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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, 24 Nov 2009 06:59:00 -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/Nov/24/t1259071197jttvcwm66err9ek.htm/, Retrieved Sun, 10 Nov 2024 19:45:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=59067, Retrieved Sun, 10 Nov 2024 19:45:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact237

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]
- R PD          [Standard Deviation-Mean Plot] [] [2009-11-24 13:59:00] [4057bfb3a128b4e91b455d276991f7f0] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
11
8
6
10
11
10
9
8
11
10
12
13
13
13
13
13
12
13
12
13
12
14
11
12
13
13
12
10
9
10
10
9
7
11
11
12
13
13
12
12
10
12
12
12
10
13
13
11
13
12
11
12
12
11
10
9
10
9
6
7
5
8
5
5
5
1
3
5
7
2
3

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time0 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 & 0 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59067&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]0 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=59067&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59067&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 time0 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
19.916666666666671.928651593652157
212.58333333333330.792961461098763
310.58333333333331.781640374554426
411.91666666666671.083624669450833
510.16666666666672.124888588879787

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 9.91666666666667 & 1.92865159365215 & 7 \tabularnewline
2 & 12.5833333333333 & 0.79296146109876 & 3 \tabularnewline
3 & 10.5833333333333 & 1.78164037455442 & 6 \tabularnewline
4 & 11.9166666666667 & 1.08362466945083 & 3 \tabularnewline
5 & 10.1666666666667 & 2.12488858887978 & 7 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59067&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]9.91666666666667[/C][C]1.92865159365215[/C][C]7[/C][/ROW]
[ROW][C]2[/C][C]12.5833333333333[/C][C]0.79296146109876[/C][C]3[/C][/ROW]
[ROW][C]3[/C][C]10.5833333333333[/C][C]1.78164037455442[/C][C]6[/C][/ROW]
[ROW][C]4[/C][C]11.9166666666667[/C][C]1.08362466945083[/C][C]3[/C][/ROW]
[ROW][C]5[/C][C]10.1666666666667[/C][C]2.12488858887978[/C][C]7[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59067&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59067&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
19.916666666666671.928651593652157
212.58333333333330.792961461098763
310.58333333333331.781640374554426
411.91666666666671.083624669450833
510.16666666666672.124888588879787






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha6.89302914541536
beta-0.484955511288958
S.D.0.0566286266266246
T-STAT-8.56378726057521
p-value0.00334622584360631

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 6.89302914541536 \tabularnewline
beta & -0.484955511288958 \tabularnewline
S.D. & 0.0566286266266246 \tabularnewline
T-STAT & -8.56378726057521 \tabularnewline
p-value & 0.00334622584360631 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59067&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]6.89302914541536[/C][/ROW]
[ROW][C]beta[/C][C]-0.484955511288958[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0566286266266246[/C][/ROW]
[ROW][C]T-STAT[/C][C]-8.56378726057521[/C][/ROW]
[ROW][C]p-value[/C][C]0.00334622584360631[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59067&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59067&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)
alpha6.89302914541536
beta-0.484955511288958
S.D.0.0566286266266246
T-STAT-8.56378726057521
p-value0.00334622584360631






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha9.97717655396098
beta-4.00982944547986
S.D.0.471176160656947
T-STAT-8.51025535733614
p-value0.00340773711042219
Lambda5.00982944547986

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 9.97717655396098 \tabularnewline
beta & -4.00982944547986 \tabularnewline
S.D. & 0.471176160656947 \tabularnewline
T-STAT & -8.51025535733614 \tabularnewline
p-value & 0.00340773711042219 \tabularnewline
Lambda & 5.00982944547986 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59067&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]9.97717655396098[/C][/ROW]
[ROW][C]beta[/C][C]-4.00982944547986[/C][/ROW]
[ROW][C]S.D.[/C][C]0.471176160656947[/C][/ROW]
[ROW][C]T-STAT[/C][C]-8.51025535733614[/C][/ROW]
[ROW][C]p-value[/C][C]0.00340773711042219[/C][/ROW]
[ROW][C]Lambda[/C][C]5.00982944547986[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59067&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59067&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)
alpha9.97717655396098
beta-4.00982944547986
S.D.0.471176160656947
T-STAT-8.51025535733614
p-value0.00340773711042219
Lambda5.00982944547986


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 2 ; par3 = 1 ; par4 = 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')