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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, 17 May 2008 15:16:15 -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/17/t1211059265o9z5f2i5r6bmet7.htm/, Retrieved Tue, 14 May 2024 01:54:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=12706, Retrieved Tue, 14 May 2024 01:54:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact187

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...] [2008-05-17 21:16:15] [b64702de7eac3a2282df81a39c87ddc7] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
20.66
20.66
20.67
20.71
20.73
20.73
20.74
20.74
20.75
20.75
20.77
20.78
20.78
20.8
20.84
20.85
20.86
20.86
20.86
20.86
20.9
20.92
20.95
20.95
20.95
20.96
21.1
21.18
21.19
21.19
21.19
21.19
21.19
21.21
21.22
21.22
21.22
21.23
21.41
21.42
21.43
21.44
21.44
21.44
21.48
21.53
21.54
21.54
21.54
21.54
21.54
21.54
21.54
21.54
21.54
21.54
21.57
21.6
21.61
21.6
21.6
21.71
21.75
21.84
21.85
21.92
21.92
21.93
22
22
21.99
22.01
22.01

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 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=12706&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]3 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=12706&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12706&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
120.72416666666670.04100073909163810.120000000000001
220.86916666666670.05299371031861510.169999999999998
321.14916666666670.09577040094397490.270000000000000
421.42666666666670.1050829398257600.32
521.55833333333330.02855085839605450.0700000000000003
621.87666666666670.1314488032611470.41

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 20.7241666666667 & 0.0410007390916381 & 0.120000000000001 \tabularnewline
2 & 20.8691666666667 & 0.0529937103186151 & 0.169999999999998 \tabularnewline
3 & 21.1491666666667 & 0.0957704009439749 & 0.270000000000000 \tabularnewline
4 & 21.4266666666667 & 0.105082939825760 & 0.32 \tabularnewline
5 & 21.5583333333333 & 0.0285508583960545 & 0.0700000000000003 \tabularnewline
6 & 21.8766666666667 & 0.131448803261147 & 0.41 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12706&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]20.7241666666667[/C][C]0.0410007390916381[/C][C]0.120000000000001[/C][/ROW]
[ROW][C]2[/C][C]20.8691666666667[/C][C]0.0529937103186151[/C][C]0.169999999999998[/C][/ROW]
[ROW][C]3[/C][C]21.1491666666667[/C][C]0.0957704009439749[/C][C]0.270000000000000[/C][/ROW]
[ROW][C]4[/C][C]21.4266666666667[/C][C]0.105082939825760[/C][C]0.32[/C][/ROW]
[ROW][C]5[/C][C]21.5583333333333[/C][C]0.0285508583960545[/C][C]0.0700000000000003[/C][/ROW]
[ROW][C]6[/C][C]21.8766666666667[/C][C]0.131448803261147[/C][C]0.41[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12706&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12706&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
120.72416666666670.04100073909163810.120000000000001
220.86916666666670.05299371031861510.169999999999998
321.14916666666670.09577040094397490.270000000000000
421.42666666666670.1050829398257600.32
521.55833333333330.02855085839605450.0700000000000003
621.87666666666670.1314488032611470.41






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-1.05487353751311
beta0.0531651031007283
S.D.0.0385297609560882
T-STAT1.37984513221662
p-value0.239745021888156

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -1.05487353751311 \tabularnewline
beta & 0.0531651031007283 \tabularnewline
S.D. & 0.0385297609560882 \tabularnewline
T-STAT & 1.37984513221662 \tabularnewline
p-value & 0.239745021888156 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12706&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.05487353751311[/C][/ROW]
[ROW][C]beta[/C][C]0.0531651031007283[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0385297609560882[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.37984513221662[/C][/ROW]
[ROW][C]p-value[/C][C]0.239745021888156[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12706&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12706&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-1.05487353751311
beta0.0531651031007283
S.D.0.0385297609560882
T-STAT1.37984513221662
p-value0.239745021888156






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-40.5486142081915
beta12.3746598183344
S.D.13.3123818067933
T-STAT0.929560164208903
p-value0.405216888642434
Lambda-11.3746598183344

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -40.5486142081915 \tabularnewline
beta & 12.3746598183344 \tabularnewline
S.D. & 13.3123818067933 \tabularnewline
T-STAT & 0.929560164208903 \tabularnewline
p-value & 0.405216888642434 \tabularnewline
Lambda & -11.3746598183344 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12706&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-40.5486142081915[/C][/ROW]
[ROW][C]beta[/C][C]12.3746598183344[/C][/ROW]
[ROW][C]S.D.[/C][C]13.3123818067933[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.929560164208903[/C][/ROW]
[ROW][C]p-value[/C][C]0.405216888642434[/C][/ROW]
[ROW][C]Lambda[/C][C]-11.3746598183344[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12706&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12706&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-40.5486142081915
beta12.3746598183344
S.D.13.3123818067933
T-STAT0.929560164208903
p-value0.405216888642434
Lambda-11.3746598183344


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')