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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 computationMon, 08 Dec 2008 05:41:29 -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/08/t12287401620xngpmrof1aytbm.htm/, Retrieved Thu, 16 May 2024 17:44:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30437, Retrieved Thu, 16 May 2024 17:44:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsSMP
Estimated Impact209

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
F RMP   [Standard Deviation-Mean Plot] [q1] [2008-12-08 12:37:39] [3ffd109c9e040b1ae7e5dbe576d4698c]
F    D      [Standard Deviation-Mean Plot] [SMP] [2008-12-08 12:41:29] [962e6c9020896982bc8283b8971710a9] [Current]
- RMP         [(Partial) Autocorrelation Function] [ACF] [2008-12-08 12:44:57] [3ffd109c9e040b1ae7e5dbe576d4698c]
- RM          [Variance Reduction Matrix] [VRM] [2008-12-08 13:10:17] [3ffd109c9e040b1ae7e5dbe576d4698c]
- RM            [(Partial) Autocorrelation Function] [ACF] [2008-12-08 13:14:12] [3ffd109c9e040b1ae7e5dbe576d4698c]
F                 [(Partial) Autocorrelation Function] [ACF] [2008-12-08 13:16:18] [3ffd109c9e040b1ae7e5dbe576d4698c]
-   P               [(Partial) Autocorrelation Function] [ACF met meer lags] [2008-12-15 14:07:02] [f77c9ab3b413812d7baee6b7ec69a15d]
-   P               [(Partial) Autocorrelation Function] [ACF] [2008-12-16 11:53:49] [3ffd109c9e040b1ae7e5dbe576d4698c]
- R P               [(Partial) Autocorrelation Function] [ACF] [2008-12-18 16:25:12] [3ffd109c9e040b1ae7e5dbe576d4698c]
-   P                 [(Partial) Autocorrelation Function] [ACF] [2008-12-24 12:57:31] [b28ef2aea2cd58ceb5ad90223572c703]
F                 [(Partial) Autocorrelation Function] [ACF] [2008-12-08 13:17:45] [3ffd109c9e040b1ae7e5dbe576d4698c]
F RM                [Spectral Analysis] [spectraal] [2008-12-08 13:20:34] [3ffd109c9e040b1ae7e5dbe576d4698c]
- R P                 [Spectral Analysis] [Spectraal] [2008-12-18 16:27:12] [3ffd109c9e040b1ae7e5dbe576d4698c]
-                       [Spectral Analysis] [spectraal analyse] [2008-12-24 12:59:19] [b28ef2aea2cd58ceb5ad90223572c703]
- R P                 [Spectral Analysis] [spectraal] [2008-12-18 18:22:50] [3ffd109c9e040b1ae7e5dbe576d4698c]
- RM                [Spectral Analysis] [spectraal] [2008-12-08 13:22:13] [3ffd109c9e040b1ae7e5dbe576d4698c]
- R P                 [Spectral Analysis] [spectraal] [2008-12-18 18:23:46] [3ffd109c9e040b1ae7e5dbe576d4698c]
-                       [Spectral Analysis] [spectraal analyse] [2008-12-24 13:02:50] [b28ef2aea2cd58ceb5ad90223572c703]
-   P                   [Spectral Analysis] [spectraal] [2008-12-24 13:21:21] [3ffd109c9e040b1ae7e5dbe576d4698c]
- RM                [Spectral Analysis] [spectraal] [2008-12-08 13:23:27] [3ffd109c9e040b1ae7e5dbe576d4698c]
F RM                  [(Partial) Autocorrelation Function] [ACF] [2008-12-08 13:40:41] [3ffd109c9e040b1ae7e5dbe576d4698c]
- R P                   [(Partial) Autocorrelation Function] [acf] [2008-12-18 18:26:49] [3ffd109c9e040b1ae7e5dbe576d4698c]
-   P                   [(Partial) Autocorrelation Function] [autocorrelatie en...] [2008-12-19 10:44:18] [3f66c6f083b1153972739491b89fa2dd]
-                     [Spectral Analysis] [spectraal] [2008-12-08 13:42:55] [3ffd109c9e040b1ae7e5dbe576d4698c]
- R P                   [Spectral Analysis] [spectraal] [2008-12-18 18:28:37] [3ffd109c9e040b1ae7e5dbe576d4698c]
- R P                 [Spectral Analysis] [spectraal] [2008-12-18 18:25:11] [3ffd109c9e040b1ae7e5dbe576d4698c]
-   P                   [Spectral Analysis] [spectraal analyse] [2008-12-24 13:07:13] [b28ef2aea2cd58ceb5ad90223572c703]
-   P               [(Partial) Autocorrelation Function] [ACF met meer lags] [2008-12-15 14:18:46] [f77c9ab3b413812d7baee6b7ec69a15d]
- R P               [(Partial) Autocorrelation Function] [ACF] [2008-12-18 16:54:54] [3ffd109c9e040b1ae7e5dbe576d4698c]
-   P                 [(Partial) Autocorrelation Function] [ACF] [2008-12-24 13:04:28] [b28ef2aea2cd58ceb5ad90223572c703]
- R P             [(Partial) Autocorrelation Function] [ACF] [2008-12-18 16:48:38] [3ffd109c9e040b1ae7e5dbe576d4698c]
-   P               [(Partial) Autocorrelation Function] [ACF] [2008-12-24 13:00:55] [b28ef2aea2cd58ceb5ad90223572c703]
- R             [Variance Reduction Matrix] [VRM] [2008-12-18 18:18:02] [3ffd109c9e040b1ae7e5dbe576d4698c]
- R           [Standard Deviation-Mean Plot] [plot] [2008-12-18 18:16:11] [3ffd109c9e040b1ae7e5dbe576d4698c]
-               [Standard Deviation-Mean Plot] [plot] [2008-12-24 12:54:32] [b28ef2aea2cd58ceb5ad90223572c703]
Feedback Forum
2008-12-15 14:04:15 [Charis Berrevoets] [reply] 
Heel goed. Het enige wat je nog had kunnen doen is de grafiek bespreken. Hierop zie je immers een verband tussen het gemiddelde en de standaardfout want we kunnen een regressierechte tekenen. In de eerste tabel kan je inderdaad zien dat de p-waarde zeer klein is waardoor we weten dat de helling van de regressierechte niet aan toeval te wijten is.
De beta-waarde is dus significant verschillend van 0, een transformatie is nodig. De correcte lambda-waarde is inderdaad -0,1

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
147768
137507
136919
136151
133001
125554
119647
114158
116193
152803
161761
160942
149470
139208
134588
130322
126611
122401
117352
112135
112879
148729
157230
157221
146681
136524
132111
125326
122716
116615
113719
110737
112093
143565
149946
149147
134339
122683
115614
116566
111272
104609
101802
94542
93051
124129
130374
123946
114971
105531
104919
104782
101281
94545
93248
84031
87486
115867
120327
117008
108811

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time0 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 & 0 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30437&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]0 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=30437&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30437&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 time0 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
113686716391.796728851947603
2134012.16666666716422.190889344245095
3129931.66666666715028.864079335939209
4114410.58333333313577.259346276841288
5103666.33333333311997.349005155936296

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 136867 & 16391.7967288519 & 47603 \tabularnewline
2 & 134012.166666667 & 16422.1908893442 & 45095 \tabularnewline
3 & 129931.666666667 & 15028.8640793359 & 39209 \tabularnewline
4 & 114410.583333333 & 13577.2593462768 & 41288 \tabularnewline
5 & 103666.333333333 & 11997.3490051559 & 36296 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30437&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]136867[/C][C]16391.7967288519[/C][C]47603[/C][/ROW]
[ROW][C]2[/C][C]134012.166666667[/C][C]16422.1908893442[/C][C]45095[/C][/ROW]
[ROW][C]3[/C][C]129931.666666667[/C][C]15028.8640793359[/C][C]39209[/C][/ROW]
[ROW][C]4[/C][C]114410.583333333[/C][C]13577.2593462768[/C][C]41288[/C][/ROW]
[ROW][C]5[/C][C]103666.333333333[/C][C]11997.3490051559[/C][C]36296[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30437&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30437&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
113686716391.796728851947603
2134012.16666666716422.190889344245095
3129931.66666666715028.864079335939209
4114410.58333333313577.259346276841288
5103666.33333333311997.349005155936296






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-1693.88139946398
beta0.132312955049255
S.D.0.0126439928428552
T-STAT10.4644914540601
p-value0.00186303109755164

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -1693.88139946398 \tabularnewline
beta & 0.132312955049255 \tabularnewline
S.D. & 0.0126439928428552 \tabularnewline
T-STAT & 10.4644914540601 \tabularnewline
p-value & 0.00186303109755164 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30437&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1693.88139946398[/C][/ROW]
[ROW][C]beta[/C][C]0.132312955049255[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0126439928428552[/C][/ROW]
[ROW][C]T-STAT[/C][C]10.4644914540601[/C][/ROW]
[ROW][C]p-value[/C][C]0.00186303109755164[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30437&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30437&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-1693.88139946398
beta0.132312955049255
S.D.0.0126439928428552
T-STAT10.4644914540601
p-value0.00186303109755164






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.51376047019633
beta1.11778014068067
S.D.0.0974739995460318
T-STAT11.4674697446144
p-value0.00142332727663895
Lambda-0.117780140680673

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.51376047019633 \tabularnewline
beta & 1.11778014068067 \tabularnewline
S.D. & 0.0974739995460318 \tabularnewline
T-STAT & 11.4674697446144 \tabularnewline
p-value & 0.00142332727663895 \tabularnewline
Lambda & -0.117780140680673 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30437&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.51376047019633[/C][/ROW]
[ROW][C]beta[/C][C]1.11778014068067[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0974739995460318[/C][/ROW]
[ROW][C]T-STAT[/C][C]11.4674697446144[/C][/ROW]
[ROW][C]p-value[/C][C]0.00142332727663895[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.117780140680673[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30437&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30437&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-3.51376047019633
beta1.11778014068067
S.D.0.0974739995460318
T-STAT11.4674697446144
p-value0.00142332727663895
Lambda-0.117780140680673


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')