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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, 20 Dec 2011 14:19:22 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/20/t13244088017z2bo5e4g7tfcok.htm/, Retrieved Mon, 10 Nov 2025 00:56:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=158174, Retrieved Mon, 10 Nov 2025 00:56:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact343

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] [WS 8 30] [2009-11-22 15:55:09] [6e4e01d7eb22a9f33d58ebb35753a195]
-    D          [Standard Deviation-Mean Plot] [Paper heteroskeda...] [2010-12-21 11:22:29] [a9e130f95bad0a0597234e75c6380c5a]
-    D              [Standard Deviation-Mean Plot] [] [2011-12-20 19:19:22] [3b32143baae8ca4a077b118800e50af3] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
103.7
103.75
103.85
104.02
104.13
104.17
104.18
104.2
104.5
104.78
104.88
104.89
104.9
104.95
105.24
105.35
105.44
105.46
105.47
105.48
105.75
106.1
106.19
106.23
106.24
106.25
106.35
106.48
106.52
106.55
106.55
106.56
106.89
107.09
107.24
107.28
107.3
107.31
107.47
107.35
107.31
107.32
107.32
107.34
107.53
107.72
107.75
107.79
107.81
107.9
107.8
107.86
107.8
107.74
107.75
107.83
107.8
107.81
107.86
107.83

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'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158174&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158174&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158174&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'Gertrude Mary Cox' @ cox.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1104.2541666666670.4203128344315441.19
2105.5466666666670.4435873047886921.33
3106.6666666666670.3674069661667831.04000000000001
4107.4591666666670.1911428943502920.490000000000009
5107.8158333333330.04501683186892780.160000000000011

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 104.254166666667 & 0.420312834431544 & 1.19 \tabularnewline
2 & 105.546666666667 & 0.443587304788692 & 1.33 \tabularnewline
3 & 106.666666666667 & 0.367406966166783 & 1.04000000000001 \tabularnewline
4 & 107.459166666667 & 0.191142894350292 & 0.490000000000009 \tabularnewline
5 & 107.815833333333 & 0.0450168318689278 & 0.160000000000011 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158174&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]104.254166666667[/C][C]0.420312834431544[/C][C]1.19[/C][/ROW]
[ROW][C]2[/C][C]105.546666666667[/C][C]0.443587304788692[/C][C]1.33[/C][/ROW]
[ROW][C]3[/C][C]106.666666666667[/C][C]0.367406966166783[/C][C]1.04000000000001[/C][/ROW]
[ROW][C]4[/C][C]107.459166666667[/C][C]0.191142894350292[/C][C]0.490000000000009[/C][/ROW]
[ROW][C]5[/C][C]107.815833333333[/C][C]0.0450168318689278[/C][C]0.160000000000011[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158174&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158174&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
1104.2541666666670.4203128344315441.19
2105.5466666666670.4435873047886921.33
3106.6666666666670.3674069661667831.04000000000001
4107.4591666666670.1911428943502920.490000000000009
5107.8158333333330.04501683186892780.160000000000011






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha10.7910692515507
beta-0.0987092049744891
S.D.0.0361034652387599
T-STAT-2.73406456476419
p-value0.0716951193758454

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 10.7910692515507 \tabularnewline
beta & -0.0987092049744891 \tabularnewline
S.D. & 0.0361034652387599 \tabularnewline
T-STAT & -2.73406456476419 \tabularnewline
p-value & 0.0716951193758454 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158174&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]10.7910692515507[/C][/ROW]
[ROW][C]beta[/C][C]-0.0987092049744891[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0361034652387599[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.73406456476419[/C][/ROW]
[ROW][C]p-value[/C][C]0.0716951193758454[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158174&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158174&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)
alpha10.7910692515507
beta-0.0987092049744891
S.D.0.0361034652387599
T-STAT-2.73406456476419
p-value0.0716951193758454






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha243.974771369762
beta-52.5992438426602
S.D.26.6304621322218
T-STAT-1.97515325049569
p-value0.142728873961931
Lambda53.5992438426602

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 243.974771369762 \tabularnewline
beta & -52.5992438426602 \tabularnewline
S.D. & 26.6304621322218 \tabularnewline
T-STAT & -1.97515325049569 \tabularnewline
p-value & 0.142728873961931 \tabularnewline
Lambda & 53.5992438426602 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158174&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]243.974771369762[/C][/ROW]
[ROW][C]beta[/C][C]-52.5992438426602[/C][/ROW]
[ROW][C]S.D.[/C][C]26.6304621322218[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.97515325049569[/C][/ROW]
[ROW][C]p-value[/C][C]0.142728873961931[/C][/ROW]
[ROW][C]Lambda[/C][C]53.5992438426602[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158174&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158174&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)
alpha243.974771369762
beta-52.5992438426602
S.D.26.6304621322218
T-STAT-1.97515325049569
p-value0.142728873961931
Lambda53.5992438426602


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')