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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 computationTue, 13 May 2008 11:47:40 -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/13/t1210700990fsqghjvddsyfrex.htm/, Retrieved Sun, 19 May 2024 17:02:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=12501, Retrieved Sun, 19 May 2024 17:02:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact239

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] [sdp - mean plot k...] [2008-05-13 17:47:40] [303435f2616c8b7fa1931e576f2293ac] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
20.18
20.19
20.3
20.47
20.47
20.46
20.46
20.46
20.52
20.64
20.65
20.66
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
22.06
22.03
22.05
22.05
22.06
22.06
22.13
22.06
22.25
22.28
22.18

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=12501&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=12501&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12501&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
120.4550.1620605947281330.48
220.72416666666670.04100073909163810.120000000000001
320.86916666666670.05299371031861510.169999999999998
421.14916666666670.09577040094397490.270000000000000
521.42666666666670.1050829398257600.32
621.55833333333330.02855085839605450.0700000000000003
721.87666666666670.1314488032611470.41
822.10166666666670.08871131252380940.270000000000000

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 20.455 & 0.162060594728133 & 0.48 \tabularnewline
2 & 20.7241666666667 & 0.0410007390916381 & 0.120000000000001 \tabularnewline
3 & 20.8691666666667 & 0.0529937103186151 & 0.169999999999998 \tabularnewline
4 & 21.1491666666667 & 0.0957704009439749 & 0.270000000000000 \tabularnewline
5 & 21.4266666666667 & 0.105082939825760 & 0.32 \tabularnewline
6 & 21.5583333333333 & 0.0285508583960545 & 0.0700000000000003 \tabularnewline
7 & 21.8766666666667 & 0.131448803261147 & 0.41 \tabularnewline
8 & 22.1016666666667 & 0.0887113125238094 & 0.270000000000000 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12501&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]20.455[/C][C]0.162060594728133[/C][C]0.48[/C][/ROW]
[ROW][C]2[/C][C]20.7241666666667[/C][C]0.0410007390916381[/C][C]0.120000000000001[/C][/ROW]
[ROW][C]3[/C][C]20.8691666666667[/C][C]0.0529937103186151[/C][C]0.169999999999998[/C][/ROW]
[ROW][C]4[/C][C]21.1491666666667[/C][C]0.0957704009439749[/C][C]0.270000000000000[/C][/ROW]
[ROW][C]5[/C][C]21.4266666666667[/C][C]0.105082939825760[/C][C]0.32[/C][/ROW]
[ROW][C]6[/C][C]21.5583333333333[/C][C]0.0285508583960545[/C][C]0.0700000000000003[/C][/ROW]
[ROW][C]7[/C][C]21.8766666666667[/C][C]0.131448803261147[/C][C]0.41[/C][/ROW]
[ROW][C]8[/C][C]22.1016666666667[/C][C]0.0887113125238094[/C][C]0.270000000000000[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12501&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12501&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
120.4550.1620605947281330.48
220.72416666666670.04100073909163810.120000000000001
320.86916666666670.05299371031861510.169999999999998
421.14916666666670.09577040094397490.270000000000000
521.42666666666670.1050829398257600.32
621.55833333333330.02855085839605450.0700000000000003
721.87666666666670.1314488032611470.41
822.10166666666670.08871131252380940.270000000000000






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.172434425008346
beta-0.00396011248756404
S.D.0.0325564372603491
T-STAT-0.121638386162945
p-value0.907156993167881

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.172434425008346 \tabularnewline
beta & -0.00396011248756404 \tabularnewline
S.D. & 0.0325564372603491 \tabularnewline
T-STAT & -0.121638386162945 \tabularnewline
p-value & 0.907156993167881 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12501&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.172434425008346[/C][/ROW]
[ROW][C]beta[/C][C]-0.00396011248756404[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0325564372603491[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.121638386162945[/C][/ROW]
[ROW][C]p-value[/C][C]0.907156993167881[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12501&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12501&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)
alpha0.172434425008346
beta-0.00396011248756404
S.D.0.0325564372603491
T-STAT-0.121638386162945
p-value0.907156993167881






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-4.10280109575566
beta0.501494892908931
S.D.9.08752467818155
T-STAT0.0551849827833736
p-value0.957782794015004
Lambda0.498505107091069

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -4.10280109575566 \tabularnewline
beta & 0.501494892908931 \tabularnewline
S.D. & 9.08752467818155 \tabularnewline
T-STAT & 0.0551849827833736 \tabularnewline
p-value & 0.957782794015004 \tabularnewline
Lambda & 0.498505107091069 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12501&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.10280109575566[/C][/ROW]
[ROW][C]beta[/C][C]0.501494892908931[/C][/ROW]
[ROW][C]S.D.[/C][C]9.08752467818155[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.0551849827833736[/C][/ROW]
[ROW][C]p-value[/C][C]0.957782794015004[/C][/ROW]
[ROW][C]Lambda[/C][C]0.498505107091069[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12501&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12501&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-4.10280109575566
beta0.501494892908931
S.D.9.08752467818155
T-STAT0.0551849827833736
p-value0.957782794015004
Lambda0.498505107091069


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')