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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 computationThu, 18 Dec 2008 07:48:14 -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/18/t1229611735q0mnsn3zhlbtoil.htm/, Retrieved Sun, 12 May 2024 09:54:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=34811, Retrieved Sun, 12 May 2024 09:54:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsk_vanderheggen
Estimated Impact227

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [Airline data] [2007-10-18 09:58:47] [42daae401fd3def69a25014f2252b4c2]
F RMPD  [Variance Reduction Matrix] [Non Stationary Ti...] [2008-12-02 14:04:39] [42e82fcd8ee0f4c6e81d502bb09e62b7]
- RM D    [Standard Deviation-Mean Plot] [Non Stationary Ti...] [2008-12-06 10:48:07] [42e82fcd8ee0f4c6e81d502bb09e62b7]
-             [Standard Deviation-Mean Plot] [Paper SDMP] [2008-12-18 14:48:14] [547f3960ab1cda94661cd6e0871d2c7b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
25
27
25
23
24
24
26
25
24
24
22
22
22
27
24
24
22
23
25
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22
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22
22
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20
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19
24
22
22
22
24
22
23
24
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20
22
23
23
22
20
21
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20
17
18
19
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20
21
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21
19
22
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20
21
18
19
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19
21
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17
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18

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'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34811&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34811&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34811&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'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
124.251.484771179187375
222.83333333333331.946247360403817
320.91666666666670.900336637378523
422.08333333333331.564279289951035
520.251.864744681524186
619.251.764549903980156
718.83333333333331.466804401246185

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 24.25 & 1.48477117918737 & 5 \tabularnewline
2 & 22.8333333333333 & 1.94624736040381 & 7 \tabularnewline
3 & 20.9166666666667 & 0.90033663737852 & 3 \tabularnewline
4 & 22.0833333333333 & 1.56427928995103 & 5 \tabularnewline
5 & 20.25 & 1.86474468152418 & 6 \tabularnewline
6 & 19.25 & 1.76454990398015 & 6 \tabularnewline
7 & 18.8333333333333 & 1.46680440124618 & 5 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34811&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]24.25[/C][C]1.48477117918737[/C][C]5[/C][/ROW]
[ROW][C]2[/C][C]22.8333333333333[/C][C]1.94624736040381[/C][C]7[/C][/ROW]
[ROW][C]3[/C][C]20.9166666666667[/C][C]0.90033663737852[/C][C]3[/C][/ROW]
[ROW][C]4[/C][C]22.0833333333333[/C][C]1.56427928995103[/C][C]5[/C][/ROW]
[ROW][C]5[/C][C]20.25[/C][C]1.86474468152418[/C][C]6[/C][/ROW]
[ROW][C]6[/C][C]19.25[/C][C]1.76454990398015[/C][C]6[/C][/ROW]
[ROW][C]7[/C][C]18.8333333333333[/C][C]1.46680440124618[/C][C]5[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34811&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34811&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
124.251.484771179187375
222.83333333333331.946247360403817
320.91666666666670.900336637378523
422.08333333333331.564279289951035
520.251.864744681524186
619.251.764549903980156
718.83333333333331.466804401246185






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha1.45650573956763
beta0.00536458131407846
S.D.0.079546730516016
T-STAT0.0674393690259632
p-value0.948845650953434

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.45650573956763 \tabularnewline
beta & 0.00536458131407846 \tabularnewline
S.D. & 0.079546730516016 \tabularnewline
T-STAT & 0.0674393690259632 \tabularnewline
p-value & 0.948845650953434 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34811&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.45650573956763[/C][/ROW]
[ROW][C]beta[/C][C]0.00536458131407846[/C][/ROW]
[ROW][C]S.D.[/C][C]0.079546730516016[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.0674393690259632[/C][/ROW]
[ROW][C]p-value[/C][C]0.948845650953434[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34811&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34811&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)
alpha1.45650573956763
beta0.00536458131407846
S.D.0.079546730516016
T-STAT0.0674393690259632
p-value0.948845650953434






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha0.183291218589345
beta0.0793633628275984
S.D.1.25761582782101
T-STAT0.0631062054658666
p-value0.952127048181722
Lambda0.920636637172402

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.183291218589345 \tabularnewline
beta & 0.0793633628275984 \tabularnewline
S.D. & 1.25761582782101 \tabularnewline
T-STAT & 0.0631062054658666 \tabularnewline
p-value & 0.952127048181722 \tabularnewline
Lambda & 0.920636637172402 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34811&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.183291218589345[/C][/ROW]
[ROW][C]beta[/C][C]0.0793633628275984[/C][/ROW]
[ROW][C]S.D.[/C][C]1.25761582782101[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.0631062054658666[/C][/ROW]
[ROW][C]p-value[/C][C]0.952127048181722[/C][/ROW]
[ROW][C]Lambda[/C][C]0.920636637172402[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34811&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34811&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)
alpha0.183291218589345
beta0.0793633628275984
S.D.1.25761582782101
T-STAT0.0631062054658666
p-value0.952127048181722
Lambda0.920636637172402


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = ; par3 = ; par4 = ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;
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')