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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 computationSat, 24 May 2008 07:45:09 -0600
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/May/24/t12116368178asof58xsccgwj1.htm/, Retrieved Tue, 14 May 2024 02:51:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13070, Retrieved Tue, 14 May 2024 02:51:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact199

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...] [2008-05-15 17:22:59] [938121352ceb5736f84c4583bccf5678]
-   PD    [Standard Deviation-Mean Plot] [Standard deviatio...] [2008-05-24 13:45:09] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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 time4 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 & 4 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=13070&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]4 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=13070&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13070&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 time4 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
166.26250.08147782743566770.310000000000002
266.05250.1936785058708470.61
367.17583333333330.3865337415198481.17000000000000
468.23583333333330.3455287998346170.939999999999998
568.77916666666670.1914280464553120.579999999999998
668.660.2985114585892650.780000000000001
768.480.2078460969082640.670000000000002

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 66.2625 & 0.0814778274356677 & 0.310000000000002 \tabularnewline
2 & 66.0525 & 0.193678505870847 & 0.61 \tabularnewline
3 & 67.1758333333333 & 0.386533741519848 & 1.17000000000000 \tabularnewline
4 & 68.2358333333333 & 0.345528799834617 & 0.939999999999998 \tabularnewline
5 & 68.7791666666667 & 0.191428046455312 & 0.579999999999998 \tabularnewline
6 & 68.66 & 0.298511458589265 & 0.780000000000001 \tabularnewline
7 & 68.48 & 0.207846096908264 & 0.670000000000002 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13070&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]66.2625[/C][C]0.0814778274356677[/C][C]0.310000000000002[/C][/ROW]
[ROW][C]2[/C][C]66.0525[/C][C]0.193678505870847[/C][C]0.61[/C][/ROW]
[ROW][C]3[/C][C]67.1758333333333[/C][C]0.386533741519848[/C][C]1.17000000000000[/C][/ROW]
[ROW][C]4[/C][C]68.2358333333333[/C][C]0.345528799834617[/C][C]0.939999999999998[/C][/ROW]
[ROW][C]5[/C][C]68.7791666666667[/C][C]0.191428046455312[/C][C]0.579999999999998[/C][/ROW]
[ROW][C]6[/C][C]68.66[/C][C]0.298511458589265[/C][C]0.780000000000001[/C][/ROW]
[ROW][C]7[/C][C]68.48[/C][C]0.207846096908264[/C][C]0.670000000000002[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13070&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13070&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
166.26250.08147782743566770.310000000000002
266.05250.1936785058708470.61
367.17583333333330.3865337415198481.17000000000000
468.23583333333330.3455287998346170.939999999999998
568.77916666666670.1914280464553120.579999999999998
668.660.2985114585892650.780000000000001
768.480.2078460969082640.670000000000002






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-1.97743590570502
beta0.0328242216491907
S.D.0.0379999509469686
T-STAT0.863796421605886
p-value0.42718482383001

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -1.97743590570502 \tabularnewline
beta & 0.0328242216491907 \tabularnewline
S.D. & 0.0379999509469686 \tabularnewline
T-STAT & 0.863796421605886 \tabularnewline
p-value & 0.42718482383001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13070&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.97743590570502[/C][/ROW]
[ROW][C]beta[/C][C]0.0328242216491907[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0379999509469686[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.863796421605886[/C][/ROW]
[ROW][C]p-value[/C][C]0.42718482383001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13070&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13070&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-1.97743590570502
beta0.0328242216491907
S.D.0.0379999509469686
T-STAT0.863796421605886
p-value0.42718482383001






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-61.3532992021266
beta14.1987804652299
S.D.12.0558614694676
T-STAT1.17774913897190
p-value0.29189598563616
Lambda-13.1987804652299

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -61.3532992021266 \tabularnewline
beta & 14.1987804652299 \tabularnewline
S.D. & 12.0558614694676 \tabularnewline
T-STAT & 1.17774913897190 \tabularnewline
p-value & 0.29189598563616 \tabularnewline
Lambda & -13.1987804652299 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13070&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-61.3532992021266[/C][/ROW]
[ROW][C]beta[/C][C]14.1987804652299[/C][/ROW]
[ROW][C]S.D.[/C][C]12.0558614694676[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.17774913897190[/C][/ROW]
[ROW][C]p-value[/C][C]0.29189598563616[/C][/ROW]
[ROW][C]Lambda[/C][C]-13.1987804652299[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13070&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13070&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-61.3532992021266
beta14.1987804652299
S.D.12.0558614694676
T-STAT1.17774913897190
p-value0.29189598563616
Lambda-13.1987804652299


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')