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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 computationThu, 19 Nov 2015 18:16:32 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Nov/19/t14479570096rlbca2egrfhbk8.htm/, Retrieved Thu, 23 Apr 2026 07:08:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=283673, Retrieved Thu, 23 Apr 2026 07:08:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact309

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] [] [2015-11-19 18:16:32] [db7ed3fbbcc36ff904ff15d7b0c6bd86] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
80,44
80,9
81,03
81,6
81,56
82,08
83,44
83,55
82,63
82,43
82,42
82,48
82,51
83,23
83,41
83,88
83,96
84,32
85,82
85,72
84,36
84,36
84,36
85,08
84,95
85,62
86,22
86,4
86,71
87,51
89,22
89,43
88,24
88,9
88,78
89,25
88,8
89,46
89,66
90,29
90,08
90,42
92,14
92,09
91,35
91,22
90,99
91,48
90,98
91,52
91,62
92,12
92,26
92,18
94,12
93,82
93,2
93,34
93,11
93,63
93,29
93,69
94,19
94,82
94,52
94,94
96,87
96,6
95,43
95,56
95,37
96
95,6
96,17
96,26
97,2
97,23
97,74
99,37
99,37
98,22
98,27
97,98
98,53
97,98
98,63
98,74
99,37
99,51
99,66
101,62
101,71
100,49
100,81
100,48
101,01
100,62
101,12
101,45
101,34
101,39
101,93
102,42
102,18
102,72
102,43
102,35
102,69

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'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283673&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283673&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283673&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'Herman Ole Andreas Wold' @ wold.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
182.04666666666670.9715529586775753.11
284.25083333333330.970027725314483.30999999999999
387.60251.574663744769314.48
490.6651.054708059563923.34
592.65833333333331.011756648187453.14
695.10666666666671.092056719583683.58
797.66166666666671.214299898058243.77000000000001
8100.0008333333331.205769903674023.72999999999999
9101.8866666666670.6842691301120052.09999999999999

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 82.0466666666667 & 0.971552958677575 & 3.11 \tabularnewline
2 & 84.2508333333333 & 0.97002772531448 & 3.30999999999999 \tabularnewline
3 & 87.6025 & 1.57466374476931 & 4.48 \tabularnewline
4 & 90.665 & 1.05470805956392 & 3.34 \tabularnewline
5 & 92.6583333333333 & 1.01175664818745 & 3.14 \tabularnewline
6 & 95.1066666666667 & 1.09205671958368 & 3.58 \tabularnewline
7 & 97.6616666666667 & 1.21429989805824 & 3.77000000000001 \tabularnewline
8 & 100.000833333333 & 1.20576990367402 & 3.72999999999999 \tabularnewline
9 & 101.886666666667 & 0.684269130112005 & 2.09999999999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283673&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]82.0466666666667[/C][C]0.971552958677575[/C][C]3.11[/C][/ROW]
[ROW][C]2[/C][C]84.2508333333333[/C][C]0.97002772531448[/C][C]3.30999999999999[/C][/ROW]
[ROW][C]3[/C][C]87.6025[/C][C]1.57466374476931[/C][C]4.48[/C][/ROW]
[ROW][C]4[/C][C]90.665[/C][C]1.05470805956392[/C][C]3.34[/C][/ROW]
[ROW][C]5[/C][C]92.6583333333333[/C][C]1.01175664818745[/C][C]3.14[/C][/ROW]
[ROW][C]6[/C][C]95.1066666666667[/C][C]1.09205671958368[/C][C]3.58[/C][/ROW]
[ROW][C]7[/C][C]97.6616666666667[/C][C]1.21429989805824[/C][C]3.77000000000001[/C][/ROW]
[ROW][C]8[/C][C]100.000833333333[/C][C]1.20576990367402[/C][C]3.72999999999999[/C][/ROW]
[ROW][C]9[/C][C]101.886666666667[/C][C]0.684269130112005[/C][C]2.09999999999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283673&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283673&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
182.04666666666670.9715529586775753.11
284.25083333333330.970027725314483.30999999999999
387.60251.574663744769314.48
490.6651.054708059563923.34
592.65833333333331.011756648187453.14
695.10666666666671.092056719583683.58
797.66166666666671.214299898058243.77000000000001
8100.0008333333331.205769903674023.72999999999999
9101.8866666666670.6842691301120052.09999999999999






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha1.66384706633631
beta-0.00624552100505715
S.D.0.0129522621534381
T-STAT-0.482195382634324
p-value0.644379089152957

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.66384706633631 \tabularnewline
beta & -0.00624552100505715 \tabularnewline
S.D. & 0.0129522621534381 \tabularnewline
T-STAT & -0.482195382634324 \tabularnewline
p-value & 0.644379089152957 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283673&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.66384706633631[/C][/ROW]
[ROW][C]beta[/C][C]-0.00624552100505715[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0129522621534381[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.482195382634324[/C][/ROW]
[ROW][C]p-value[/C][C]0.644379089152957[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283673&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283673&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)
alpha1.66384706633631
beta-0.00624552100505715
S.D.0.0129522621534381
T-STAT-0.482195382634324
p-value0.644379089152957






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha2.71894529019071
beta-0.587511855123301
S.D.1.10071560516605
T-STAT-0.533754452436121
p-value0.610033808518045
Lambda1.5875118551233

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 2.71894529019071 \tabularnewline
beta & -0.587511855123301 \tabularnewline
S.D. & 1.10071560516605 \tabularnewline
T-STAT & -0.533754452436121 \tabularnewline
p-value & 0.610033808518045 \tabularnewline
Lambda & 1.5875118551233 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283673&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.71894529019071[/C][/ROW]
[ROW][C]beta[/C][C]-0.587511855123301[/C][/ROW]
[ROW][C]S.D.[/C][C]1.10071560516605[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.533754452436121[/C][/ROW]
[ROW][C]p-value[/C][C]0.610033808518045[/C][/ROW]
[ROW][C]Lambda[/C][C]1.5875118551233[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283673&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283673&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)
alpha2.71894529019071
beta-0.587511855123301
S.D.1.10071560516605
T-STAT-0.533754452436121
p-value0.610033808518045
Lambda1.5875118551233


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')