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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, 28 Dec 2010 09:32:07 +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/28/t1293528593o3tpg4kxqed8790.htm/, Retrieved Sat, 04 May 2024 23:06:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116248, Retrieved Sat, 04 May 2024 23:06:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact131

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Variance Reduction Matrix] [] [2010-12-24 15:11:40] [afd301b68d203992295e6972aed62880]
- RM D    [Standard Deviation-Mean Plot] [] [2010-12-28 09:32:07] [5a59313293e5c9f616ad36f6edd018c5] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
547.344		
554.788	
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		
580.112		
574.761		
563.250		
551.531		
537.034		
544.686		
600.991		
604.378		
586.111		
563.668		
548.604

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'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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116248&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116248&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116248&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'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1569.32133333333329.214295265824775.951
2596.1537521.879810744257961.428
3594.0552518.811974378643253.034
4540.701521.914672455188167.08
5505.37308333333319.499178572248264.233
6544.97529.910813684564594.728
7569.9312521.023201292100667.344

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 569.321333333333 & 29.2142952658247 & 75.951 \tabularnewline
2 & 596.15375 & 21.8798107442579 & 61.428 \tabularnewline
3 & 594.05525 & 18.8119743786432 & 53.034 \tabularnewline
4 & 540.7015 & 21.9146724551881 & 67.08 \tabularnewline
5 & 505.373083333333 & 19.4991785722482 & 64.233 \tabularnewline
6 & 544.975 & 29.9108136845645 & 94.728 \tabularnewline
7 & 569.93125 & 21.0232012921006 & 67.344 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116248&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]569.321333333333[/C][C]29.2142952658247[/C][C]75.951[/C][/ROW]
[ROW][C]2[/C][C]596.15375[/C][C]21.8798107442579[/C][C]61.428[/C][/ROW]
[ROW][C]3[/C][C]594.05525[/C][C]18.8119743786432[/C][C]53.034[/C][/ROW]
[ROW][C]4[/C][C]540.7015[/C][C]21.9146724551881[/C][C]67.08[/C][/ROW]
[ROW][C]5[/C][C]505.373083333333[/C][C]19.4991785722482[/C][C]64.233[/C][/ROW]
[ROW][C]6[/C][C]544.975[/C][C]29.9108136845645[/C][C]94.728[/C][/ROW]
[ROW][C]7[/C][C]569.93125[/C][C]21.0232012921006[/C][C]67.344[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116248&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116248&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
1569.32133333333329.214295265824775.951
2596.1537521.879810744257961.428
3594.0552518.811974378643253.034
4540.701521.914672455188167.08
5505.37308333333319.499178572248264.233
6544.97529.910813684564594.728
7569.9312521.023201292100667.344






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha26.4645125890898
beta-0.00586598041763895
S.D.0.0625778676064413
T-STAT-0.0937388991029658
p-value0.9289569804719

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 26.4645125890898 \tabularnewline
beta & -0.00586598041763895 \tabularnewline
S.D. & 0.0625778676064413 \tabularnewline
T-STAT & -0.0937388991029658 \tabularnewline
p-value & 0.9289569804719 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116248&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]26.4645125890898[/C][/ROW]
[ROW][C]beta[/C][C]-0.00586598041763895[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0625778676064413[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.0937388991029658[/C][/ROW]
[ROW][C]p-value[/C][C]0.9289569804719[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116248&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116248&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)
alpha26.4645125890898
beta-0.00586598041763895
S.D.0.0625778676064413
T-STAT-0.0937388991029658
p-value0.9289569804719






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha3.49653247197991
beta-0.0582490222300709
S.D.1.41974552961349
T-STAT-0.0410277905547825
p-value0.968861634682753
Lambda1.05824902223007

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 3.49653247197991 \tabularnewline
beta & -0.0582490222300709 \tabularnewline
S.D. & 1.41974552961349 \tabularnewline
T-STAT & -0.0410277905547825 \tabularnewline
p-value & 0.968861634682753 \tabularnewline
Lambda & 1.05824902223007 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116248&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.49653247197991[/C][/ROW]
[ROW][C]beta[/C][C]-0.0582490222300709[/C][/ROW]
[ROW][C]S.D.[/C][C]1.41974552961349[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.0410277905547825[/C][/ROW]
[ROW][C]p-value[/C][C]0.968861634682753[/C][/ROW]
[ROW][C]Lambda[/C][C]1.05824902223007[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116248&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116248&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)
alpha3.49653247197991
beta-0.0582490222300709
S.D.1.41974552961349
T-STAT-0.0410277905547825
p-value0.968861634682753
Lambda1.05824902223007


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')