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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 computationTue, 07 Dec 2010 09:58:11 +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/07/t1291715774n147sradaepjixp.htm/, Retrieved Sat, 04 May 2024 02:14:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=106104, Retrieved Sat, 04 May 2024 02:14:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact109

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Standard Deviation-Mean Plot] [Unemployment] [2010-11-29 10:34:47] [b98453cac15ba1066b407e146608df68]
-   PD      [Standard Deviation-Mean Plot] [WS9 SMP] [2010-12-07 09:58:11] [67e3c2d70de1dbb070b545ca6c893d5e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
562.325 
560.854 
555.332 
543.599 
536.662 
542.722 
593.530 
610.763 
612.613 
611.324 
594.167 
595.454 
590.865 
589.379 
584.428 
573.100 
567.456 
569.028 
620.735 
628.884 
628.232 
612.117 
595.404 
597.141 
593.408 
590.072 
579.799 
574.205 
572.775 
572.942 
619.567 
625.809 
619.916 
587.625 
565.742 
557.274 
560.576 
548.854 
531.673 
525.919 
511.038 
498.662 
555.362 
564.591 
541.657 
527.070 
509.846 
514.258 
516.922 
507.561 
492.622 
490.243 
469.357 
477.580 
528.379 
533.590 
517.945 
506.174 
501.866 
516.141 
528.222 
532.638 
536.322 
536.535 
523.597 
536.214 
586.570 
596.594 
580.523 
564.478 
557.560 
575.093

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106104&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106104&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106104&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 time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1576.61208333333329.164685309021375.951
2596.39741666666721.872304573502561.428
3588.26116666666722.629620286989768.535
4532.45883333333321.778072975246365.929
5504.86519.560160730888264.233
6554.52883333333325.44442511483172.997

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 576.612083333333 & 29.1646853090213 & 75.951 \tabularnewline
2 & 596.397416666667 & 21.8723045735025 & 61.428 \tabularnewline
3 & 588.261166666667 & 22.6296202869897 & 68.535 \tabularnewline
4 & 532.458833333333 & 21.7780729752463 & 65.929 \tabularnewline
5 & 504.865 & 19.5601607308882 & 64.233 \tabularnewline
6 & 554.528833333333 & 25.444425114831 & 72.997 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106104&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]576.612083333333[/C][C]29.1646853090213[/C][C]75.951[/C][/ROW]
[ROW][C]2[/C][C]596.397416666667[/C][C]21.8723045735025[/C][C]61.428[/C][/ROW]
[ROW][C]3[/C][C]588.261166666667[/C][C]22.6296202869897[/C][C]68.535[/C][/ROW]
[ROW][C]4[/C][C]532.458833333333[/C][C]21.7780729752463[/C][C]65.929[/C][/ROW]
[ROW][C]5[/C][C]504.865[/C][C]19.5601607308882[/C][C]64.233[/C][/ROW]
[ROW][C]6[/C][C]554.528833333333[/C][C]25.444425114831[/C][C]72.997[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106104&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106104&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
1576.61208333333329.164685309021375.951
2596.39741666666721.872304573502561.428
3588.26116666666722.629620286989768.535
4532.45883333333321.778072975246365.929
5504.86519.560160730888264.233
6554.52883333333325.44442511483172.997






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.279611658814828
beta0.0423864334277498
S.D.0.0432499906139387
T-STAT0.980033355523769
p-value0.382558948805665

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.279611658814828 \tabularnewline
beta & 0.0423864334277498 \tabularnewline
S.D. & 0.0432499906139387 \tabularnewline
T-STAT & 0.980033355523769 \tabularnewline
p-value & 0.382558948805665 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106104&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.279611658814828[/C][/ROW]
[ROW][C]beta[/C][C]0.0423864334277498[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0432499906139387[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.980033355523769[/C][/ROW]
[ROW][C]p-value[/C][C]0.382558948805665[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106104&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106104&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-0.279611658814828
beta0.0423864334277498
S.D.0.0432499906139387
T-STAT0.980033355523769
p-value0.382558948805665






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.547080172774
beta1.05812736107082
S.D.0.955995034533258
T-STAT1.10683353244342
p-value0.330446134610728
Lambda-0.0581273610708193

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.547080172774 \tabularnewline
beta & 1.05812736107082 \tabularnewline
S.D. & 0.955995034533258 \tabularnewline
T-STAT & 1.10683353244342 \tabularnewline
p-value & 0.330446134610728 \tabularnewline
Lambda & -0.0581273610708193 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106104&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.547080172774[/C][/ROW]
[ROW][C]beta[/C][C]1.05812736107082[/C][/ROW]
[ROW][C]S.D.[/C][C]0.955995034533258[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.10683353244342[/C][/ROW]
[ROW][C]p-value[/C][C]0.330446134610728[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.0581273610708193[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106104&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106104&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-3.547080172774
beta1.05812736107082
S.D.0.955995034533258
T-STAT1.10683353244342
p-value0.330446134610728
Lambda-0.0581273610708193


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')