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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 07:50:53 -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/t1229611890i9d85a4saftapkv.htm/, Retrieved Sat, 11 May 2024 22:24:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=34812, Retrieved Sat, 11 May 2024 22:24:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsk_vanderheggen
Estimated Impact215

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]
-    D      [Standard Deviation-Mean Plot] [Non stationary Ti...] [2008-12-06 10:53:29] [42e82fcd8ee0f4c6e81d502bb09e62b7]
-               [Standard Deviation-Mean Plot] [Paper SDMP] [2008-12-18 14:50:53] [547f3960ab1cda94661cd6e0871d2c7b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
27
25
20
19
19
17
12
13
13
11
4
8
1
5
4
3
4
2
8
-2
1
0
1
7
1
0
-3
0
3
1
3
2
6
2
3
9
12
8
7
9
11
13
9
9
13
14
16
20
19
18
18
19
16
10
11
17
3
14
15
17
20
19
21
17
15
18
19
16
21
26
23
24
23
19
25
21
19
20
20
17
25
19
13
15
15
13
11
9
2
-2
-4
-2

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=34812&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=34812&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34812&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
115.66666666666676.7599533797926223
22.833333333333332.9180732539042810
32.253.0488447886789112
411.753.744693214767713
514.754.712169930567616
619.91666666666673.2879486097878811
719.66666666666673.6265017787828512

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 15.6666666666667 & 6.75995337979262 & 23 \tabularnewline
2 & 2.83333333333333 & 2.91807325390428 & 10 \tabularnewline
3 & 2.25 & 3.04884478867891 & 12 \tabularnewline
4 & 11.75 & 3.7446932147677 & 13 \tabularnewline
5 & 14.75 & 4.7121699305676 & 16 \tabularnewline
6 & 19.9166666666667 & 3.28794860978788 & 11 \tabularnewline
7 & 19.6666666666667 & 3.62650177878285 & 12 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34812&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]15.6666666666667[/C][C]6.75995337979262[/C][C]23[/C][/ROW]
[ROW][C]2[/C][C]2.83333333333333[/C][C]2.91807325390428[/C][C]10[/C][/ROW]
[ROW][C]3[/C][C]2.25[/C][C]3.04884478867891[/C][C]12[/C][/ROW]
[ROW][C]4[/C][C]11.75[/C][C]3.7446932147677[/C][C]13[/C][/ROW]
[ROW][C]5[/C][C]14.75[/C][C]4.7121699305676[/C][C]16[/C][/ROW]
[ROW][C]6[/C][C]19.9166666666667[/C][C]3.28794860978788[/C][C]11[/C][/ROW]
[ROW][C]7[/C][C]19.6666666666667[/C][C]3.62650177878285[/C][C]12[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34812&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34812&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
115.66666666666676.7599533797926223
22.833333333333332.9180732539042810
32.253.0488447886789112
411.753.744693214767713
514.754.712169930567616
619.91666666666673.2879486097878811
719.66666666666673.6265017787828512






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha3.13172904196164
beta0.0711257005284114
S.D.0.076139138685019
T-STAT0.934154257019537
p-value0.393106218324086

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 3.13172904196164 \tabularnewline
beta & 0.0711257005284114 \tabularnewline
S.D. & 0.076139138685019 \tabularnewline
T-STAT & 0.934154257019537 \tabularnewline
p-value & 0.393106218324086 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34812&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.13172904196164[/C][/ROW]
[ROW][C]beta[/C][C]0.0711257005284114[/C][/ROW]
[ROW][C]S.D.[/C][C]0.076139138685019[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.934154257019537[/C][/ROW]
[ROW][C]p-value[/C][C]0.393106218324086[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34812&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34812&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)
alpha3.13172904196164
beta0.0711257005284114
S.D.0.076139138685019
T-STAT0.934154257019537
p-value0.393106218324086






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha0.963915513195487
beta0.171544844654623
S.D.0.120076624695648
T-STAT1.42862813715349
p-value0.212483677735597
Lambda0.828455155345377

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.963915513195487 \tabularnewline
beta & 0.171544844654623 \tabularnewline
S.D. & 0.120076624695648 \tabularnewline
T-STAT & 1.42862813715349 \tabularnewline
p-value & 0.212483677735597 \tabularnewline
Lambda & 0.828455155345377 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34812&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.963915513195487[/C][/ROW]
[ROW][C]beta[/C][C]0.171544844654623[/C][/ROW]
[ROW][C]S.D.[/C][C]0.120076624695648[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.42862813715349[/C][/ROW]
[ROW][C]p-value[/C][C]0.212483677735597[/C][/ROW]
[ROW][C]Lambda[/C][C]0.828455155345377[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34812&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34812&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)
alpha0.963915513195487
beta0.171544844654623
S.D.0.120076624695648
T-STAT1.42862813715349
p-value0.212483677735597
Lambda0.828455155345377


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')