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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 computationTue, 16 Dec 2008 10:54:29 -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/16/t1229450142muwflij4rtx2tla.htm/, Retrieved Wed, 15 May 2024 11:41:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=34062, Retrieved Wed, 15 May 2024 11:41:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordspaper stan dev mean plot werk
Estimated Impact188

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [(Partial) Autocorrelation Function] [Paper: autocorrel...] [2008-12-05 10:20:24] [27f46dbe13ae2811dfd3a6f3c54d4d50]
F   PD  [(Partial) Autocorrelation Function] [Paper: autocorrel...] [2008-12-05 10:26:40] [27f46dbe13ae2811dfd3a6f3c54d4d50]
F   PD    [(Partial) Autocorrelation Function] [Paper: werklooshe...] [2008-12-05 10:43:32] [74be16979710d4c4e7c6647856088456]
F RMP       [Spectral Analysis] [paper: spectral a...] [2008-12-05 11:18:29] [74be16979710d4c4e7c6647856088456]
-   P         [Spectral Analysis] [Paper spectral an...] [2008-12-05 11:38:42] [74be16979710d4c4e7c6647856088456]
-               [Spectral Analysis] [Paper spectral an...] [2008-12-05 11:44:28] [74be16979710d4c4e7c6647856088456]
F                 [Spectral Analysis] [Paper: spectral a...] [2008-12-05 11:46:39] [74be16979710d4c4e7c6647856088456]
F   P               [Spectral Analysis] [Paper: spectral a...] [2008-12-05 11:50:13] [74be16979710d4c4e7c6647856088456]
F RMP                 [Standard Deviation-Mean Plot] [Paper: SD mean-pl...] [2008-12-05 13:05:29] [74be16979710d4c4e7c6647856088456]
-                         [Standard Deviation-Mean Plot] [paper stan dev me...] [2008-12-16 17:54:29] [d8c5724db236abb5950452133b88474d] [Current]
-    D                      [Standard Deviation-Mean Plot] [paper sdmp werk 20] [2008-12-18 13:23:55] [5de5fb433ddcb9578e0fa830f795b7e9]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
95.20
95.00
94.00
92.20
91.00
91.20
103.40
105.00
104.60
103.80
101.80
102.40
103.80
103.40
102.00
101.80
100.20
101.40
113.80
116.00
115.60
113.00
109.40
111.00
112.40
112.20
111.00
108.80
107.40
108.60
118.80
122.20
122.60
122.20
118.80
119.00
118.20
117.80
116.80
114.60
113.40
113.80
124.20
125.80
125.60
122.40
119.00
119.40
118.60
118.00
116.00
114.80
114.60
114.60
124.00
125.20
124.00
117.60
113.20
111.40
112.20
109.80
106.40
105.20
102.20
99.80
111.00
113.00
108.40
105.40
102.00
102.80

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=34062&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=34062&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34062&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
198.35.6391488719486714
2107.6166666666676.084530807836815.8
3115.3333333333335.821173473283615.2
4119.254.3951419462029612.4
5117.6666666666674.5425930386896313.8
6106.5166666666674.3663659392166813.2

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 98.3 & 5.63914887194867 & 14 \tabularnewline
2 & 107.616666666667 & 6.0845308078368 & 15.8 \tabularnewline
3 & 115.333333333333 & 5.8211734732836 & 15.2 \tabularnewline
4 & 119.25 & 4.39514194620296 & 12.4 \tabularnewline
5 & 117.666666666667 & 4.54259303868963 & 13.8 \tabularnewline
6 & 106.516666666667 & 4.36636593921668 & 13.2 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34062&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]98.3[/C][C]5.63914887194867[/C][C]14[/C][/ROW]
[ROW][C]2[/C][C]107.616666666667[/C][C]6.0845308078368[/C][C]15.8[/C][/ROW]
[ROW][C]3[/C][C]115.333333333333[/C][C]5.8211734732836[/C][C]15.2[/C][/ROW]
[ROW][C]4[/C][C]119.25[/C][C]4.39514194620296[/C][C]12.4[/C][/ROW]
[ROW][C]5[/C][C]117.666666666667[/C][C]4.54259303868963[/C][C]13.8[/C][/ROW]
[ROW][C]6[/C][C]106.516666666667[/C][C]4.36636593921668[/C][C]13.2[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34062&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34062&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
198.35.6391488719486714
2107.6166666666676.084530807836815.8
3115.3333333333335.821173473283615.2
4119.254.3951419462029612.4
5117.6666666666674.5425930386896313.8
6106.5166666666674.3663659392166813.2






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha9.67094578995037
beta-0.0408867189827595
S.D.0.0445784290669578
T-STAT-0.91718617812545
p-value0.410941964642576

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 9.67094578995037 \tabularnewline
beta & -0.0408867189827595 \tabularnewline
S.D. & 0.0445784290669578 \tabularnewline
T-STAT & -0.91718617812545 \tabularnewline
p-value & 0.410941964642576 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34062&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]9.67094578995037[/C][/ROW]
[ROW][C]beta[/C][C]-0.0408867189827595[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0445784290669578[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.91718617812545[/C][/ROW]
[ROW][C]p-value[/C][C]0.410941964642576[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34062&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34062&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)
alpha9.67094578995037
beta-0.0408867189827595
S.D.0.0445784290669578
T-STAT-0.91718617812545
p-value0.410941964642576






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha5.70284584100463
beta-0.866121070164885
S.D.0.946326825941684
T-STAT-0.915245184244897
p-value0.411846124333507
Lambda1.86612107016488

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 5.70284584100463 \tabularnewline
beta & -0.866121070164885 \tabularnewline
S.D. & 0.946326825941684 \tabularnewline
T-STAT & -0.915245184244897 \tabularnewline
p-value & 0.411846124333507 \tabularnewline
Lambda & 1.86612107016488 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34062&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]5.70284584100463[/C][/ROW]
[ROW][C]beta[/C][C]-0.866121070164885[/C][/ROW]
[ROW][C]S.D.[/C][C]0.946326825941684[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.915245184244897[/C][/ROW]
[ROW][C]p-value[/C][C]0.411846124333507[/C][/ROW]
[ROW][C]Lambda[/C][C]1.86612107016488[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34062&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34062&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)
alpha5.70284584100463
beta-0.866121070164885
S.D.0.946326825941684
T-STAT-0.915245184244897
p-value0.411846124333507
Lambda1.86612107016488


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')