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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 computationMon, 15 Dec 2008 15:52:47 -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/2008/Dec/15/t1229381606unjpc4w0fm6o09m.htm/, Retrieved Wed, 15 May 2024 21:05:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=33853, Retrieved Wed, 15 May 2024 21:05:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact156

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] [SDM plot] [2008-12-15 22:52:47] [0bb3b56b7083c5944c3818446f605d68] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
7.6
7.7
7.6
8.2
8
8.1
8.3
8.2
8.1
7.7
7.6
7.7
8.2
8.4
8.4
8.6
8.4
8.5
8.7
8.7
8.6
7.4
7.3
7.4
9
9.2
9.2
8.5
8.3
8.3
8.6
8.6
8.5
8.1
8.1
8
8.6
8.7
8.7
8.6
8.4
8.4
8.7
8.7
8.5
8.3
8.3
8.3
8.1
8.2
8.1
8.1
7.9
7.7
8.1
8
7.7
7.8
7.6
7.4
7.7

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=33853&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=33853&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33853&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
17.90.2730301348669310.700000000000001
28.216666666666670.5322906474223771.4
38.533333333333330.4141438777950861.2
48.516666666666670.1696699112626590.399999999999999
57.891666666666670.2503028468705760.799999999999999

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 7.9 & 0.273030134866931 & 0.700000000000001 \tabularnewline
2 & 8.21666666666667 & 0.532290647422377 & 1.4 \tabularnewline
3 & 8.53333333333333 & 0.414143877795086 & 1.2 \tabularnewline
4 & 8.51666666666667 & 0.169669911262659 & 0.399999999999999 \tabularnewline
5 & 7.89166666666667 & 0.250302846870576 & 0.799999999999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33853&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]7.9[/C][C]0.273030134866931[/C][C]0.700000000000001[/C][/ROW]
[ROW][C]2[/C][C]8.21666666666667[/C][C]0.532290647422377[/C][C]1.4[/C][/ROW]
[ROW][C]3[/C][C]8.53333333333333[/C][C]0.414143877795086[/C][C]1.2[/C][/ROW]
[ROW][C]4[/C][C]8.51666666666667[/C][C]0.169669911262659[/C][C]0.399999999999999[/C][/ROW]
[ROW][C]5[/C][C]7.89166666666667[/C][C]0.250302846870576[/C][C]0.799999999999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33853&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33853&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
17.90.2730301348669310.700000000000001
28.216666666666670.5322906474223771.4
38.533333333333330.4141438777950861.2
48.516666666666670.1696699112626590.399999999999999
57.891666666666670.2503028468705760.799999999999999






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.137286983145661
beta0.0566479967675081
S.D.0.262723176350278
T-STAT0.215618574480014
p-value0.843112711926535

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.137286983145661 \tabularnewline
beta & 0.0566479967675081 \tabularnewline
S.D. & 0.262723176350278 \tabularnewline
T-STAT & 0.215618574480014 \tabularnewline
p-value & 0.843112711926535 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33853&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.137286983145661[/C][/ROW]
[ROW][C]beta[/C][C]0.0566479967675081[/C][/ROW]
[ROW][C]S.D.[/C][C]0.262723176350278[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.215618574480014[/C][/ROW]
[ROW][C]p-value[/C][C]0.843112711926535[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33853&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33853&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-0.137286983145661
beta0.0566479967675081
S.D.0.262723176350278
T-STAT0.215618574480014
p-value0.843112711926535






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.20550043627101
beta0.480599950906333
S.D.6.72207461872425
T-STAT0.0714957774446043
p-value0.947502691782655
Lambda0.519400049093667

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.20550043627101 \tabularnewline
beta & 0.480599950906333 \tabularnewline
S.D. & 6.72207461872425 \tabularnewline
T-STAT & 0.0714957774446043 \tabularnewline
p-value & 0.947502691782655 \tabularnewline
Lambda & 0.519400049093667 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33853&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.20550043627101[/C][/ROW]
[ROW][C]beta[/C][C]0.480599950906333[/C][/ROW]
[ROW][C]S.D.[/C][C]6.72207461872425[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.0714957774446043[/C][/ROW]
[ROW][C]p-value[/C][C]0.947502691782655[/C][/ROW]
[ROW][C]Lambda[/C][C]0.519400049093667[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33853&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33853&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-2.20550043627101
beta0.480599950906333
S.D.6.72207461872425
T-STAT0.0714957774446043
p-value0.947502691782655
Lambda0.519400049093667


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')