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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, 26 Nov 2009 11:11:50 -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/2009/Nov/26/t12592591857tkejoqs06toiv2.htm/, Retrieved Sun, 28 Apr 2024 23:41:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=60217, Retrieved Sun, 28 Apr 2024 23:41:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact189

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Standard Deviation-Mean Plot] [Identifying Integ...] [2009-11-22 12:50:05] [b98453cac15ba1066b407e146608df68]
-    D        [Standard Deviation-Mean Plot] [standard deviatio...] [2009-11-24 21:20:13] [8b1aef4e7013bd33fbc2a5833375c5f5]
-    D            [Standard Deviation-Mean Plot] [SHw WS8] [2009-11-26 18:11:50] [d9efc2d105d810fc0b0ac636e31105d1] [Current]
-    D              [Standard Deviation-Mean Plot] [WS8 - review ] [2009-12-03 16:26:13] [af2352cd9a951bedd08ebe247d0de1a2]
-    D                [Standard Deviation-Mean Plot] [WS8 - review ] [2009-12-03 17:45:49] [af2352cd9a951bedd08ebe247d0de1a2]
- RM                [Variance Reduction Matrix] [] [2009-12-04 20:51:28] [badc6a9acdc45286bea7f74742e15a21]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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
707
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

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=60217&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=60217&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60217&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
1661.25147.816916856938487
2656.5144.512660659574487
3634.75135.84959932353409
4639.833333333333145.229494458275508
5706.333333333333163.343104222277560

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 661.25 & 147.816916856938 & 487 \tabularnewline
2 & 656.5 & 144.512660659574 & 487 \tabularnewline
3 & 634.75 & 135.84959932353 & 409 \tabularnewline
4 & 639.833333333333 & 145.229494458275 & 508 \tabularnewline
5 & 706.333333333333 & 163.343104222277 & 560 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60217&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]661.25[/C][C]147.816916856938[/C][C]487[/C][/ROW]
[ROW][C]2[/C][C]656.5[/C][C]144.512660659574[/C][C]487[/C][/ROW]
[ROW][C]3[/C][C]634.75[/C][C]135.84959932353[/C][C]409[/C][/ROW]
[ROW][C]4[/C][C]639.833333333333[/C][C]145.229494458275[/C][C]508[/C][/ROW]
[ROW][C]5[/C][C]706.333333333333[/C][C]163.343104222277[/C][C]560[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60217&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60217&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
1661.25147.816916856938487
2656.5144.512660659574487
3634.75135.84959932353409
4639.833333333333145.229494458275508
5706.333333333333163.343104222277560






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-75.9604951297975
beta0.338486535318183
S.D.0.0591676809408599
T-STAT5.72080111871399
p-value0.0105993145070679

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -75.9604951297975 \tabularnewline
beta & 0.338486535318183 \tabularnewline
S.D. & 0.0591676809408599 \tabularnewline
T-STAT & 5.72080111871399 \tabularnewline
p-value & 0.0105993145070679 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60217&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-75.9604951297975[/C][/ROW]
[ROW][C]beta[/C][C]0.338486535318183[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0591676809408599[/C][/ROW]
[ROW][C]T-STAT[/C][C]5.72080111871399[/C][/ROW]
[ROW][C]p-value[/C][C]0.0105993145070679[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60217&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60217&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-75.9604951297975
beta0.338486535318183
S.D.0.0591676809408599
T-STAT5.72080111871399
p-value0.0105993145070679






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-4.7821201704456
beta1.50561652599907
S.D.0.280398324429335
T-STAT5.36956320642533
p-value0.012645064199145
Lambda-0.50561652599907

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -4.7821201704456 \tabularnewline
beta & 1.50561652599907 \tabularnewline
S.D. & 0.280398324429335 \tabularnewline
T-STAT & 5.36956320642533 \tabularnewline
p-value & 0.012645064199145 \tabularnewline
Lambda & -0.50561652599907 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60217&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.7821201704456[/C][/ROW]
[ROW][C]beta[/C][C]1.50561652599907[/C][/ROW]
[ROW][C]S.D.[/C][C]0.280398324429335[/C][/ROW]
[ROW][C]T-STAT[/C][C]5.36956320642533[/C][/ROW]
[ROW][C]p-value[/C][C]0.012645064199145[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.50561652599907[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60217&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60217&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-4.7821201704456
beta1.50561652599907
S.D.0.280398324429335
T-STAT5.36956320642533
p-value0.012645064199145
Lambda-0.50561652599907


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')