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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 computationThu, 08 Jan 2009 13:44:55 -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/2009/Jan/08/t1231447681tioujgxdph3sehk.htm/, Retrieved Wed, 08 May 2024 21:49:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36829, Retrieved Wed, 08 May 2024 21:49:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact195

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Standard Deviation-Mean Plot] [standard deviatio...] [2009-01-08 20:44:55] [0ebe94bd950a0b1969e8ed777006e521] [Current]
-    D    [Standard Deviation-Mean Plot] [Maxime Jonckheere...] [2009-05-27 21:51:58] [74be16979710d4c4e7c6647856088456]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
66,2
66,2
66,2
66,08
66,31
66,39
66,37
66,23
66,27
66,27
66,27
66,28
66,28
66,28
66,26
66,13
65,86
65,9
65,94
65,94
65,91
65,95
65,91
66,08
66,47
66,47
66,56
66,78
67,08
67,28
67,27
67,27
67,26
67,37
67,5
67,63
67,64
67,64
67,71
67,87
67,93
68,33
68,39
68,39
68,58
68,44
68,49
68,52
68,54
68,54
68,54
68,62
68,75
68,71
68,72
68,72
68,72
68,92
68,9
69,12
69,09
69,09
69,1
69,16
68,83
68,52
68,53
68,53
68,51
68,38
68,44
68,41
68,42
68,42
68,45
68,63
68,84
68,72
68,37
68,37
68,47
68,69
68,46
68,17
68,17

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 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=36829&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]2 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=36829&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36829&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 time2 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
166.25583333333330.08317105411394220.310000000000002
266.03666666666670.1615455653893660.420000000000002
367.07833333333330.4058847425592931.16000000000000
468.16083333333330.3702936999766850.939999999999998
568.73333333333330.1754129327321590.579999999999998
668.71583333333330.3118991192774690.780000000000001
768.50083333333330.1852496268347760.670000000000002

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 66.2558333333333 & 0.0831710541139422 & 0.310000000000002 \tabularnewline
2 & 66.0366666666667 & 0.161545565389366 & 0.420000000000002 \tabularnewline
3 & 67.0783333333333 & 0.405884742559293 & 1.16000000000000 \tabularnewline
4 & 68.1608333333333 & 0.370293699976685 & 0.939999999999998 \tabularnewline
5 & 68.7333333333333 & 0.175412932732159 & 0.579999999999998 \tabularnewline
6 & 68.7158333333333 & 0.311899119277469 & 0.780000000000001 \tabularnewline
7 & 68.5008333333333 & 0.185249626834776 & 0.670000000000002 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36829&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]66.2558333333333[/C][C]0.0831710541139422[/C][C]0.310000000000002[/C][/ROW]
[ROW][C]2[/C][C]66.0366666666667[/C][C]0.161545565389366[/C][C]0.420000000000002[/C][/ROW]
[ROW][C]3[/C][C]67.0783333333333[/C][C]0.405884742559293[/C][C]1.16000000000000[/C][/ROW]
[ROW][C]4[/C][C]68.1608333333333[/C][C]0.370293699976685[/C][C]0.939999999999998[/C][/ROW]
[ROW][C]5[/C][C]68.7333333333333[/C][C]0.175412932732159[/C][C]0.579999999999998[/C][/ROW]
[ROW][C]6[/C][C]68.7158333333333[/C][C]0.311899119277469[/C][C]0.780000000000001[/C][/ROW]
[ROW][C]7[/C][C]68.5008333333333[/C][C]0.185249626834776[/C][C]0.670000000000002[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36829&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36829&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
166.25583333333330.08317105411394220.310000000000002
266.03666666666670.1615455653893660.420000000000002
367.07833333333330.4058847425592931.16000000000000
468.16083333333330.3702936999766850.939999999999998
568.73333333333330.1754129327321590.579999999999998
668.71583333333330.3118991192774690.780000000000001
768.50083333333330.1852496268347760.670000000000002






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-2.05348973318265
beta0.0339356008993567
S.D.0.0437470704540173
T-STAT0.775722820914982
p-value0.472988655896576

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -2.05348973318265 \tabularnewline
beta & 0.0339356008993567 \tabularnewline
S.D. & 0.0437470704540173 \tabularnewline
T-STAT & 0.775722820914982 \tabularnewline
p-value & 0.472988655896576 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36829&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.05348973318265[/C][/ROW]
[ROW][C]beta[/C][C]0.0339356008993567[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0437470704540173[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.775722820914982[/C][/ROW]
[ROW][C]p-value[/C][C]0.472988655896576[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36829&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36829&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-2.05348973318265
beta0.0339356008993567
S.D.0.0437470704540173
T-STAT0.775722820914982
p-value0.472988655896576






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-62.7045464737369
beta14.5137806734736
S.D.12.9465657991262
T-STAT1.12105255545476
p-value0.313201168448143
Lambda-13.5137806734736

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -62.7045464737369 \tabularnewline
beta & 14.5137806734736 \tabularnewline
S.D. & 12.9465657991262 \tabularnewline
T-STAT & 1.12105255545476 \tabularnewline
p-value & 0.313201168448143 \tabularnewline
Lambda & -13.5137806734736 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36829&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-62.7045464737369[/C][/ROW]
[ROW][C]beta[/C][C]14.5137806734736[/C][/ROW]
[ROW][C]S.D.[/C][C]12.9465657991262[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.12105255545476[/C][/ROW]
[ROW][C]p-value[/C][C]0.313201168448143[/C][/ROW]
[ROW][C]Lambda[/C][C]-13.5137806734736[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36829&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36829&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-62.7045464737369
beta14.5137806734736
S.D.12.9465657991262
T-STAT1.12105255545476
p-value0.313201168448143
Lambda-13.5137806734736


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')