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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 computationFri, 30 May 2008 03:37:02 -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/30/t1212140344q7mu1ftx2p1og9q.htm/, Retrieved Tue, 14 May 2024 08:14:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13527, Retrieved Tue, 14 May 2024 08:14:55 +0000
QR Codes:

Original text written by user:Sorry maar werkte op die moment niet ! vandaar de late blog
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact235

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...] [2008-05-12 08:59:13] [991bb66222c59d3452b479d72b2552fb]
-   PD    [Standard Deviation-Mean Plot] [standard deviatio...] [2008-05-30 09:37:02] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
104.7
104.7
104.7
104.7
106
107
107
107
107
107
107
107
107
107
107
107
107.6
109.9
109.9
109.9
109.9
109.9
109.9
109.9
109.9
109.9
109.9
109.9
110.6
114.3
114.3
114.3
114.3
114.3
114.3
114.3
114.3
114.3
114.3
114.3
114.3
119.01
119.01
119.01
119.01
119.01
119.01
119.01
119.01
119.01
119.01
119.01
121.27
123.54
123.54
123.54
123.54
123.54
123.54
123.54
123.54
123.54
123.54
123.54
123.54
125.24
125.24
125.24
125.24
125.24
125.24
125.24
125.24
125.24
125.24
125.24
125.24
128.35
128.35
128.35
128.35
128.35
128.35
128.35

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=13527&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=13527&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13527&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
1106.151.107413037833512.30000000000000
2108.7416666666671.440617502281162.90000000000001
3112.5252.201703885630404.39999999999999
4117.04752.425313944064304.71000000000001
5121.8408333333332.18653922623834.53
6124.5316666666670.8753787059255371.69999999999999
7127.0541666666671.60142810319323.11

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 106.15 & 1.10741303783351 & 2.30000000000000 \tabularnewline
2 & 108.741666666667 & 1.44061750228116 & 2.90000000000001 \tabularnewline
3 & 112.525 & 2.20170388563040 & 4.39999999999999 \tabularnewline
4 & 117.0475 & 2.42531394406430 & 4.71000000000001 \tabularnewline
5 & 121.840833333333 & 2.1865392262383 & 4.53 \tabularnewline
6 & 124.531666666667 & 0.875378705925537 & 1.69999999999999 \tabularnewline
7 & 127.054166666667 & 1.6014281031932 & 3.11 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13527&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]106.15[/C][C]1.10741303783351[/C][C]2.30000000000000[/C][/ROW]
[ROW][C]2[/C][C]108.741666666667[/C][C]1.44061750228116[/C][C]2.90000000000001[/C][/ROW]
[ROW][C]3[/C][C]112.525[/C][C]2.20170388563040[/C][C]4.39999999999999[/C][/ROW]
[ROW][C]4[/C][C]117.0475[/C][C]2.42531394406430[/C][C]4.71000000000001[/C][/ROW]
[ROW][C]5[/C][C]121.840833333333[/C][C]2.1865392262383[/C][C]4.53[/C][/ROW]
[ROW][C]6[/C][C]124.531666666667[/C][C]0.875378705925537[/C][C]1.69999999999999[/C][/ROW]
[ROW][C]7[/C][C]127.054166666667[/C][C]1.6014281031932[/C][C]3.11[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13527&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13527&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
1106.151.107413037833512.30000000000000
2108.7416666666671.440617502281162.90000000000001
3112.5252.201703885630404.39999999999999
4117.04752.425313944064304.71000000000001
5121.8408333333332.18653922623834.53
6124.5316666666670.8753787059255371.69999999999999
7127.0541666666671.60142810319323.11






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha1.23695256058818
beta0.00388771502437565
S.D.0.0330699534467175
T-STAT0.117560341614619
p-value0.910992504220597

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.23695256058818 \tabularnewline
beta & 0.00388771502437565 \tabularnewline
S.D. & 0.0330699534467175 \tabularnewline
T-STAT & 0.117560341614619 \tabularnewline
p-value & 0.910992504220597 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13527&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.23695256058818[/C][/ROW]
[ROW][C]beta[/C][C]0.00388771502437565[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0330699534467175[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.117560341614619[/C][/ROW]
[ROW][C]p-value[/C][C]0.910992504220597[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13527&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13527&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)
alpha1.23695256058818
beta0.00388771502437565
S.D.0.0330699534467175
T-STAT0.117560341614619
p-value0.910992504220597






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-0.570254736378933
beta0.21776855888794
S.D.2.48224097588045
T-STAT0.087730627688433
p-value0.933496073806501
Lambda0.78223144111206

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -0.570254736378933 \tabularnewline
beta & 0.21776855888794 \tabularnewline
S.D. & 2.48224097588045 \tabularnewline
T-STAT & 0.087730627688433 \tabularnewline
p-value & 0.933496073806501 \tabularnewline
Lambda & 0.78223144111206 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13527&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.570254736378933[/C][/ROW]
[ROW][C]beta[/C][C]0.21776855888794[/C][/ROW]
[ROW][C]S.D.[/C][C]2.48224097588045[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.087730627688433[/C][/ROW]
[ROW][C]p-value[/C][C]0.933496073806501[/C][/ROW]
[ROW][C]Lambda[/C][C]0.78223144111206[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13527&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13527&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-0.570254736378933
beta0.21776855888794
S.D.2.48224097588045
T-STAT0.087730627688433
p-value0.933496073806501
Lambda0.78223144111206


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')