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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, 17 Dec 2009 06:19:05 -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/17/t1261056006vlvaa90x7h3a7xw.htm/, Retrieved Tue, 30 Apr 2024 03:39:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=68860, Retrieved Tue, 30 Apr 2024 03:39:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsSHW Paper: Standard deviation - mean plot
Estimated Impact97

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]
-   PD        [Standard Deviation-Mean Plot] [WS 8 Methode SMP] [2009-11-25 13:37:57] [b103a1dc147def8132c7f643ad8c8f84]
-   PD            [Standard Deviation-Mean Plot] [Paper: Standard d...] [2009-12-17 13:19:05] [a45cc820faa25ce30779915639528ec2] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
15.5
15.1
11.7
16.3
16.7
15
14.9
14.6
15.3
17.9
16.4
15.4
17.9
15.9
13.9
17.8
17.9
17.4
16.7
16
16.6
19.1
17.8
17.2
18.6
16.3
15.1
19.2
17.7
19.1
18
17.5
17.8
21.1
17.2
19.4
19.8
17.6
16.2
19.5
19.9
20
17.3
18.9
18.6
21.4
18.6
19.8
20.8
19.6
17.7
19.8
22.2
20.7
17.9
20.9
21.2
21.4
23
21.3
23.9
22.4
18.3
22.8
22.3
17.8
16.4
16
16.4
17.7
16.6
16.2
18.3

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=68860&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=68860&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68860&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
115.41.495447637452966.2
217.01666666666671.334052836171415.2
318.08333333333331.561370804094536
418.96666666666671.417637813299635.2
520.54166666666671.573911360177885.3
618.93.022942576064237.9

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 15.4 & 1.49544763745296 & 6.2 \tabularnewline
2 & 17.0166666666667 & 1.33405283617141 & 5.2 \tabularnewline
3 & 18.0833333333333 & 1.56137080409453 & 6 \tabularnewline
4 & 18.9666666666667 & 1.41763781329963 & 5.2 \tabularnewline
5 & 20.5416666666667 & 1.57391136017788 & 5.3 \tabularnewline
6 & 18.9 & 3.02294257606423 & 7.9 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68860&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]15.4[/C][C]1.49544763745296[/C][C]6.2[/C][/ROW]
[ROW][C]2[/C][C]17.0166666666667[/C][C]1.33405283617141[/C][C]5.2[/C][/ROW]
[ROW][C]3[/C][C]18.0833333333333[/C][C]1.56137080409453[/C][C]6[/C][/ROW]
[ROW][C]4[/C][C]18.9666666666667[/C][C]1.41763781329963[/C][C]5.2[/C][/ROW]
[ROW][C]5[/C][C]20.5416666666667[/C][C]1.57391136017788[/C][C]5.3[/C][/ROW]
[ROW][C]6[/C][C]18.9[/C][C]3.02294257606423[/C][C]7.9[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68860&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68860&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
115.41.495447637452966.2
217.01666666666671.334052836171415.2
318.08333333333331.561370804094536
418.96666666666671.417637813299635.2
520.54166666666671.573911360177885.3
618.93.022942576064237.9






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.0728197324557637
beta0.0915305957535485
S.D.0.173445497498283
T-STAT0.527719641465206
p-value0.625611199964018

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.0728197324557637 \tabularnewline
beta & 0.0915305957535485 \tabularnewline
S.D. & 0.173445497498283 \tabularnewline
T-STAT & 0.527719641465206 \tabularnewline
p-value & 0.625611199964018 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68860&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.0728197324557637[/C][/ROW]
[ROW][C]beta[/C][C]0.0915305957535485[/C][/ROW]
[ROW][C]S.D.[/C][C]0.173445497498283[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.527719641465206[/C][/ROW]
[ROW][C]p-value[/C][C]0.625611199964018[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68860&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68860&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)
alpha0.0728197324557637
beta0.0915305957535485
S.D.0.173445497498283
T-STAT0.527719641465206
p-value0.625611199964018






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.93834733047015
beta0.844956646660772
S.D.1.43885308925410
T-STAT0.587243168167223
p-value0.588588164760268
Lambda0.155043353339228

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.93834733047015 \tabularnewline
beta & 0.844956646660772 \tabularnewline
S.D. & 1.43885308925410 \tabularnewline
T-STAT & 0.587243168167223 \tabularnewline
p-value & 0.588588164760268 \tabularnewline
Lambda & 0.155043353339228 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68860&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.93834733047015[/C][/ROW]
[ROW][C]beta[/C][C]0.844956646660772[/C][/ROW]
[ROW][C]S.D.[/C][C]1.43885308925410[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.587243168167223[/C][/ROW]
[ROW][C]p-value[/C][C]0.588588164760268[/C][/ROW]
[ROW][C]Lambda[/C][C]0.155043353339228[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68860&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68860&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-1.93834733047015
beta0.844956646660772
S.D.1.43885308925410
T-STAT0.587243168167223
p-value0.588588164760268
Lambda0.155043353339228


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')