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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 computationSat, 06 Dec 2008 05:33:55 -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/06/t1228566882z5234ax3dzp3f0d.htm/, Retrieved Sun, 19 May 2024 09:18:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29545, Retrieved Sun, 19 May 2024 09:18:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact216

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [Standard Deviation-Mean Plot] [step 1] [2008-12-06 12:33:55] [3dc594a6c62226e1e98766c4d385bfaa] [Current]
F RM      [Variance Reduction Matrix] [VRM] [2008-12-07 19:46:08] [c45c87b96bbf32ffc2144fc37d767b2e]
F RMP       [ARIMA Backward Selection] [backward estimation] [2008-12-07 23:13:24] [c45c87b96bbf32ffc2144fc37d767b2e]
- RMP     [(Partial) Autocorrelation Function] [acf] [2008-12-07 19:58:05] [c45c87b96bbf32ffc2144fc37d767b2e]
- RMP     [(Partial) Autocorrelation Function] [acf] [2008-12-07 20:04:18] [c45c87b96bbf32ffc2144fc37d767b2e]
-   P       [(Partial) Autocorrelation Function] [acf] [2008-12-07 20:21:09] [c45c87b96bbf32ffc2144fc37d767b2e]
F   P         [(Partial) Autocorrelation Function] [acf] [2008-12-07 23:16:53] [c45c87b96bbf32ffc2144fc37d767b2e]
- RMP       [Spectral Analysis] [rp] [2008-12-07 20:26:25] [c45c87b96bbf32ffc2144fc37d767b2e]
- RMP     [Spectral Analysis] [cp] [2008-12-07 20:09:07] [c45c87b96bbf32ffc2144fc37d767b2e]
F   P       [Spectral Analysis] [cp] [2008-12-08 07:14:35] [c45c87b96bbf32ffc2144fc37d767b2e]
- RMP     [Spectral Analysis] [rp] [2008-12-07 20:14:14] [c45c87b96bbf32ffc2144fc37d767b2e]
Feedback Forum
2008-12-14 20:52:03 [Michaël De Kuyer] [reply] 
Ik had me in de eerste plaats moeten baseren op de beta coëfficiënt. Die is niet significant verschillend van nul, dus we moeten niet meer naar de volgende tabel kijken. Er is dus geen verband tussen het gemiddelde en de standaardafwijking. We veronderstellen wel dat er een transformatie moet gebeuren, maar we vinden deze niet, daarom stellen we de lambda gelijk aan 1.
2008-12-15 19:53:42 [8e2cc0b2ef568da46d009b2f601285b2] [reply] 
In je taak vermeld je slechts 1 tabel, op deze tabel zou je de lambda kunnen aflezen indien een lambda transformatie nodig is/was.
De te controlere beta kan je terugvinden in de tabel 'Regression: S.E.(k) = alpha + beta * Mean(k)'. Daar merk je correct op dat deze niet significant verschillend is van nul en je daarom verder moet werken met lambda = 1.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3595
3914
4159
3676
3794
3446
3504
3958
3353
3480
3098
2944
3389
3497
4404
3849
3734
3060
3507
3287
3215
3764
2734
2837
2766
3851
3289
3848
3348
3682
4058
3655
3811
3341
3032
3475
3353
3186
3902
4164
3499
4145
3796
3711
3949
3740
3243
4407
4814
3908
5250
3937
4004
5560
3922
3759
4138
4634
3996
4308
4142
4429
5219
4929
5754
5592
4163
4962
5208
4755
4491
5732
5730
5024
6056
4901
5353
5578
4618
4724
5011
5298
4143
4617
4736
4214
5112
4197
4119
5104
4194
4583
3790
5557
4304
3838
4277
4951
4479
4677
4274
4782

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'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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29545&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29545&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29545&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'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
13576.75352.5068987074771215
23439.75465.0323791268341670
33513376.4453358843631292
43757.91666666667383.8222738179581221
54352.5584.6611295131881801
64948572.2321525077361612
75087.75540.7795929783391913
84479548.308473232161767

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 3576.75 & 352.506898707477 & 1215 \tabularnewline
2 & 3439.75 & 465.032379126834 & 1670 \tabularnewline
3 & 3513 & 376.445335884363 & 1292 \tabularnewline
4 & 3757.91666666667 & 383.822273817958 & 1221 \tabularnewline
5 & 4352.5 & 584.661129513188 & 1801 \tabularnewline
6 & 4948 & 572.232152507736 & 1612 \tabularnewline
7 & 5087.75 & 540.779592978339 & 1913 \tabularnewline
8 & 4479 & 548.30847323216 & 1767 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29545&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]3576.75[/C][C]352.506898707477[/C][C]1215[/C][/ROW]
[ROW][C]2[/C][C]3439.75[/C][C]465.032379126834[/C][C]1670[/C][/ROW]
[ROW][C]3[/C][C]3513[/C][C]376.445335884363[/C][C]1292[/C][/ROW]
[ROW][C]4[/C][C]3757.91666666667[/C][C]383.822273817958[/C][C]1221[/C][/ROW]
[ROW][C]5[/C][C]4352.5[/C][C]584.661129513188[/C][C]1801[/C][/ROW]
[ROW][C]6[/C][C]4948[/C][C]572.232152507736[/C][C]1612[/C][/ROW]
[ROW][C]7[/C][C]5087.75[/C][C]540.779592978339[/C][C]1913[/C][/ROW]
[ROW][C]8[/C][C]4479[/C][C]548.30847323216[/C][C]1767[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29545&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29545&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
13576.75352.5068987074771215
23439.75465.0323791268341670
33513376.4453358843631292
43757.91666666667383.8222738179581221
54352.5584.6611295131881801
64948572.2321525077361612
75087.75540.7795929783391913
84479548.308473232161767






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-12.0741448232000
beta0.118245236297162
S.D.0.0342227025882287
T-STAT3.45516944467835
p-value0.0135470518024782

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -12.0741448232000 \tabularnewline
beta & 0.118245236297162 \tabularnewline
S.D. & 0.0342227025882287 \tabularnewline
T-STAT & 3.45516944467835 \tabularnewline
p-value & 0.0135470518024782 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29545&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-12.0741448232000[/C][/ROW]
[ROW][C]beta[/C][C]0.118245236297162[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0342227025882287[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.45516944467835[/C][/ROW]
[ROW][C]p-value[/C][C]0.0135470518024782[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29545&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29545&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-12.0741448232000
beta0.118245236297162
S.D.0.0342227025882287
T-STAT3.45516944467835
p-value0.0135470518024782






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.77715934897944
beta1.07329471651572
S.D.0.312661479025899
T-STAT3.43276926809015
p-value0.0139238079669055
Lambda-0.07329471651572

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.77715934897944 \tabularnewline
beta & 1.07329471651572 \tabularnewline
S.D. & 0.312661479025899 \tabularnewline
T-STAT & 3.43276926809015 \tabularnewline
p-value & 0.0139238079669055 \tabularnewline
Lambda & -0.07329471651572 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29545&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.77715934897944[/C][/ROW]
[ROW][C]beta[/C][C]1.07329471651572[/C][/ROW]
[ROW][C]S.D.[/C][C]0.312661479025899[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.43276926809015[/C][/ROW]
[ROW][C]p-value[/C][C]0.0139238079669055[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.07329471651572[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29545&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29545&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-2.77715934897944
beta1.07329471651572
S.D.0.312661479025899
T-STAT3.43276926809015
p-value0.0139238079669055
Lambda-0.07329471651572


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')