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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 computationMon, 02 Dec 2013 08:46:18 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Dec/02/t1385992091i9r8xx5bxc5swnf.htm/, Retrieved Fri, 19 Apr 2024 09:56:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=229998, Retrieved Fri, 19 Apr 2024 09:56:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact68

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] [] [2013-12-02 13:46:18] [3d308039bd6152c26e5d01eb1ba12dd8] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
104.4
104.4
104.4
104.4
104.4
104.41
104.42
104.68
106.02
106.35
106.38
106.47
106.5
106.56
113.07
116.26
118
118.02
118.04
118.12
118.12
118.17
118.22
118.22
118.23
118.23
118.23
119.94
120.88
121.14
121.16
121.2
121.2
121.2
121.2
121.2
121.22
121.22
121.95
123.05
123.44
123.65
123.79
123.87
123.91
123.94
124.28
126.28
126.68
126.69
126.69
126.99
128.79
128.84
128.95
128.97
128.97
128.97
128.97
128.97
128.97
128.98
128.99
129.07
129.76
130.47
130.76
130.88
131.04
131.06
131.13
131.15
131.16
131.33
131.42
131.86
134.39
135.59
136.01
136.14
136.74
136.89
136.82
136.82

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'Gwilym Jenkins' @ jenkins.wessa.net

\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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=229998&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=229998&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=229998&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'Gwilym Jenkins' @ jenkins.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1105.0608333333330.9278857525024092.06999999999999
2115.6083333333334.4921321791718811.72
3120.31751.307747021685492.97
4123.3833333333331.407256087913535.06
5128.2066666666671.07106008093372.28999999999999
6130.1883333333330.9532607516341272.18000000000001
7134.59752.434801186582145.72999999999999

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 105.060833333333 & 0.927885752502409 & 2.06999999999999 \tabularnewline
2 & 115.608333333333 & 4.49213217917188 & 11.72 \tabularnewline
3 & 120.3175 & 1.30774702168549 & 2.97 \tabularnewline
4 & 123.383333333333 & 1.40725608791353 & 5.06 \tabularnewline
5 & 128.206666666667 & 1.0710600809337 & 2.28999999999999 \tabularnewline
6 & 130.188333333333 & 0.953260751634127 & 2.18000000000001 \tabularnewline
7 & 134.5975 & 2.43480118658214 & 5.72999999999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=229998&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]105.060833333333[/C][C]0.927885752502409[/C][C]2.06999999999999[/C][/ROW]
[ROW][C]2[/C][C]115.608333333333[/C][C]4.49213217917188[/C][C]11.72[/C][/ROW]
[ROW][C]3[/C][C]120.3175[/C][C]1.30774702168549[/C][C]2.97[/C][/ROW]
[ROW][C]4[/C][C]123.383333333333[/C][C]1.40725608791353[/C][C]5.06[/C][/ROW]
[ROW][C]5[/C][C]128.206666666667[/C][C]1.0710600809337[/C][C]2.28999999999999[/C][/ROW]
[ROW][C]6[/C][C]130.188333333333[/C][C]0.953260751634127[/C][C]2.18000000000001[/C][/ROW]
[ROW][C]7[/C][C]134.5975[/C][C]2.43480118658214[/C][C]5.72999999999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=229998&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=229998&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
1105.0608333333330.9278857525024092.06999999999999
2115.6083333333334.4921321791718811.72
3120.31751.307747021685492.97
4123.3833333333331.407256087913535.06
5128.2066666666671.07106008093372.28999999999999
6130.1883333333330.9532607516341272.18000000000001
7134.59752.434801186582145.72999999999999






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha2.95307129465095
beta-0.00942116782823299
S.D.0.0579772361204
T-STAT-0.162497705283299
p-value0.877276996514439

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 2.95307129465095 \tabularnewline
beta & -0.00942116782823299 \tabularnewline
S.D. & 0.0579772361204 \tabularnewline
T-STAT & -0.162497705283299 \tabularnewline
p-value & 0.877276996514439 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=229998&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.95307129465095[/C][/ROW]
[ROW][C]beta[/C][C]-0.00942116782823299[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0579772361204[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.162497705283299[/C][/ROW]
[ROW][C]p-value[/C][C]0.877276996514439[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=229998&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=229998&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)
alpha2.95307129465095
beta-0.00942116782823299
S.D.0.0579772361204
T-STAT-0.162497705283299
p-value0.877276996514439






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.33221539774857
beta0.364904109357026
S.D.3.09233148333778
T-STAT0.118002908589592
p-value0.910659282728742
Lambda0.635095890642974

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.33221539774857 \tabularnewline
beta & 0.364904109357026 \tabularnewline
S.D. & 3.09233148333778 \tabularnewline
T-STAT & 0.118002908589592 \tabularnewline
p-value & 0.910659282728742 \tabularnewline
Lambda & 0.635095890642974 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=229998&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.33221539774857[/C][/ROW]
[ROW][C]beta[/C][C]0.364904109357026[/C][/ROW]
[ROW][C]S.D.[/C][C]3.09233148333778[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.118002908589592[/C][/ROW]
[ROW][C]p-value[/C][C]0.910659282728742[/C][/ROW]
[ROW][C]Lambda[/C][C]0.635095890642974[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=229998&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=229998&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-1.33221539774857
beta0.364904109357026
S.D.3.09233148333778
T-STAT0.118002908589592
p-value0.910659282728742
Lambda0.635095890642974


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 <- '12'
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')