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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 computationSun, 19 Dec 2010 15:26:38 +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/19/t1292772373lql3udq0mtmyhql.htm/, Retrieved Sun, 05 May 2024 01:11:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112498, Retrieved Sun, 05 May 2024 01:11:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact140

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] [Paper: Standard D...] [2010-12-19 15:26:38] [6f3869f9d1e39c73f93153f1f7803f84] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
608
651
691
627
634
731
475
337
803
722
590
724
627
696
825
677
656
785
412
352
839
729
696
641
695
638
762
635
721
854
418
367
824
687
601
676
740
691
683
594
729
731
386
331
706
715
657
653
642
643
718
654
632
731
392
344
792
852
649
629
685
617
715
715
629
916
531
357
917
828
708
858
775
785
1.006
789
734
906
532
387
991
841
892
782

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=112498&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=112498&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112498&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
1632.75125.583818442288466
2661.25147.816916856938487
3656.5144.512660659574487
4634.666666666667135.801548614368409
5639.833333333333145.229494458275508
6706.333333333333163.343104222277560
7701.2505274.239418795296989.994

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 632.75 & 125.583818442288 & 466 \tabularnewline
2 & 661.25 & 147.816916856938 & 487 \tabularnewline
3 & 656.5 & 144.512660659574 & 487 \tabularnewline
4 & 634.666666666667 & 135.801548614368 & 409 \tabularnewline
5 & 639.833333333333 & 145.229494458275 & 508 \tabularnewline
6 & 706.333333333333 & 163.343104222277 & 560 \tabularnewline
7 & 701.2505 & 274.239418795296 & 989.994 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112498&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]632.75[/C][C]125.583818442288[/C][C]466[/C][/ROW]
[ROW][C]2[/C][C]661.25[/C][C]147.816916856938[/C][C]487[/C][/ROW]
[ROW][C]3[/C][C]656.5[/C][C]144.512660659574[/C][C]487[/C][/ROW]
[ROW][C]4[/C][C]634.666666666667[/C][C]135.801548614368[/C][C]409[/C][/ROW]
[ROW][C]5[/C][C]639.833333333333[/C][C]145.229494458275[/C][C]508[/C][/ROW]
[ROW][C]6[/C][C]706.333333333333[/C][C]163.343104222277[/C][C]560[/C][/ROW]
[ROW][C]7[/C][C]701.2505[/C][C]274.239418795296[/C][C]989.994[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112498&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112498&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
1632.75125.583818442288466
2661.25147.816916856938487
3656.5144.512660659574487
4634.666666666667135.801548614368409
5639.833333333333145.229494458275508
6706.333333333333163.343104222277560
7701.2505274.239418795296989.994






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-628.106636781303
beta1.19442488654042
S.D.0.511522256992022
T-STAT2.33503991314897
p-value0.0667910153984364

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -628.106636781303 \tabularnewline
beta & 1.19442488654042 \tabularnewline
S.D. & 0.511522256992022 \tabularnewline
T-STAT & 2.33503991314897 \tabularnewline
p-value & 0.0667910153984364 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112498&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-628.106636781303[/C][/ROW]
[ROW][C]beta[/C][C]1.19442488654042[/C][/ROW]
[ROW][C]S.D.[/C][C]0.511522256992022[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.33503991314897[/C][/ROW]
[ROW][C]p-value[/C][C]0.0667910153984364[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112498&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112498&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-628.106636781303
beta1.19442488654042
S.D.0.511522256992022
T-STAT2.33503991314897
p-value0.0667910153984364






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-23.0295697794917
beta4.32502486317148
S.D.1.62172372397113
T-STAT2.66693074735366
p-value0.0445120866899449
Lambda-3.32502486317148

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -23.0295697794917 \tabularnewline
beta & 4.32502486317148 \tabularnewline
S.D. & 1.62172372397113 \tabularnewline
T-STAT & 2.66693074735366 \tabularnewline
p-value & 0.0445120866899449 \tabularnewline
Lambda & -3.32502486317148 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112498&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-23.0295697794917[/C][/ROW]
[ROW][C]beta[/C][C]4.32502486317148[/C][/ROW]
[ROW][C]S.D.[/C][C]1.62172372397113[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.66693074735366[/C][/ROW]
[ROW][C]p-value[/C][C]0.0445120866899449[/C][/ROW]
[ROW][C]Lambda[/C][C]-3.32502486317148[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112498&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112498&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-23.0295697794917
beta4.32502486317148
S.D.1.62172372397113
T-STAT2.66693074735366
p-value0.0445120866899449
Lambda-3.32502486317148


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
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')