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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 computationSun, 19 Dec 2010 16:28:02 +0000
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/Dec/19/t1292775935ggqn10tbhi360uq.htm/, Retrieved Sun, 05 May 2024 07:25:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112584, Retrieved Sun, 05 May 2024 07:25:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact135

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [] [2008-12-08 19:22:39] [d2d412c7f4d35ffbf5ee5ee89db327d4]
- RMP   [Spectral Analysis] [spectrum analyse ...] [2010-12-14 18:46:58] [d6e648f00513dd750579ba7880c5fbf5]
- RMP     [Standard Deviation-Mean Plot] [standard deviatio...] [2010-12-14 19:01:46] [d6e648f00513dd750579ba7880c5fbf5]
-   PD      [Standard Deviation-Mean Plot] [] [2010-12-16 10:24:09] [126c9e58bb659a0bfb4675d843c2c69e]
-    D          [Standard Deviation-Mean Plot] [] [2010-12-19 16:28:02] [a3cd012a7211edfe9ed4466e21aef6a6] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
104.31
103.88
103.88
103.86
103.89
103.98
103.98
104.29
104.29
104.24
103.98
103.54
103.44
103.32
103.3
103.26
103.14
103.11
102.91
103.23
103.23
103.14
102.91
102.42
102.1
102.07
102.06
101.98
101.83
101.75
101.56
101.66
101.65
101.61
101.52
101.31
101.19
101.11
101.1
101.07
100.98
100.93
100.92
101.02
101.01
100.97
100.89
100.62
100.53
100.48
100.48
100.47
100.52
100.49
100.47
100.44

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=112584&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=112584&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112584&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
1103.98250.2185368008673470.450000000000003
2104.0350.1752141546793540.400000000000006
3104.01250.3430621906690750.75
4103.330.07745966692414640.179999999999993
5103.09750.1350000000000030.320000000000007
6102.9250.3626292872893750.810000000000002
7102.05250.05123475382979370.119999999999990
8101.70.1163328557774330.269999999999996
9101.52250.1517399090549360.340000000000003
10101.11750.05123475382979970.120000000000005
11100.96250.04645786621588460.0999999999999943
12100.87250.1755704986607930.390000000000001
13100.490.02708012801545310.0600000000000023
14100.480.03366501646120590.0799999999999983

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 103.9825 & 0.218536800867347 & 0.450000000000003 \tabularnewline
2 & 104.035 & 0.175214154679354 & 0.400000000000006 \tabularnewline
3 & 104.0125 & 0.343062190669075 & 0.75 \tabularnewline
4 & 103.33 & 0.0774596669241464 & 0.179999999999993 \tabularnewline
5 & 103.0975 & 0.135000000000003 & 0.320000000000007 \tabularnewline
6 & 102.925 & 0.362629287289375 & 0.810000000000002 \tabularnewline
7 & 102.0525 & 0.0512347538297937 & 0.119999999999990 \tabularnewline
8 & 101.7 & 0.116332855777433 & 0.269999999999996 \tabularnewline
9 & 101.5225 & 0.151739909054936 & 0.340000000000003 \tabularnewline
10 & 101.1175 & 0.0512347538297997 & 0.120000000000005 \tabularnewline
11 & 100.9625 & 0.0464578662158846 & 0.0999999999999943 \tabularnewline
12 & 100.8725 & 0.175570498660793 & 0.390000000000001 \tabularnewline
13 & 100.49 & 0.0270801280154531 & 0.0600000000000023 \tabularnewline
14 & 100.48 & 0.0336650164612059 & 0.0799999999999983 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112584&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]103.9825[/C][C]0.218536800867347[/C][C]0.450000000000003[/C][/ROW]
[ROW][C]2[/C][C]104.035[/C][C]0.175214154679354[/C][C]0.400000000000006[/C][/ROW]
[ROW][C]3[/C][C]104.0125[/C][C]0.343062190669075[/C][C]0.75[/C][/ROW]
[ROW][C]4[/C][C]103.33[/C][C]0.0774596669241464[/C][C]0.179999999999993[/C][/ROW]
[ROW][C]5[/C][C]103.0975[/C][C]0.135000000000003[/C][C]0.320000000000007[/C][/ROW]
[ROW][C]6[/C][C]102.925[/C][C]0.362629287289375[/C][C]0.810000000000002[/C][/ROW]
[ROW][C]7[/C][C]102.0525[/C][C]0.0512347538297937[/C][C]0.119999999999990[/C][/ROW]
[ROW][C]8[/C][C]101.7[/C][C]0.116332855777433[/C][C]0.269999999999996[/C][/ROW]
[ROW][C]9[/C][C]101.5225[/C][C]0.151739909054936[/C][C]0.340000000000003[/C][/ROW]
[ROW][C]10[/C][C]101.1175[/C][C]0.0512347538297997[/C][C]0.120000000000005[/C][/ROW]
[ROW][C]11[/C][C]100.9625[/C][C]0.0464578662158846[/C][C]0.0999999999999943[/C][/ROW]
[ROW][C]12[/C][C]100.8725[/C][C]0.175570498660793[/C][C]0.390000000000001[/C][/ROW]
[ROW][C]13[/C][C]100.49[/C][C]0.0270801280154531[/C][C]0.0600000000000023[/C][/ROW]
[ROW][C]14[/C][C]100.48[/C][C]0.0336650164612059[/C][C]0.0799999999999983[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112584&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112584&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
1103.98250.2185368008673470.450000000000003
2104.0350.1752141546793540.400000000000006
3104.01250.3430621906690750.75
4103.330.07745966692414640.179999999999993
5103.09750.1350000000000030.320000000000007
6102.9250.3626292872893750.810000000000002
7102.05250.05123475382979370.119999999999990
8101.70.1163328557774330.269999999999996
9101.52250.1517399090549360.340000000000003
10101.11750.05123475382979970.120000000000005
11100.96250.04645786621588460.0999999999999943
12100.87250.1755704986607930.390000000000001
13100.490.02708012801545310.0600000000000023
14100.480.03366501646120590.0799999999999983






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-5.14671475479763
beta0.0517407096768034
S.D.0.0178323699875527
T-STAT2.90150494370177
p-value0.0132891167380992

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -5.14671475479763 \tabularnewline
beta & 0.0517407096768034 \tabularnewline
S.D. & 0.0178323699875527 \tabularnewline
T-STAT & 2.90150494370177 \tabularnewline
p-value & 0.0132891167380992 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112584&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-5.14671475479763[/C][/ROW]
[ROW][C]beta[/C][C]0.0517407096768034[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0178323699875527[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.90150494370177[/C][/ROW]
[ROW][C]p-value[/C][C]0.0132891167380992[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112584&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112584&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-5.14671475479763
beta0.0517407096768034
S.D.0.0178323699875527
T-STAT2.90150494370177
p-value0.0132891167380992






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-210.810671171149
beta45.0746279318583
S.D.13.0057959243687
T-STAT3.46573390771132
p-value0.00466753324110638
Lambda-44.0746279318583

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -210.810671171149 \tabularnewline
beta & 45.0746279318583 \tabularnewline
S.D. & 13.0057959243687 \tabularnewline
T-STAT & 3.46573390771132 \tabularnewline
p-value & 0.00466753324110638 \tabularnewline
Lambda & -44.0746279318583 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112584&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-210.810671171149[/C][/ROW]
[ROW][C]beta[/C][C]45.0746279318583[/C][/ROW]
[ROW][C]S.D.[/C][C]13.0057959243687[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.46573390771132[/C][/ROW]
[ROW][C]p-value[/C][C]0.00466753324110638[/C][/ROW]
[ROW][C]Lambda[/C][C]-44.0746279318583[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112584&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112584&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-210.810671171149
beta45.0746279318583
S.D.13.0057959243687
T-STAT3.46573390771132
p-value0.00466753324110638
Lambda-44.0746279318583


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 4 ;
Parameters (R input):
par1 = 4 ;
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')