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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 computationFri, 03 Dec 2010 10:13:26 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/03/t1291371228tbdkcw9drmzic2o.htm/, Retrieved Tue, 07 May 2024 10:01:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=104601, Retrieved Tue, 07 May 2024 10:01:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact138

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]
- RMP   [Standard Deviation-Mean Plot] [Unemployment] [2010-11-29 10:34:47] [b98453cac15ba1066b407e146608df68]
F   PD      [Standard Deviation-Mean Plot] [stationarity in t...] [2010-12-03 10:13:26] [e665313c9926a9f4bdf6ad1ee5aefad6] [Current]
-   PD        [Standard Deviation-Mean Plot] [standard devianti...] [2010-12-18 20:37:24] [74deae64b71f9d77c839af86f7c687b5]
- RM          [Standard Deviation-Mean Plot] [] [2011-12-06 19:20:41] [46d7ccc24e5d35a2decd922dfb3b3a39]
Feedback Forum
2010-12-12 19:11:59 [00c625c7d009d84797af914265b614f9] [reply] 
correct, we kunnen zien dat er een verband is tussen de variantie en het gemiddelde. Beta is significant verschillend van 0. de kans dat we ons vergissen bij het verwerpen van de nulhypothese (beta = 0) is zeer klein. dus er moet een lambda-transformatie doorgevoerd worden om de heteroskedasticiteit te verwijderen.
2010-12-13 11:43:42 [Stefanie Van Esbroeck] [reply] 
Je maakt een correcte berekening. Je interpretatie is wat kort en verklaart niet veel. Je had kunnen opmerken dat de Betacoëfficiënt gelijk is aan -6 en dat de p-waarde gelijk is aan 5%. Deze waarden tonen aan dat er een verband is tussen de spreiding en het middel. Je kan best daarna ook eens kijken naar de lambda-waarde en dan zal je zien dat die gelijk is aan - 5,9. Deze waarde is zeker niet gelijk aan 1 waardoor we kunnen stellen dat een transformatie nodig is.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
101,76
102,37
102,38
102,86
102,87
102,92
102,95
103,02
104,08
104,16
104,24
104,33
104,73
104,86
105,03
105,62
105,63
105,63
105,94
106,61
107,69
107,78
107,93
108,48
108,14
108,48
108,48
108,89
108,93
109,21
109,47
109,80
111,73
111,85
112,12
112,15
112,17
112,67
112,80
113,44
113,53
114,53
114,51
115,05
116,67
117,07
116,92
117,00
117,02
117,35
117,36
117,82
117,88
118,24
118,50
118,80
119,76
120,09

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=104601&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=104601&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104601&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
1103.1616666666670.845822174877882.56999999999999
2106.32751.323220073773213.75
3109.93751.563440989379754.01000000000001
4114.6966666666671.833820320995754.89999999999999

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 103.161666666667 & 0.84582217487788 & 2.56999999999999 \tabularnewline
2 & 106.3275 & 1.32322007377321 & 3.75 \tabularnewline
3 & 109.9375 & 1.56344098937975 & 4.01000000000001 \tabularnewline
4 & 114.696666666667 & 1.83382032099575 & 4.89999999999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104601&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]103.161666666667[/C][C]0.84582217487788[/C][C]2.56999999999999[/C][/ROW]
[ROW][C]2[/C][C]106.3275[/C][C]1.32322007377321[/C][C]3.75[/C][/ROW]
[ROW][C]3[/C][C]109.9375[/C][C]1.56344098937975[/C][C]4.01000000000001[/C][/ROW]
[ROW][C]4[/C][C]114.696666666667[/C][C]1.83382032099575[/C][C]4.89999999999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104601&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104601&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
1103.1616666666670.845822174877882.56999999999999
2106.32751.323220073773213.75
3109.93751.563440989379754.01000000000001
4114.6966666666671.833820320995754.89999999999999






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-7.51936951554501
beta0.082105196575182
S.D.0.0144922686066554
T-STAT5.66544816437342
p-value0.0297709887296646

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -7.51936951554501 \tabularnewline
beta & 0.082105196575182 \tabularnewline
S.D. & 0.0144922686066554 \tabularnewline
T-STAT & 5.66544816437342 \tabularnewline
p-value & 0.0297709887296646 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104601&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-7.51936951554501[/C][/ROW]
[ROW][C]beta[/C][C]0.082105196575182[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0144922686066554[/C][/ROW]
[ROW][C]T-STAT[/C][C]5.66544816437342[/C][/ROW]
[ROW][C]p-value[/C][C]0.0297709887296646[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104601&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104601&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-7.51936951554501
beta0.082105196575182
S.D.0.0144922686066554
T-STAT5.66544816437342
p-value0.0297709887296646






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-32.0898425760819
beta6.9098487700907
S.D.1.73717451692906
T-STAT3.97763650269623
p-value0.0577810333269001
Lambda-5.9098487700907

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -32.0898425760819 \tabularnewline
beta & 6.9098487700907 \tabularnewline
S.D. & 1.73717451692906 \tabularnewline
T-STAT & 3.97763650269623 \tabularnewline
p-value & 0.0577810333269001 \tabularnewline
Lambda & -5.9098487700907 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104601&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-32.0898425760819[/C][/ROW]
[ROW][C]beta[/C][C]6.9098487700907[/C][/ROW]
[ROW][C]S.D.[/C][C]1.73717451692906[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.97763650269623[/C][/ROW]
[ROW][C]p-value[/C][C]0.0577810333269001[/C][/ROW]
[ROW][C]Lambda[/C][C]-5.9098487700907[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104601&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104601&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-32.0898425760819
beta6.9098487700907
S.D.1.73717451692906
T-STAT3.97763650269623
p-value0.0577810333269001
Lambda-5.9098487700907


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')