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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 computationSun, 03 Jan 2010 09:46:28 -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/03/t1262538610arwsvxnk2pqycef.htm/, Retrieved Fri, 03 May 2024 14:57:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=71544, Retrieved Fri, 03 May 2024 14:57:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W83
Estimated Impact147

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Standard Deviation-Mean Plot] [] [2010-01-03 16:46:28] [6f76491bc22dc2a03dd3886755cb7a25] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3.81
3.95
3.99
4
4.06
4.16
4.19
4.2
4.2
4.2
4.2
4.2
4.23
4.38
4.43
4.44
4.44
4.44
4.44
4.44
4.45
4.45
4.45
4.45
4.45
4.45
4.45
4.45
4.46
4.46
4.46
4.48
4.58
4.67
4.68
4.68
4.69
4.69
4.69
4.69
4.69
4.69
4.69
4.73
4.78
4.79
4.79
4.8
4.8
4.81
5.16
5.26
5.29
5.29
5.29
5.3
5.3
5.3
5.3
5.3
5.3
5.3
5.3
5.35
5.44
5.47
5.47
5.48
5.48
5.48
5.48
5.48

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=71544&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=71544&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71544&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
14.096666666666670.1320697703580360.39
24.420.0628128533459080.220000000000000
34.52250.09964710459689950.230000000000000
44.726666666666670.04830458915396460.109999999999999
55.20.1886796226411320.5
65.419166666666670.08061787906068020.180000000000001

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 4.09666666666667 & 0.132069770358036 & 0.39 \tabularnewline
2 & 4.42 & 0.062812853345908 & 0.220000000000000 \tabularnewline
3 & 4.5225 & 0.0996471045968995 & 0.230000000000000 \tabularnewline
4 & 4.72666666666667 & 0.0483045891539646 & 0.109999999999999 \tabularnewline
5 & 5.2 & 0.188679622641132 & 0.5 \tabularnewline
6 & 5.41916666666667 & 0.0806178790606802 & 0.180000000000001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71544&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]4.09666666666667[/C][C]0.132069770358036[/C][C]0.39[/C][/ROW]
[ROW][C]2[/C][C]4.42[/C][C]0.062812853345908[/C][C]0.220000000000000[/C][/ROW]
[ROW][C]3[/C][C]4.5225[/C][C]0.0996471045968995[/C][C]0.230000000000000[/C][/ROW]
[ROW][C]4[/C][C]4.72666666666667[/C][C]0.0483045891539646[/C][C]0.109999999999999[/C][/ROW]
[ROW][C]5[/C][C]5.2[/C][C]0.188679622641132[/C][C]0.5[/C][/ROW]
[ROW][C]6[/C][C]5.41916666666667[/C][C]0.0806178790606802[/C][C]0.180000000000001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71544&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71544&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
14.096666666666670.1320697703580360.39
24.420.0628128533459080.220000000000000
34.52250.09964710459689950.230000000000000
44.726666666666670.04830458915396460.109999999999999
55.20.1886796226411320.5
65.419166666666670.08061787906068020.180000000000001






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.0263420091693673
beta0.0159971733007017
S.D.0.0512415770752937
T-STAT0.312191275401138
p-value0.770492257956763

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.0263420091693673 \tabularnewline
beta & 0.0159971733007017 \tabularnewline
S.D. & 0.0512415770752937 \tabularnewline
T-STAT & 0.312191275401138 \tabularnewline
p-value & 0.770492257956763 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71544&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.0263420091693673[/C][/ROW]
[ROW][C]beta[/C][C]0.0159971733007017[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0512415770752937[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.312191275401138[/C][/ROW]
[ROW][C]p-value[/C][C]0.770492257956763[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71544&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71544&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)
alpha0.0263420091693673
beta0.0159971733007017
S.D.0.0512415770752937
T-STAT0.312191275401138
p-value0.770492257956763






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.97723887086164
beta0.381762724536689
S.D.2.36588437862026
T-STAT0.161361530591502
p-value0.879630873996645
Lambda0.618237275463311

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.97723887086164 \tabularnewline
beta & 0.381762724536689 \tabularnewline
S.D. & 2.36588437862026 \tabularnewline
T-STAT & 0.161361530591502 \tabularnewline
p-value & 0.879630873996645 \tabularnewline
Lambda & 0.618237275463311 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71544&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.97723887086164[/C][/ROW]
[ROW][C]beta[/C][C]0.381762724536689[/C][/ROW]
[ROW][C]S.D.[/C][C]2.36588437862026[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.161361530591502[/C][/ROW]
[ROW][C]p-value[/C][C]0.879630873996645[/C][/ROW]
[ROW][C]Lambda[/C][C]0.618237275463311[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71544&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71544&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-2.97723887086164
beta0.381762724536689
S.D.2.36588437862026
T-STAT0.161361530591502
p-value0.879630873996645
Lambda0.618237275463311


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')