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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 computationTue, 07 Dec 2010 21:38:02 +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/07/t1291757761uh515j04kgb12hk.htm/, Retrieved Sat, 04 May 2024 00:07:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=106765, Retrieved Sat, 04 May 2024 00:07:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W83
Estimated Impact95

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] [] [2010-12-07 21:38:02] [ca3ac3c31c98d146c448f7dbe5015da7] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
13.2
13.8
16.2
14.7
13.9
16.0
14.4
12.3
15.9
15.9
15.5
15.1
14.5
15.1
17.4
16.2
15.6
17.2
14.9
13.8
17.5
16.2
17.5
16.6
16.2
16.6
19.6
15.9
18.0
18.3
16.3
14.9
18.2
18.4
18.5
16.0
17.4
17.2
19.6
17.2
18.3
19.3
18.1
16.2
18.4
20.5
19.0
16.5
18.7
19.0
19.2
20.5
19.3
20.6
20.1
16.1
20.4
19.7
15.6
14.4
13.9
14.3
15.3
14.4
13.8
15.7
14.7
12.5
16.2
16.1
16
15.8
15.2

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time7 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 & 7 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106765&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]7 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=106765&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106765&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 time7 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
114.74166666666671.248605282511313.9
216.04166666666671.264521708597823.7
317.24166666666671.424115887351194.7
418.14166666666671.302067121111194.3
518.63333333333332.093424047445776.2
614.89166666666671.150856071352843.7

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 14.7416666666667 & 1.24860528251131 & 3.9 \tabularnewline
2 & 16.0416666666667 & 1.26452170859782 & 3.7 \tabularnewline
3 & 17.2416666666667 & 1.42411588735119 & 4.7 \tabularnewline
4 & 18.1416666666667 & 1.30206712111119 & 4.3 \tabularnewline
5 & 18.6333333333333 & 2.09342404744577 & 6.2 \tabularnewline
6 & 14.8916666666667 & 1.15085607135284 & 3.7 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106765&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]14.7416666666667[/C][C]1.24860528251131[/C][C]3.9[/C][/ROW]
[ROW][C]2[/C][C]16.0416666666667[/C][C]1.26452170859782[/C][C]3.7[/C][/ROW]
[ROW][C]3[/C][C]17.2416666666667[/C][C]1.42411588735119[/C][C]4.7[/C][/ROW]
[ROW][C]4[/C][C]18.1416666666667[/C][C]1.30206712111119[/C][C]4.3[/C][/ROW]
[ROW][C]5[/C][C]18.6333333333333[/C][C]2.09342404744577[/C][C]6.2[/C][/ROW]
[ROW][C]6[/C][C]14.8916666666667[/C][C]1.15085607135284[/C][C]3.7[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106765&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106765&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
114.74166666666671.248605282511313.9
216.04166666666671.264521708597823.7
317.24166666666671.424115887351194.7
418.14166666666671.302067121111194.3
518.63333333333332.093424047445776.2
614.89166666666671.150856071352843.7






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-1.09671029889886
beta0.151104424426281
S.D.0.0720560750236891
T-STAT2.09703934576791
p-value0.104000352161109

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -1.09671029889886 \tabularnewline
beta & 0.151104424426281 \tabularnewline
S.D. & 0.0720560750236891 \tabularnewline
T-STAT & 2.09703934576791 \tabularnewline
p-value & 0.104000352161109 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106765&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.09671029889886[/C][/ROW]
[ROW][C]beta[/C][C]0.151104424426281[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0720560750236891[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.09703934576791[/C][/ROW]
[ROW][C]p-value[/C][C]0.104000352161109[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106765&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106765&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-1.09671029889886
beta0.151104424426281
S.D.0.0720560750236891
T-STAT2.09703934576791
p-value0.104000352161109






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-4.12803245482593
beta1.58706840875719
S.D.0.721531127660672
T-STAT2.19958411760105
p-value0.0926956399961305
Lambda-0.587068408757188

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -4.12803245482593 \tabularnewline
beta & 1.58706840875719 \tabularnewline
S.D. & 0.721531127660672 \tabularnewline
T-STAT & 2.19958411760105 \tabularnewline
p-value & 0.0926956399961305 \tabularnewline
Lambda & -0.587068408757188 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106765&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.12803245482593[/C][/ROW]
[ROW][C]beta[/C][C]1.58706840875719[/C][/ROW]
[ROW][C]S.D.[/C][C]0.721531127660672[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.19958411760105[/C][/ROW]
[ROW][C]p-value[/C][C]0.0926956399961305[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.587068408757188[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106765&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106765&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-4.12803245482593
beta1.58706840875719
S.D.0.721531127660672
T-STAT2.19958411760105
p-value0.0926956399961305
Lambda-0.587068408757188


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')