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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, 20 May 2008 02:48:23 -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/20/t1211273423e7aeqb9k41z17lo.htm/, Retrieved Tue, 14 May 2024 22:31:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=12949, Retrieved Tue, 14 May 2024 22:31:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsstandard deviation mean plot
Estimated Impact219

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] [Tinneke Hermans -...] [2008-05-20 08:48:23] [f67a51b398175e73046faa38adf770f9] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4.07
4.08
4.09
4.08
4.09
4.12
4.14
4.14
4.14
4.14
4.14
4.23
4.29
4.32
4.33
4.35
4.35
4.35
4.35
4.36
4.36
4.38
4.4
4.4
4.4
4.43
4.44
4.46
4.47
4.49
4.49
4.57
4.62
4.64
4.66
4.67
4.68
4.72
4.74
4.75
4.76
4.77
4.76
4.77
4.77
4.78
4.81
4.81
4.85
4.92
4.96
4.95
4.96
4.97
5
5
5.01
5.01
5.02
5.04
5.04
5.19
5.22
5.22
5.22
5.24
5.28
5.34
5.36
5.38
5.39
5.41
5.44
5.51
5.55
5.56
5.57
5.58
5.58
5.59
5.61
5.63
5.64
5.64

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=12949&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=12949&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12949&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
14.121666666666670.04427873147015460.16
24.353333333333330.03143053909621650.110000000000000
34.528333333333330.09768533279067150.270000000000000
44.760.03592922335521720.13
54.974166666666670.05195423393952050.190000000000000
65.274166666666670.1073192631470430.37
75.5750.05744562646538020.199999999999999

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 4.12166666666667 & 0.0442787314701546 & 0.16 \tabularnewline
2 & 4.35333333333333 & 0.0314305390962165 & 0.110000000000000 \tabularnewline
3 & 4.52833333333333 & 0.0976853327906715 & 0.270000000000000 \tabularnewline
4 & 4.76 & 0.0359292233552172 & 0.13 \tabularnewline
5 & 4.97416666666667 & 0.0519542339395205 & 0.190000000000000 \tabularnewline
6 & 5.27416666666667 & 0.107319263147043 & 0.37 \tabularnewline
7 & 5.575 & 0.0574456264653802 & 0.199999999999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12949&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]4.12166666666667[/C][C]0.0442787314701546[/C][C]0.16[/C][/ROW]
[ROW][C]2[/C][C]4.35333333333333[/C][C]0.0314305390962165[/C][C]0.110000000000000[/C][/ROW]
[ROW][C]3[/C][C]4.52833333333333[/C][C]0.0976853327906715[/C][C]0.270000000000000[/C][/ROW]
[ROW][C]4[/C][C]4.76[/C][C]0.0359292233552172[/C][C]0.13[/C][/ROW]
[ROW][C]5[/C][C]4.97416666666667[/C][C]0.0519542339395205[/C][C]0.190000000000000[/C][/ROW]
[ROW][C]6[/C][C]5.27416666666667[/C][C]0.107319263147043[/C][C]0.37[/C][/ROW]
[ROW][C]7[/C][C]5.575[/C][C]0.0574456264653802[/C][C]0.199999999999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12949&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12949&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
14.121666666666670.04427873147015460.16
24.353333333333330.03143053909621650.110000000000000
34.528333333333330.09768533279067150.270000000000000
44.760.03592922335521720.13
54.974166666666670.05195423393952050.190000000000000
65.274166666666670.1073192631470430.37
75.5750.05744562646538020.199999999999999






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.0393263182878455
beta0.0208811188451505
S.D.0.0242421778647793
T-STAT0.861354906379432
p-value0.428407416173944

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.0393263182878455 \tabularnewline
beta & 0.0208811188451505 \tabularnewline
S.D. & 0.0242421778647793 \tabularnewline
T-STAT & 0.861354906379432 \tabularnewline
p-value & 0.428407416173944 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12949&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.0393263182878455[/C][/ROW]
[ROW][C]beta[/C][C]0.0208811188451505[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0242421778647793[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.861354906379432[/C][/ROW]
[ROW][C]p-value[/C][C]0.428407416173944[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12949&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12949&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-0.0393263182878455
beta0.0208811188451505
S.D.0.0242421778647793
T-STAT0.861354906379432
p-value0.428407416173944






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-5.75521164151775
beta1.82860982050323
S.D.1.7863035810773
T-STAT1.02368367833670
p-value0.352934704015798
Lambda-0.828609820503228

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -5.75521164151775 \tabularnewline
beta & 1.82860982050323 \tabularnewline
S.D. & 1.7863035810773 \tabularnewline
T-STAT & 1.02368367833670 \tabularnewline
p-value & 0.352934704015798 \tabularnewline
Lambda & -0.828609820503228 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12949&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-5.75521164151775[/C][/ROW]
[ROW][C]beta[/C][C]1.82860982050323[/C][/ROW]
[ROW][C]S.D.[/C][C]1.7863035810773[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.02368367833670[/C][/ROW]
[ROW][C]p-value[/C][C]0.352934704015798[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.828609820503228[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12949&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12949&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-5.75521164151775
beta1.82860982050323
S.D.1.7863035810773
T-STAT1.02368367833670
p-value0.352934704015798
Lambda-0.828609820503228


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')