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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 computationWed, 16 Dec 2009 05:46:02 -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/16/t1260967624m0yd099bwz9k6u8.htm/, Retrieved Sat, 21 Dec 2024 13:56:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=68283, Retrieved Sat, 21 Dec 2024 13:56:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact196

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  D        [Standard Deviation-Mean Plot] [] [2009-11-24 13:08:08] [3445d50c581a74ea3ff7b84cc82fcfeb]
-    D            [Standard Deviation-Mean Plot] [SMP] [2009-12-16 12:46:02] [d1818fb1d9a1b0f34f8553ada228d3d5] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
107.11
107.57
107.81
108.75
109.43
109.62
109.54
109.53
109.84
109.67
109.79
109.56
110.22
110.40
110.69
110.72
110.89
110.58
110.94
110.91
111.22
111.09
111.00
111.06
111.55
112.32
112.64
112.36
112.04
112.37
112.59
112.89
113.22
112.85
113.06
112.99
113.32
113.74
113.91
114.52
114.96
114.91
115.30
115.44
115.52
116.08
115.94
115.56
115.88
116.66
117.41
117.68
117.85
118.21
118.92
119.03
119.17
118.95
118.92
118.90

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=68283&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=68283&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68283&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
1109.0183333333330.9688590603322472.73000000000000
2110.810.2969542358374741
3112.5733333333330.4760506721182551.67000000000000
4114.9333333333330.8894567630488492.76000000000001
5118.1316666666671.063192733176253.29000000000001

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 109.018333333333 & 0.968859060332247 & 2.73000000000000 \tabularnewline
2 & 110.81 & 0.296954235837474 & 1 \tabularnewline
3 & 112.573333333333 & 0.476050672118255 & 1.67000000000000 \tabularnewline
4 & 114.933333333333 & 0.889456763048849 & 2.76000000000001 \tabularnewline
5 & 118.131666666667 & 1.06319273317625 & 3.29000000000001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68283&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]109.018333333333[/C][C]0.968859060332247[/C][C]2.73000000000000[/C][/ROW]
[ROW][C]2[/C][C]110.81[/C][C]0.296954235837474[/C][C]1[/C][/ROW]
[ROW][C]3[/C][C]112.573333333333[/C][C]0.476050672118255[/C][C]1.67000000000000[/C][/ROW]
[ROW][C]4[/C][C]114.933333333333[/C][C]0.889456763048849[/C][C]2.76000000000001[/C][/ROW]
[ROW][C]5[/C][C]118.131666666667[/C][C]1.06319273317625[/C][C]3.29000000000001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68283&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68283&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
1109.0183333333330.9688590603322472.73000000000000
2110.810.2969542358374741
3112.5733333333330.4760506721182551.67000000000000
4114.9333333333330.8894567630488492.76000000000001
5118.1316666666671.063192733176253.29000000000001






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-3.9743402120491
beta0.0416756918028034
S.D.0.0483563167524001
T-STAT0.861845868373235
p-value0.452154987702556

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -3.9743402120491 \tabularnewline
beta & 0.0416756918028034 \tabularnewline
S.D. & 0.0483563167524001 \tabularnewline
T-STAT & 0.861845868373235 \tabularnewline
p-value & 0.452154987702556 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68283&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.9743402120491[/C][/ROW]
[ROW][C]beta[/C][C]0.0416756918028034[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0483563167524001[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.861845868373235[/C][/ROW]
[ROW][C]p-value[/C][C]0.452154987702556[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68283&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68283&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-3.9743402120491
beta0.0416756918028034
S.D.0.0483563167524001
T-STAT0.861845868373235
p-value0.452154987702556






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-35.5592354416771
beta7.4348151613314
S.D.9.14844900637546
T-STAT0.812685861412153
p-value0.47589980832091
Lambda-6.4348151613314

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -35.5592354416771 \tabularnewline
beta & 7.4348151613314 \tabularnewline
S.D. & 9.14844900637546 \tabularnewline
T-STAT & 0.812685861412153 \tabularnewline
p-value & 0.47589980832091 \tabularnewline
Lambda & -6.4348151613314 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68283&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-35.5592354416771[/C][/ROW]
[ROW][C]beta[/C][C]7.4348151613314[/C][/ROW]
[ROW][C]S.D.[/C][C]9.14844900637546[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.812685861412153[/C][/ROW]
[ROW][C]p-value[/C][C]0.47589980832091[/C][/ROW]
[ROW][C]Lambda[/C][C]-6.4348151613314[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68283&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68283&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-35.5592354416771
beta7.4348151613314
S.D.9.14844900637546
T-STAT0.812685861412153
p-value0.47589980832091
Lambda-6.4348151613314


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')