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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, 22 Dec 2008 09:20:28 -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/2008/Dec/22/t1229962920j9xild3ye7fgcj4.htm/, Retrieved Mon, 13 May 2024 18:01:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36117, Retrieved Mon, 13 May 2024 18:01:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact181

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Spectral Analysis] [Q6 - 3e methode -...] [2008-12-02 20:05:14] [7a664918911e34206ce9d0436dd7c1c8]
F RMPD  [Cross Correlation Function] [Q7 - cross correl...] [2008-12-02 20:56:08] [7a664918911e34206ce9d0436dd7c1c8]
F RMPD    [ARIMA Forecasting] [arima forecasting] [2008-12-14 12:01:13] [7a664918911e34206ce9d0436dd7c1c8]
F           [ARIMA Forecasting] [] [2008-12-16 22:07:39] [74be16979710d4c4e7c6647856088456]
- RMPD          [Standard Deviation-Mean Plot] [] [2008-12-22 16:20:28] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9,2
9,1
9,1
9,1
9,1
9,2
9,3
9,3
9,3
9,3
9,3
9,4
9,4
9,4
9,5
9,5
9,4
9,4
9,3
9,4
9,4
9,2
9,1
9,1
9,1
9,1
9
8,9
8,8
8,7
8,5
8,3
8,1
7,8
7,6
7,5
7,4
7,3
7,1
6,9
6,8
6,8
6,8
6,9
6,7
6,6
6,5
6,4
6,3
6,3
6,3
6,5
6,6
6,5
6,4
6,5
6,7
7,1
7,1
7,2
7,2
7,3
7,3
7,3
7,4
7,4
7,6
7,6
7,6
7,7
7,8
7,9
8,1
8,1
8,1
8,2
8,2
8,2
8,2
8,2
8,2
8,3
8,3
8,4
8,4
8,4
8,3
8
8
8,2
8,6
8,7
8,7
8,5
8,4
8,4
8,4
8,5
8,5
8,5
8,5
8,5
8,4
8,4
8,4
8,5
8,5
8,6
8,6
8,6
8,5
8,4
8,4
8,3
8,2
8,1
8,2
8,1
8
7,9
7,8
7,7
7,7
7,9
7,8
7,6
7,4
7,3
7,1
7,1
7
7

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36117&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36117&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36117&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
19.2250.1055289706022180.300000000000001
29.341666666666670.1378954368902450.4
38.450.582315128681121.6
46.850.31
56.6250.3306330017076060.9
67.508333333333330.2234373344457960.7
78.208333333333330.09003366373785240.300000000000001
88.383333333333330.2329000305762630.699999999999999
98.4750.06215815605080590.199999999999999
108.2750.2301185465244930.699999999999999
117.450.3397860289278320.9

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 9.225 & 0.105528970602218 & 0.300000000000001 \tabularnewline
2 & 9.34166666666667 & 0.137895436890245 & 0.4 \tabularnewline
3 & 8.45 & 0.58231512868112 & 1.6 \tabularnewline
4 & 6.85 & 0.3 & 1 \tabularnewline
5 & 6.625 & 0.330633001707606 & 0.9 \tabularnewline
6 & 7.50833333333333 & 0.223437334445796 & 0.7 \tabularnewline
7 & 8.20833333333333 & 0.0900336637378524 & 0.300000000000001 \tabularnewline
8 & 8.38333333333333 & 0.232900030576263 & 0.699999999999999 \tabularnewline
9 & 8.475 & 0.0621581560508059 & 0.199999999999999 \tabularnewline
10 & 8.275 & 0.230118546524493 & 0.699999999999999 \tabularnewline
11 & 7.45 & 0.339786028927832 & 0.9 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36117&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]9.225[/C][C]0.105528970602218[/C][C]0.300000000000001[/C][/ROW]
[ROW][C]2[/C][C]9.34166666666667[/C][C]0.137895436890245[/C][C]0.4[/C][/ROW]
[ROW][C]3[/C][C]8.45[/C][C]0.58231512868112[/C][C]1.6[/C][/ROW]
[ROW][C]4[/C][C]6.85[/C][C]0.3[/C][C]1[/C][/ROW]
[ROW][C]5[/C][C]6.625[/C][C]0.330633001707606[/C][C]0.9[/C][/ROW]
[ROW][C]6[/C][C]7.50833333333333[/C][C]0.223437334445796[/C][C]0.7[/C][/ROW]
[ROW][C]7[/C][C]8.20833333333333[/C][C]0.0900336637378524[/C][C]0.300000000000001[/C][/ROW]
[ROW][C]8[/C][C]8.38333333333333[/C][C]0.232900030576263[/C][C]0.699999999999999[/C][/ROW]
[ROW][C]9[/C][C]8.475[/C][C]0.0621581560508059[/C][C]0.199999999999999[/C][/ROW]
[ROW][C]10[/C][C]8.275[/C][C]0.230118546524493[/C][C]0.699999999999999[/C][/ROW]
[ROW][C]11[/C][C]7.45[/C][C]0.339786028927832[/C][C]0.9[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36117&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36117&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
19.2250.1055289706022180.300000000000001
29.341666666666670.1378954368902450.4
38.450.582315128681121.6
46.850.31
56.6250.3306330017076060.9
67.508333333333330.2234373344457960.7
78.208333333333330.09003366373785240.300000000000001
88.383333333333330.2329000305762630.699999999999999
98.4750.06215815605080590.199999999999999
108.2750.2301185465244930.699999999999999
117.450.3397860289278320.9






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.77326002888324
beta-0.0661216783058253
S.D.0.0521501248794436
T-STAT-1.26791025829142
p-value0.236647356930588

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.77326002888324 \tabularnewline
beta & -0.0661216783058253 \tabularnewline
S.D. & 0.0521501248794436 \tabularnewline
T-STAT & -1.26791025829142 \tabularnewline
p-value & 0.236647356930588 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36117&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.77326002888324[/C][/ROW]
[ROW][C]beta[/C][C]-0.0661216783058253[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0521501248794436[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.26791025829142[/C][/ROW]
[ROW][C]p-value[/C][C]0.236647356930588[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36117&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36117&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)
alpha0.77326002888324
beta-0.0661216783058253
S.D.0.0521501248794436
T-STAT-1.26791025829142
p-value0.236647356930588






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha4.6122641016194
beta-2.990025256705
S.D.1.73573207541037
T-STAT-1.72263064044494
p-value0.119053505294454
Lambda3.990025256705

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 4.6122641016194 \tabularnewline
beta & -2.990025256705 \tabularnewline
S.D. & 1.73573207541037 \tabularnewline
T-STAT & -1.72263064044494 \tabularnewline
p-value & 0.119053505294454 \tabularnewline
Lambda & 3.990025256705 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36117&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]4.6122641016194[/C][/ROW]
[ROW][C]beta[/C][C]-2.990025256705[/C][/ROW]
[ROW][C]S.D.[/C][C]1.73573207541037[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.72263064044494[/C][/ROW]
[ROW][C]p-value[/C][C]0.119053505294454[/C][/ROW]
[ROW][C]Lambda[/C][C]3.990025256705[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36117&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36117&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)
alpha4.6122641016194
beta-2.990025256705
S.D.1.73573207541037
T-STAT-1.72263064044494
p-value0.119053505294454
Lambda3.990025256705


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')