61
1,65
1,6
1,57
1,56
1,55
1,54
1,51
1,5
1,5
1,49
1,47
1,47
1,49
1,49
1,49
1,51
1,49
1,48
1,46
1,46
1,45
1,45
1,44
1,47
1,47
1,45
1,43
1,44
1,38
1,4
1,37
1,41

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=40165&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=40165&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40165&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
11.538333333333330.008348471099367230.02
21.533333333333330.007784989441615240.03
31.540833333333330.02314316444667970.08
41.610.009534625892455930.03
51.630833333333330.04077841080619480.110000000000000
61.5650.04210376791603420.15
71.483333333333330.01556997888323050.05
81.430.03302891295379080.0999999999999999

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 1.53833333333333 & 0.00834847109936723 & 0.02 \tabularnewline
2 & 1.53333333333333 & 0.00778498944161524 & 0.03 \tabularnewline
3 & 1.54083333333333 & 0.0231431644466797 & 0.08 \tabularnewline
4 & 1.61 & 0.00953462589245593 & 0.03 \tabularnewline
5 & 1.63083333333333 & 0.0407784108061948 & 0.110000000000000 \tabularnewline
6 & 1.565 & 0.0421037679160342 & 0.15 \tabularnewline
7 & 1.48333333333333 & 0.0155699788832305 & 0.05 \tabularnewline
8 & 1.43 & 0.0330289129537908 & 0.0999999999999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40165&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]1.53833333333333[/C][C]0.00834847109936723[/C][C]0.02[/C][/ROW]
[ROW][C]2[/C][C]1.53333333333333[/C][C]0.00778498944161524[/C][C]0.03[/C][/ROW]
[ROW][C]3[/C][C]1.54083333333333[/C][C]0.0231431644466797[/C][C]0.08[/C][/ROW]
[ROW][C]4[/C][C]1.61[/C][C]0.00953462589245593[/C][C]0.03[/C][/ROW]
[ROW][C]5[/C][C]1.63083333333333[/C][C]0.0407784108061948[/C][C]0.110000000000000[/C][/ROW]
[ROW][C]6[/C][C]1.565[/C][C]0.0421037679160342[/C][C]0.15[/C][/ROW]
[ROW][C]7[/C][C]1.48333333333333[/C][C]0.0155699788832305[/C][C]0.05[/C][/ROW]
[ROW][C]8[/C][C]1.43[/C][C]0.0330289129537908[/C][C]0.0999999999999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40165&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40165&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
11.538333333333330.008348471099367230.02
21.533333333333330.007784989441615240.03
31.540833333333330.02314316444667970.08
41.610.009534625892455930.03
51.630833333333330.04077841080619480.110000000000000
61.5650.04210376791603420.15
71.483333333333330.01556997888323050.05
81.430.03302891295379080.0999999999999999






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.0091803697526636
beta0.0205759112956354
S.D.0.0911107140102872
T-STAT0.225834157037911
p-value0.82882659130374

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.0091803697526636 \tabularnewline
beta & 0.0205759112956354 \tabularnewline
S.D. & 0.0911107140102872 \tabularnewline
T-STAT & 0.225834157037911 \tabularnewline
p-value & 0.82882659130374 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40165&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.0091803697526636[/C][/ROW]
[ROW][C]beta[/C][C]0.0205759112956354[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0911107140102872[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.225834157037911[/C][/ROW]
[ROW][C]p-value[/C][C]0.82882659130374[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40165&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40165&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-0.0091803697526636
beta0.0205759112956354
S.D.0.0911107140102872
T-STAT0.225834157037911
p-value0.82882659130374






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.90750982213363
beta-0.214154076438839
S.D.6.88478129694886
T-STAT-0.0311054290909351
p-value0.97619434430773
Lambda1.21415407643884

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.90750982213363 \tabularnewline
beta & -0.214154076438839 \tabularnewline
S.D. & 6.88478129694886 \tabularnewline
T-STAT & -0.0311054290909351 \tabularnewline
p-value & 0.97619434430773 \tabularnewline
Lambda & 1.21415407643884 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40165&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.90750982213363[/C][/ROW]
[ROW][C]beta[/C][C]-0.214154076438839[/C][/ROW]
[ROW][C]S.D.[/C][C]6.88478129694886[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.0311054290909351[/C][/ROW]
[ROW][C]p-value[/C][C]0.97619434430773[/C][/ROW]
[ROW][C]Lambda[/C][C]1.21415407643884[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40165&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40165&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-3.90750982213363
beta-0.214154076438839
S.D.6.88478129694886
T-STAT-0.0311054290909351
p-value0.97619434430773
Lambda1.21415407643884


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')