FreeStatistics.org

Free Statistics

of Irreproducible Research!

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, 01 Dec 2007 04:24:53 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Dec/01/t1196507689zwbuzrzpn2hd712.htm/, Retrieved Tue, 10 Feb 2026 01:39:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2208, Retrieved Tue, 10 Feb 2026 01:39:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact476

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...] [2007-12-01 11:24:53] [bd02e85be52eb1cb060a2c60779eb820] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9,1
11,2
7,7
7,9
-2,4
-2,8
-4,9
2,3
7,9
6,7
6
3,8
4,7
6,4
9,3
11
8,5
8,8
10
16,8
11,6
11,5
6
2,9
2,1
2,7
11,2
7,3
11,6
4,6
6
-0,5
1,8
3,7
8,3
8,3
12
7,8
5,3
1
-0,3
2,4
2,7
5,7
3,5
0,6
5,2
2,9
1
-5,5
-7,1
-7,9
-8,8
-7
-5,5
-7,3
-7,5
-3,5
2,2
3,1
4,1
4,2
6
5,5
5,1
5,5
1
1,5
1,2
1,7
-8,6
-11,2
-12,7
-3,1
-1
0,3
-2,9
-2,2
3,2
5,9
13,3
7,3
6,9
8,3
11,8
9,2
5,8
8,8
14,6
28,1
19,7
16,5
-5,3
-2,4
1,9
1,6
-0,1
-1,9
3,4
3,3
3,3
-9,8
-4,6
-6,1
10,6
8,8
10,7
11,7

Tables (Output of Computation)





Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2208&T=0

[TABLE]
[ROW][C]Summary of compuational 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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2208&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2208&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
14.3755.2301790339598123.9
28.958333333333333.7009724356845722.3
35.591666666666673.8365368695628618.7
44.066666666666673.4267220842117119.9
5-4.483333333333334.2189687092578611.9
61.333333333333335.5808655785693915.8
71.941666666666676.9526264930251518.8
89.191666666666679.6495368078504535.4
92.441666666666677.1414867733080219.2

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 4.375 & 5.23017903395981 & 23.9 \tabularnewline
2 & 8.95833333333333 & 3.70097243568457 & 22.3 \tabularnewline
3 & 5.59166666666667 & 3.83653686956286 & 18.7 \tabularnewline
4 & 4.06666666666667 & 3.42672208421171 & 19.9 \tabularnewline
5 & -4.48333333333333 & 4.21896870925786 & 11.9 \tabularnewline
6 & 1.33333333333333 & 5.58086557856939 & 15.8 \tabularnewline
7 & 1.94166666666667 & 6.95262649302515 & 18.8 \tabularnewline
8 & 9.19166666666667 & 9.64953680785045 & 35.4 \tabularnewline
9 & 2.44166666666667 & 7.14148677330802 & 19.2 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2208&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]4.375[/C][C]5.23017903395981[/C][C]23.9[/C][/ROW]
[ROW][C]2[/C][C]8.95833333333333[/C][C]3.70097243568457[/C][C]22.3[/C][/ROW]
[ROW][C]3[/C][C]5.59166666666667[/C][C]3.83653686956286[/C][C]18.7[/C][/ROW]
[ROW][C]4[/C][C]4.06666666666667[/C][C]3.42672208421171[/C][C]19.9[/C][/ROW]
[ROW][C]5[/C][C]-4.48333333333333[/C][C]4.21896870925786[/C][C]11.9[/C][/ROW]
[ROW][C]6[/C][C]1.33333333333333[/C][C]5.58086557856939[/C][C]15.8[/C][/ROW]
[ROW][C]7[/C][C]1.94166666666667[/C][C]6.95262649302515[/C][C]18.8[/C][/ROW]
[ROW][C]8[/C][C]9.19166666666667[/C][C]9.64953680785045[/C][C]35.4[/C][/ROW]
[ROW][C]9[/C][C]2.44166666666667[/C][C]7.14148677330802[/C][C]19.2[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2208&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2208&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
14.3755.2301790339598123.9
28.958333333333333.7009724356845722.3
35.591666666666673.8365368695628618.7
44.066666666666673.4267220842117119.9
5-4.483333333333334.2189687092578611.9
61.333333333333335.5808655785693915.8
71.941666666666676.9526264930251518.8
89.191666666666679.6495368078504535.4
92.441666666666677.1414867733080219.2






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha5.12884045786348
beta0.107082214403744
S.D.0.182458184692464
T-STAT0.586886330060957
p-value0.575710713527531

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 5.12884045786348 \tabularnewline
beta & 0.107082214403744 \tabularnewline
S.D. & 0.182458184692464 \tabularnewline
T-STAT & 0.586886330060957 \tabularnewline
p-value & 0.575710713527531 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2208&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]5.12884045786348[/C][/ROW]
[ROW][C]beta[/C][C]0.107082214403744[/C][/ROW]
[ROW][C]S.D.[/C][C]0.182458184692464[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.586886330060957[/C][/ROW]
[ROW][C]p-value[/C][C]0.575710713527531[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2208&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2208&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)
alpha5.12884045786348
beta0.107082214403744
S.D.0.182458184692464
T-STAT0.586886330060957
p-value0.575710713527531






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha1.79955711683198
beta-0.0889880422085147
S.D.0.211456072082675
T-STAT-0.420834650582757
p-value0.68853317631935
Lambda1.08898804220851

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.79955711683198 \tabularnewline
beta & -0.0889880422085147 \tabularnewline
S.D. & 0.211456072082675 \tabularnewline
T-STAT & -0.420834650582757 \tabularnewline
p-value & 0.68853317631935 \tabularnewline
Lambda & 1.08898804220851 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2208&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.79955711683198[/C][/ROW]
[ROW][C]beta[/C][C]-0.0889880422085147[/C][/ROW]
[ROW][C]S.D.[/C][C]0.211456072082675[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.420834650582757[/C][/ROW]
[ROW][C]p-value[/C][C]0.68853317631935[/C][/ROW]
[ROW][C]Lambda[/C][C]1.08898804220851[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2208&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2208&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)
alpha1.79955711683198
beta-0.0889880422085147
S.D.0.211456072082675
T-STAT-0.420834650582757
p-value0.68853317631935
Lambda1.08898804220851


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')