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Description of Statistical Computation

Author's title

Standard Deviation Mean Plot_Gem consumptieprijs roze zalm_Dominique Van Sa...

Author*Unverified author*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationWed, 16 Jul 2008 03:34:59 -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/2008/Jul/16/t1216200947sm598ew7ozs0nb8.htm/, Retrieved Mon, 03 Aug 2026 12:17:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13845, Retrieved Mon, 03 Aug 2026 12:17:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact594

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] [Standard Deviatio...] [2008-07-16 09:34:59] [934a640f32b984cc814aae4d8bf2ca79] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
11.73
11.74
11.65
11.38
11.53
11.75
11.82
11.83
11.63
11.55
11.4
11.4
11.63
11.46
11.35
11.7
11.52
11.64
11.9
11.73
11.7
11.54
11.97
11.64
11.98
11.79
11.66
11.96
11.83
12.36
12.53
12.55
12.53
12.24
12.34
12.05
12.22
12.23
11.92
12.13
12.1
12.15
12.23
12.08
12.02
11.93
12.16
11.87
11.93
11.79
11.43
11.63
11.93
11.89
11.83
11.59
12.04
11.81
11.9
11.72
11.91
11.94
11.91
11.84
12.01
11.89
11.8
11.7
11.5
11.76
11.61
11.27
11.64
11.39
11.54
11.62
11.59
11.44
11.31
11.56
11.4
11.51
11.5
11.24
11.8
11.87
11.86
12.11
11.92
12.61
13.34
13.31
13.47
13.3
13.18
13.24

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13845&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]2 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=13845&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13845&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
111.6250.1682260384126070.359999999999999
211.73250.1396125591294230.300000000000001
311.4950.1144552314225960.230000000000000
411.5350.1592691642053370.350
511.69750.1600781059358210.380000000000001
611.71250.1839157415774960.430000000000001
711.84750.1512999228904850.32
812.31750.3359935515254220.72
912.290.2001665972800320.479999999999999
1012.1250.1438749456993820.310000000000000
1112.140.06683312551921170.150000000000000
1211.9950.1260952021291850.290000000000001
1311.6950.2150193789716020.5
1411.810.1523154621172780.34
1511.86750.1364734406395610.319999999999999
1611.90.04242640687119280.0999999999999996
1711.850.1319090595827290.310000000000000
1811.5350.2063169083392500.49
1911.54750.1135414755350070.25
2011.4750.1276714533480370.279999999999999
2111.41250.1252663828274240.270000000000000
2211.910.1368697677843180.309999999999999
2312.7950.6738199561702921.42
2413.29750.1250000000000000.290000000000001

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 11.625 & 0.168226038412607 & 0.359999999999999 \tabularnewline
2 & 11.7325 & 0.139612559129423 & 0.300000000000001 \tabularnewline
3 & 11.495 & 0.114455231422596 & 0.230000000000000 \tabularnewline
4 & 11.535 & 0.159269164205337 & 0.350 \tabularnewline
5 & 11.6975 & 0.160078105935821 & 0.380000000000001 \tabularnewline
6 & 11.7125 & 0.183915741577496 & 0.430000000000001 \tabularnewline
7 & 11.8475 & 0.151299922890485 & 0.32 \tabularnewline
8 & 12.3175 & 0.335993551525422 & 0.72 \tabularnewline
9 & 12.29 & 0.200166597280032 & 0.479999999999999 \tabularnewline
10 & 12.125 & 0.143874945699382 & 0.310000000000000 \tabularnewline
11 & 12.14 & 0.0668331255192117 & 0.150000000000000 \tabularnewline
12 & 11.995 & 0.126095202129185 & 0.290000000000001 \tabularnewline
13 & 11.695 & 0.215019378971602 & 0.5 \tabularnewline
14 & 11.81 & 0.152315462117278 & 0.34 \tabularnewline
15 & 11.8675 & 0.136473440639561 & 0.319999999999999 \tabularnewline
16 & 11.9 & 0.0424264068711928 & 0.0999999999999996 \tabularnewline
17 & 11.85 & 0.131909059582729 & 0.310000000000000 \tabularnewline
18 & 11.535 & 0.206316908339250 & 0.49 \tabularnewline
19 & 11.5475 & 0.113541475535007 & 0.25 \tabularnewline
20 & 11.475 & 0.127671453348037 & 0.279999999999999 \tabularnewline
21 & 11.4125 & 0.125266382827424 & 0.270000000000000 \tabularnewline
22 & 11.91 & 0.136869767784318 & 0.309999999999999 \tabularnewline
23 & 12.795 & 0.673819956170292 & 1.42 \tabularnewline
24 & 13.2975 & 0.125000000000000 & 0.290000000000001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13845&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]11.625[/C][C]0.168226038412607[/C][C]0.359999999999999[/C][/ROW]
[ROW][C]2[/C][C]11.7325[/C][C]0.139612559129423[/C][C]0.300000000000001[/C][/ROW]
[ROW][C]3[/C][C]11.495[/C][C]0.114455231422596[/C][C]0.230000000000000[/C][/ROW]
[ROW][C]4[/C][C]11.535[/C][C]0.159269164205337[/C][C]0.350[/C][/ROW]
[ROW][C]5[/C][C]11.6975[/C][C]0.160078105935821[/C][C]0.380000000000001[/C][/ROW]
[ROW][C]6[/C][C]11.7125[/C][C]0.183915741577496[/C][C]0.430000000000001[/C][/ROW]
[ROW][C]7[/C][C]11.8475[/C][C]0.151299922890485[/C][C]0.32[/C][/ROW]
[ROW][C]8[/C][C]12.3175[/C][C]0.335993551525422[/C][C]0.72[/C][/ROW]
[ROW][C]9[/C][C]12.29[/C][C]0.200166597280032[/C][C]0.479999999999999[/C][/ROW]
[ROW][C]10[/C][C]12.125[/C][C]0.143874945699382[/C][C]0.310000000000000[/C][/ROW]
[ROW][C]11[/C][C]12.14[/C][C]0.0668331255192117[/C][C]0.150000000000000[/C][/ROW]
[ROW][C]12[/C][C]11.995[/C][C]0.126095202129185[/C][C]0.290000000000001[/C][/ROW]
[ROW][C]13[/C][C]11.695[/C][C]0.215019378971602[/C][C]0.5[/C][/ROW]
[ROW][C]14[/C][C]11.81[/C][C]0.152315462117278[/C][C]0.34[/C][/ROW]
[ROW][C]15[/C][C]11.8675[/C][C]0.136473440639561[/C][C]0.319999999999999[/C][/ROW]
[ROW][C]16[/C][C]11.9[/C][C]0.0424264068711928[/C][C]0.0999999999999996[/C][/ROW]
[ROW][C]17[/C][C]11.85[/C][C]0.131909059582729[/C][C]0.310000000000000[/C][/ROW]
[ROW][C]18[/C][C]11.535[/C][C]0.206316908339250[/C][C]0.49[/C][/ROW]
[ROW][C]19[/C][C]11.5475[/C][C]0.113541475535007[/C][C]0.25[/C][/ROW]
[ROW][C]20[/C][C]11.475[/C][C]0.127671453348037[/C][C]0.279999999999999[/C][/ROW]
[ROW][C]21[/C][C]11.4125[/C][C]0.125266382827424[/C][C]0.270000000000000[/C][/ROW]
[ROW][C]22[/C][C]11.91[/C][C]0.136869767784318[/C][C]0.309999999999999[/C][/ROW]
[ROW][C]23[/C][C]12.795[/C][C]0.673819956170292[/C][C]1.42[/C][/ROW]
[ROW][C]24[/C][C]13.2975[/C][C]0.125000000000000[/C][C]0.290000000000001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13845&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13845&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
111.6250.1682260384126070.359999999999999
211.73250.1396125591294230.300000000000001
311.4950.1144552314225960.230000000000000
411.5350.1592691642053370.350
511.69750.1600781059358210.380000000000001
611.71250.1839157415774960.430000000000001
711.84750.1512999228904850.32
812.31750.3359935515254220.72
912.290.2001665972800320.479999999999999
1012.1250.1438749456993820.310000000000000
1112.140.06683312551921170.150000000000000
1211.9950.1260952021291850.290000000000001
1311.6950.2150193789716020.5
1411.810.1523154621172780.34
1511.86750.1364734406395610.319999999999999
1611.90.04242640687119280.0999999999999996
1711.850.1319090595827290.310000000000000
1811.5350.2063169083392500.49
1911.54750.1135414755350070.25
2011.4750.1276714533480370.279999999999999
2111.41250.1252663828274240.270000000000000
2211.910.1368697677843180.309999999999999
2312.7950.6738199561702921.42
2413.29750.1250000000000000.290000000000001






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-1.19968979697791
beta0.115294608878911
S.D.0.0531814471020427
T-STAT2.16794794353166
p-value0.0412543545077481

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -1.19968979697791 \tabularnewline
beta & 0.115294608878911 \tabularnewline
S.D. & 0.0531814471020427 \tabularnewline
T-STAT & 2.16794794353166 \tabularnewline
p-value & 0.0412543545077481 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13845&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.19968979697791[/C][/ROW]
[ROW][C]beta[/C][C]0.115294608878911[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0531814471020427[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.16794794353166[/C][/ROW]
[ROW][C]p-value[/C][C]0.0412543545077481[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13845&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13845&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-1.19968979697791
beta0.115294608878911
S.D.0.0531814471020427
T-STAT2.16794794353166
p-value0.0412543545077481






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-11.5814652734706
beta3.91134793402164
S.D.2.88654940235535
T-STAT1.35502546079069
p-value0.189160835774739
Lambda-2.91134793402164

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -11.5814652734706 \tabularnewline
beta & 3.91134793402164 \tabularnewline
S.D. & 2.88654940235535 \tabularnewline
T-STAT & 1.35502546079069 \tabularnewline
p-value & 0.189160835774739 \tabularnewline
Lambda & -2.91134793402164 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13845&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-11.5814652734706[/C][/ROW]
[ROW][C]beta[/C][C]3.91134793402164[/C][/ROW]
[ROW][C]S.D.[/C][C]2.88654940235535[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.35502546079069[/C][/ROW]
[ROW][C]p-value[/C][C]0.189160835774739[/C][/ROW]
[ROW][C]Lambda[/C][C]-2.91134793402164[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13845&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13845&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-11.5814652734706
beta3.91134793402164
S.D.2.88654940235535
T-STAT1.35502546079069
p-value0.189160835774739
Lambda-2.91134793402164


Figures (Output of Computation)

Input Parameters & R Code

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')