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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationMon, 18 Aug 2014 13:02:43 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Aug/18/t1408363387a9we4t7i4047tko.htm/, Retrieved Sun, 06 Apr 2025 04:16:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235711, Retrieved Sun, 06 Apr 2025 04:16:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsVan Reusel Raphael
Estimated Impact142

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] [Tijdreeks 2] [2014-08-18 12:02:43] [bf566d88435d8cc6ce5d208f6f8dd684] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
770
710
890
730
790
820
810
810
760
840
830
890
800
710
850
790
800
840
850
810
760
860
860
880
770
740
850
790
860
820
900
800
660
820
850
850
760
730
770
880
890
790
930
770
680
810
870
850
820
740
800
920
970
780
880
750
620
760
930
820
900
700
810
970
820
740
930
720
580
800
910
810
890
710
830
900
830
680
980
690
530
740
930
770
870
660
770
900
830
660
1000
710
460
740
940
870
810
650
760
950
870
670
960
750
480
690
850
890

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'Sir Maurice George Kendall' @ kendall.wessa.net

\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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235711&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235711&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235711&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'Sir Maurice George Kendall' @ kendall.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1804.16666666666756.1585957693734180
2817.549.012985292397170
3809.16666666666764.0253264282379240
4810.83333333333374.034185387972250
5815.83333333333397.6504278567486350
6807.5111.283830402673390
7790127.920429813366450
8784.166666666667149.14656204451540
9777.5140.008116647831480

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 804.166666666667 & 56.1585957693734 & 180 \tabularnewline
2 & 817.5 & 49.012985292397 & 170 \tabularnewline
3 & 809.166666666667 & 64.0253264282379 & 240 \tabularnewline
4 & 810.833333333333 & 74.034185387972 & 250 \tabularnewline
5 & 815.833333333333 & 97.6504278567486 & 350 \tabularnewline
6 & 807.5 & 111.283830402673 & 390 \tabularnewline
7 & 790 & 127.920429813366 & 450 \tabularnewline
8 & 784.166666666667 & 149.14656204451 & 540 \tabularnewline
9 & 777.5 & 140.008116647831 & 480 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235711&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]804.166666666667[/C][C]56.1585957693734[/C][C]180[/C][/ROW]
[ROW][C]2[/C][C]817.5[/C][C]49.012985292397[/C][C]170[/C][/ROW]
[ROW][C]3[/C][C]809.166666666667[/C][C]64.0253264282379[/C][C]240[/C][/ROW]
[ROW][C]4[/C][C]810.833333333333[/C][C]74.034185387972[/C][C]250[/C][/ROW]
[ROW][C]5[/C][C]815.833333333333[/C][C]97.6504278567486[/C][C]350[/C][/ROW]
[ROW][C]6[/C][C]807.5[/C][C]111.283830402673[/C][C]390[/C][/ROW]
[ROW][C]7[/C][C]790[/C][C]127.920429813366[/C][C]450[/C][/ROW]
[ROW][C]8[/C][C]784.166666666667[/C][C]149.14656204451[/C][C]540[/C][/ROW]
[ROW][C]9[/C][C]777.5[/C][C]140.008116647831[/C][C]480[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235711&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235711&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
1804.16666666666756.1585957693734180
2817.549.012985292397170
3809.16666666666764.0253264282379240
4810.83333333333374.034185387972250
5815.83333333333397.6504278567486350
6807.5111.283830402673390
7790127.920429813366450
8784.166666666667149.14656204451540
9777.5140.008116647831480






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha1808.18693283923
beta-2.13456470243557
S.D.0.569094845149826
T-STAT-3.7508066021466
p-value0.00716058223048944

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1808.18693283923 \tabularnewline
beta & -2.13456470243557 \tabularnewline
S.D. & 0.569094845149826 \tabularnewline
T-STAT & -3.7508066021466 \tabularnewline
p-value & 0.00716058223048944 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235711&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1808.18693283923[/C][/ROW]
[ROW][C]beta[/C][C]-2.13456470243557[/C][/ROW]
[ROW][C]S.D.[/C][C]0.569094845149826[/C][/ROW]
[ROW][C]T-STAT[/C][C]-3.7508066021466[/C][/ROW]
[ROW][C]p-value[/C][C]0.00716058223048944[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235711&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235711&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)
alpha1808.18693283923
beta-2.13456470243557
S.D.0.569094845149826
T-STAT-3.7508066021466
p-value0.00716058223048944






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha121.491315566703
beta-17.4963189330074
S.D.5.60712907037403
T-STAT-3.12037028458136
p-value0.0168349781953997
Lambda18.4963189330074

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 121.491315566703 \tabularnewline
beta & -17.4963189330074 \tabularnewline
S.D. & 5.60712907037403 \tabularnewline
T-STAT & -3.12037028458136 \tabularnewline
p-value & 0.0168349781953997 \tabularnewline
Lambda & 18.4963189330074 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235711&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]121.491315566703[/C][/ROW]
[ROW][C]beta[/C][C]-17.4963189330074[/C][/ROW]
[ROW][C]S.D.[/C][C]5.60712907037403[/C][/ROW]
[ROW][C]T-STAT[/C][C]-3.12037028458136[/C][/ROW]
[ROW][C]p-value[/C][C]0.0168349781953997[/C][/ROW]
[ROW][C]Lambda[/C][C]18.4963189330074[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235711&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235711&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)
alpha121.491315566703
beta-17.4963189330074
S.D.5.60712907037403
T-STAT-3.12037028458136
p-value0.0168349781953997
Lambda18.4963189330074


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 60 ; 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')