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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 computationWed, 26 Apr 2017 15:55:30 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Apr/26/t1493218548y5eqgt6abtnirxq.htm/, Retrieved Sun, 19 Apr 2026 21:29:11 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sun, 19 Apr 2026 21:29:11 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0

Tree of Dependent Computations

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
92,49
92,46
92,55
92,24
92,41
92,83
92,85
93,04
93,04
92,83
92,96
92,83
93,01
93,21
93,58
94,07
94,57
95,03
95,21
95,89
96,43
96,35
96,71
96,32
97,23
97,88
98,2
98,56
99,31
99,69
99,77
101,06
101,77
101,91
102,52
102,09
102,22
102,74
103,56
104,4
104,76
104,86
104,84
104,96
104,83
104,58
104,8
104,17
104,63
105,32
106,16
107,22
107,51
107,87
107,79
108,04
107,74
107,71
111,19
110,82
113,65
114,72
114,32
116,76
116,47
117,34
116,92
116,48
115,07
116,45
116,84
114,31

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'Sir Maurice George Kendall' @ kendall.wessa.net

\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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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'Sir Maurice George Kendall' @ kendall.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
192.71083333333330.268072525238750.800000000000011
295.03166666666671.334485487051663.69999999999999
399.99916666666671.827295360179455.28999999999999
4104.2266666666670.9111265088622522.73999999999999
5107.6666666666671.901742422733496.56
6115.77751.26811330867413.69

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 92.7108333333333 & 0.26807252523875 & 0.800000000000011 \tabularnewline
2 & 95.0316666666667 & 1.33448548705166 & 3.69999999999999 \tabularnewline
3 & 99.9991666666667 & 1.82729536017945 & 5.28999999999999 \tabularnewline
4 & 104.226666666667 & 0.911126508862252 & 2.73999999999999 \tabularnewline
5 & 107.666666666667 & 1.90174242273349 & 6.56 \tabularnewline
6 & 115.7775 & 1.2681133086741 & 3.69 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]92.7108333333333[/C][C]0.26807252523875[/C][C]0.800000000000011[/C][/ROW]
[ROW][C]2[/C][C]95.0316666666667[/C][C]1.33448548705166[/C][C]3.69999999999999[/C][/ROW]
[ROW][C]3[/C][C]99.9991666666667[/C][C]1.82729536017945[/C][C]5.28999999999999[/C][/ROW]
[ROW][C]4[/C][C]104.226666666667[/C][C]0.911126508862252[/C][C]2.73999999999999[/C][/ROW]
[ROW][C]5[/C][C]107.666666666667[/C][C]1.90174242273349[/C][C]6.56[/C][/ROW]
[ROW][C]6[/C][C]115.7775[/C][C]1.2681133086741[/C][C]3.69[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
192.71083333333330.268072525238750.800000000000011
295.03166666666671.334485487051663.69999999999999
399.99916666666671.827295360179455.28999999999999
4104.2266666666670.9111265088622522.73999999999999
5107.6666666666671.901742422733496.56
6115.77751.26811330867413.69






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-1.72534085335861
beta0.0290258659563973
S.D.0.03251012113714
T-STAT0.892825524517587
p-value0.422410341535078

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -1.72534085335861 \tabularnewline
beta & 0.0290258659563973 \tabularnewline
S.D. & 0.03251012113714 \tabularnewline
T-STAT & 0.892825524517587 \tabularnewline
p-value & 0.422410341535078 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.72534085335861[/C][/ROW]
[ROW][C]beta[/C][C]0.0290258659563973[/C][/ROW]
[ROW][C]S.D.[/C][C]0.03251012113714[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.892825524517587[/C][/ROW]
[ROW][C]p-value[/C][C]0.422410341535078[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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-1.72534085335861
beta0.0290258659563973
S.D.0.03251012113714
T-STAT0.892825524517587
p-value0.422410341535078






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-21.1166947180792
beta4.57616004499071
S.D.3.76790275524425
T-STAT1.21451118626178
p-value0.291345984161365
Lambda-3.57616004499071

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -21.1166947180792 \tabularnewline
beta & 4.57616004499071 \tabularnewline
S.D. & 3.76790275524425 \tabularnewline
T-STAT & 1.21451118626178 \tabularnewline
p-value & 0.291345984161365 \tabularnewline
Lambda & -3.57616004499071 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-21.1166947180792[/C][/ROW]
[ROW][C]beta[/C][C]4.57616004499071[/C][/ROW]
[ROW][C]S.D.[/C][C]3.76790275524425[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.21451118626178[/C][/ROW]
[ROW][C]p-value[/C][C]0.291345984161365[/C][/ROW]
[ROW][C]Lambda[/C][C]-3.57616004499071[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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-21.1166947180792
beta4.57616004499071
S.D.3.76790275524425
T-STAT1.21451118626178
p-value0.291345984161365
Lambda-3.57616004499071


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')