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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationThu, 21 Jan 2010 17:17:28 -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/2010/Jan/22/t1264119579meyfjy6rujnsppt.htm/, Retrieved Wed, 01 May 2024 23:23:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72341, Retrieved Wed, 01 May 2024 23:23:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W83
Estimated Impact197

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [(Partial) Autocorrelation Function] [] [2010-01-10 13:29:02] [81991108d3b0081a8a67d5344e667e0b]
- RMPD    [Standard Deviation-Mean Plot] [] [2010-01-22 00:17:28] [d7e29fbdd9c070952bc7bcf8a141229f] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
103.6
103.7
103.8
104
104
104.1
104.2
104.3
104.4
104.5
104.7
104.7
104.9
105
105.2
105.3
105.4
105.5
105.7
105.8
105.9
106
106.1
106.2
106.6
106.8
107
107.1
107.3
107.4
107.6
107.7
107.9
108.2
108.3
108.5
108.92
109.23
109.41
109.65
109.91
110.01
110.2
110.49
110.57
110.72
110.94
111.09
111.28
111.41
111.62
111.76
111.89
112.04
112.12
112.3
112.47
112.59
112.78
112.73
112.99
113.1
113.33
113.38
113.68
113.65
113.81
113.88
114.02
114.25
114.28
114.38
114.73
114.97
115.05
115.29
115.37
115.54
115.76
115.92
116.02
116.21
116.26
116.51

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=72341&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=72341&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72341&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
1104.1666666666670.3676295896027911.10000000000001
2105.5833333333330.4323999271157391.30000000000000
3107.5333333333330.6095204274797961.90000000000001
4110.0950.6957598854359292.17
5112.08250.5058947968249381.5
6113.7291666666670.4616464277371001.39
7115.6358333333330.5667845242856381.78

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 104.166666666667 & 0.367629589602791 & 1.10000000000001 \tabularnewline
2 & 105.583333333333 & 0.432399927115739 & 1.30000000000000 \tabularnewline
3 & 107.533333333333 & 0.609520427479796 & 1.90000000000001 \tabularnewline
4 & 110.095 & 0.695759885435929 & 2.17 \tabularnewline
5 & 112.0825 & 0.505894796824938 & 1.5 \tabularnewline
6 & 113.729166666667 & 0.461646427737100 & 1.39 \tabularnewline
7 & 115.635833333333 & 0.566784524285638 & 1.78 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72341&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]104.166666666667[/C][C]0.367629589602791[/C][C]1.10000000000001[/C][/ROW]
[ROW][C]2[/C][C]105.583333333333[/C][C]0.432399927115739[/C][C]1.30000000000000[/C][/ROW]
[ROW][C]3[/C][C]107.533333333333[/C][C]0.609520427479796[/C][C]1.90000000000001[/C][/ROW]
[ROW][C]4[/C][C]110.095[/C][C]0.695759885435929[/C][C]2.17[/C][/ROW]
[ROW][C]5[/C][C]112.0825[/C][C]0.505894796824938[/C][C]1.5[/C][/ROW]
[ROW][C]6[/C][C]113.729166666667[/C][C]0.461646427737100[/C][C]1.39[/C][/ROW]
[ROW][C]7[/C][C]115.635833333333[/C][C]0.566784524285638[/C][C]1.78[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72341&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72341&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
1104.1666666666670.3676295896027911.10000000000001
2105.5833333333330.4323999271157391.30000000000000
3107.5333333333330.6095204274797961.90000000000001
4110.0950.6957598854359292.17
5112.08250.5058947968249381.5
6113.7291666666670.4616464277371001.39
7115.6358333333330.5667845242856381.78






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.57221127220221
beta0.00994388345504875
S.D.0.0108795525281630
T-STAT0.913997467203534
p-value0.402642015128107

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.57221127220221 \tabularnewline
beta & 0.00994388345504875 \tabularnewline
S.D. & 0.0108795525281630 \tabularnewline
T-STAT & 0.913997467203534 \tabularnewline
p-value & 0.402642015128107 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72341&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.57221127220221[/C][/ROW]
[ROW][C]beta[/C][C]0.00994388345504875[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0108795525281630[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.913997467203534[/C][/ROW]
[ROW][C]p-value[/C][C]0.402642015128107[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72341&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72341&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)
alpha-0.57221127220221
beta0.00994388345504875
S.D.0.0108795525281630
T-STAT0.913997467203534
p-value0.402642015128107






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-12.3629737772844
beta2.48787997938260
S.D.2.2372961177491
T-STAT1.11200299309758
p-value0.316724585514422
Lambda-1.48787997938260

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -12.3629737772844 \tabularnewline
beta & 2.48787997938260 \tabularnewline
S.D. & 2.2372961177491 \tabularnewline
T-STAT & 1.11200299309758 \tabularnewline
p-value & 0.316724585514422 \tabularnewline
Lambda & -1.48787997938260 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72341&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-12.3629737772844[/C][/ROW]
[ROW][C]beta[/C][C]2.48787997938260[/C][/ROW]
[ROW][C]S.D.[/C][C]2.2372961177491[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.11200299309758[/C][/ROW]
[ROW][C]p-value[/C][C]0.316724585514422[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.48787997938260[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72341&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72341&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-12.3629737772844
beta2.48787997938260
S.D.2.2372961177491
T-STAT1.11200299309758
p-value0.316724585514422
Lambda-1.48787997938260


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')