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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 computationThu, 10 Dec 2009 12:24:58 -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/2009/Dec/10/t1260473210tw0gd7u7c137tvp.htm/, Retrieved Sat, 07 Jun 2025 18:32:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=65746, Retrieved Sat, 07 Jun 2025 18:32:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact243

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] [SHWWS8hetero] [2009-11-24 19:05:24] [a66d3a79ef9e5308cd94a469bc5ca464]
-    D            [Standard Deviation-Mean Plot] [SHWPAPER] [2009-12-10 19:24:58] [db49399df1e4a3dbe31268849cebfd7f] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
452
462
455
461
461
463
462
456
455
456
472
472
471
465
459
465
468
467
463
460
462
461
476
476
471
453
443
442
444
438
427
424
416
406
431
434
418
412
404
409
412
406
398
397
385
390
413
413
401
397
397
409
419
424
428
430
424
433
456
459

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'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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65746&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65746&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65746&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'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1460.5833333333336.3883179367190320
2466.0833333333335.7754705960692617
3435.7517.109938632268765
4404.7510.225858488077333
5423.08333333333320.469304439634162

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 460.583333333333 & 6.38831793671903 & 20 \tabularnewline
2 & 466.083333333333 & 5.77547059606926 & 17 \tabularnewline
3 & 435.75 & 17.1099386322687 & 65 \tabularnewline
4 & 404.75 & 10.2258584880773 & 33 \tabularnewline
5 & 423.083333333333 & 20.4693044396341 & 62 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65746&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]460.583333333333[/C][C]6.38831793671903[/C][C]20[/C][/ROW]
[ROW][C]2[/C][C]466.083333333333[/C][C]5.77547059606926[/C][C]17[/C][/ROW]
[ROW][C]3[/C][C]435.75[/C][C]17.1099386322687[/C][C]65[/C][/ROW]
[ROW][C]4[/C][C]404.75[/C][C]10.2258584880773[/C][C]33[/C][/ROW]
[ROW][C]5[/C][C]423.083333333333[/C][C]20.4693044396341[/C][C]62[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65746&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65746&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
1460.5833333333336.3883179367190320
2466.0833333333335.7754705960692617
3435.7517.109938632268765
4404.7510.225858488077333
5423.08333333333320.469304439634162






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha75.3053707289581
beta-0.144530516403160
S.D.0.121340398963367
T-STAT-1.19111621222537
p-value0.319257892402612

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 75.3053707289581 \tabularnewline
beta & -0.144530516403160 \tabularnewline
S.D. & 0.121340398963367 \tabularnewline
T-STAT & -1.19111621222537 \tabularnewline
p-value & 0.319257892402612 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65746&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]75.3053707289581[/C][/ROW]
[ROW][C]beta[/C][C]-0.144530516403160[/C][/ROW]
[ROW][C]S.D.[/C][C]0.121340398963367[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.19111621222537[/C][/ROW]
[ROW][C]p-value[/C][C]0.319257892402612[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65746&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65746&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)
alpha75.3053707289581
beta-0.144530516403160
S.D.0.121340398963367
T-STAT-1.19111621222537
p-value0.319257892402612






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha39.9826768208172
beta-6.18724675291107
S.D.4.27483289250814
T-STAT-1.44736575873048
p-value0.243604906161566
Lambda7.18724675291107

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 39.9826768208172 \tabularnewline
beta & -6.18724675291107 \tabularnewline
S.D. & 4.27483289250814 \tabularnewline
T-STAT & -1.44736575873048 \tabularnewline
p-value & 0.243604906161566 \tabularnewline
Lambda & 7.18724675291107 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65746&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]39.9826768208172[/C][/ROW]
[ROW][C]beta[/C][C]-6.18724675291107[/C][/ROW]
[ROW][C]S.D.[/C][C]4.27483289250814[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.44736575873048[/C][/ROW]
[ROW][C]p-value[/C][C]0.243604906161566[/C][/ROW]
[ROW][C]Lambda[/C][C]7.18724675291107[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65746&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65746&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)
alpha39.9826768208172
beta-6.18724675291107
S.D.4.27483289250814
T-STAT-1.44736575873048
p-value0.243604906161566
Lambda7.18724675291107


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')