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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, 16 Dec 2008 13:59:02 -0700
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/Dec/16/t1229461223rxq6qh0w56anr1e.htm/, Retrieved Thu, 16 May 2024 01:26:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=34201, Retrieved Thu, 16 May 2024 01:26:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact169

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] [TAAK] [2008-12-16 20:59:02] [59094f58b9d90d3694e930ebd2901ecd] [Current]
-    D    [Standard Deviation-Mean Plot] [TAAK] [2008-12-17 18:04:55] [74be16979710d4c4e7c6647856088456]
- RM D    [Variance Reduction Matrix] [TAAK] [2008-12-17 18:15:17] [f3161d5a04a14312cd010aa8f92941cc]
-    D      [Variance Reduction Matrix] [Taak] [2008-12-17 18:20:01] [f3161d5a04a14312cd010aa8f92941cc]
- RMPD      [(Partial) Autocorrelation Function] [Taak] [2008-12-17 18:25:12] [f3161d5a04a14312cd010aa8f92941cc]
-   P         [(Partial) Autocorrelation Function] [Taak] [2008-12-17 18:31:00] [f3161d5a04a14312cd010aa8f92941cc]
-   P           [(Partial) Autocorrelation Function] [Taak] [2008-12-17 18:33:23] [f3161d5a04a14312cd010aa8f92941cc]
-   PD          [(Partial) Autocorrelation Function] [Taak] [2008-12-17 18:43:02] [f3161d5a04a14312cd010aa8f92941cc]
-   P             [(Partial) Autocorrelation Function] [Taak] [2008-12-17 18:46:14] [f3161d5a04a14312cd010aa8f92941cc]
-   P               [(Partial) Autocorrelation Function] [Taak] [2008-12-17 18:47:42] [f3161d5a04a14312cd010aa8f92941cc]
- RMP               [Spectral Analysis] [Taak] [2008-12-17 18:53:33] [f3161d5a04a14312cd010aa8f92941cc]
-                     [Spectral Analysis] [Taak] [2008-12-17 18:55:19] [f3161d5a04a14312cd010aa8f92941cc]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
106.4
106.2
106.4
106.3
109.5
109.3
109.1
109
108.9
108.9
108.9
108.9
108.9
109
108.9
108.9
108.9
108.8
109.1
109.1
109.1
109.1
109.1
109.1
109.1
109.1
109.1
109.3
112.9
112
112.2
115.7
117.4
118.4
118.4
118.4
119
120.3
122.1
122.1
126.2
125.2
121.4
120.2
122.7
123.4
123.7
122
121.4
121.4
121.4
121.4
128.9
130.1
130.1
129.1
129.1
133.5
130.4
126.8
129.8
129.8
131
131.1
131.3
131.3
128.6
125.1
124.6
123.3
123.1
123.3
124.9

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34201&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34201&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34201&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1108.151.360815263662993.3
21090.1128152149635490.299999999999997
3113.53.955433547091219.30000000000001
4122.3583333333332.071213229588947.2
5126.9666666666674.3789441096172412.1
6127.6916666666673.493489615981388.20000000000002

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 108.15 & 1.36081526366299 & 3.3 \tabularnewline
2 & 109 & 0.112815214963549 & 0.299999999999997 \tabularnewline
3 & 113.5 & 3.95543354709121 & 9.30000000000001 \tabularnewline
4 & 122.358333333333 & 2.07121322958894 & 7.2 \tabularnewline
5 & 126.966666666667 & 4.37894410961724 & 12.1 \tabularnewline
6 & 127.691666666667 & 3.49348961598138 & 8.20000000000002 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34201&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]108.15[/C][C]1.36081526366299[/C][C]3.3[/C][/ROW]
[ROW][C]2[/C][C]109[/C][C]0.112815214963549[/C][C]0.299999999999997[/C][/ROW]
[ROW][C]3[/C][C]113.5[/C][C]3.95543354709121[/C][C]9.30000000000001[/C][/ROW]
[ROW][C]4[/C][C]122.358333333333[/C][C]2.07121322958894[/C][C]7.2[/C][/ROW]
[ROW][C]5[/C][C]126.966666666667[/C][C]4.37894410961724[/C][C]12.1[/C][/ROW]
[ROW][C]6[/C][C]127.691666666667[/C][C]3.49348961598138[/C][C]8.20000000000002[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34201&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34201&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
1108.151.360815263662993.3
21090.1128152149635490.299999999999997
3113.53.955433547091219.30000000000001
4122.3583333333332.071213229588947.2
5126.9666666666674.3789441096172412.1
6127.6916666666673.493489615981388.20000000000002






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-12.7343085159674
beta0.129691797564828
S.D.0.0678301523347683
T-STAT1.91200805395141
p-value0.12844836730121

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -12.7343085159674 \tabularnewline
beta & 0.129691797564828 \tabularnewline
S.D. & 0.0678301523347683 \tabularnewline
T-STAT & 1.91200805395141 \tabularnewline
p-value & 0.12844836730121 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34201&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-12.7343085159674[/C][/ROW]
[ROW][C]beta[/C][C]0.129691797564828[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0678301523347683[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.91200805395141[/C][/ROW]
[ROW][C]p-value[/C][C]0.12844836730121[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34201&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34201&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-12.7343085159674
beta0.129691797564828
S.D.0.0678301523347683
T-STAT1.91200805395141
p-value0.12844836730121






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-55.9213166109517
beta11.8321718036283
S.D.7.04285878955506
T-STAT1.68002400121610
p-value0.168250148364649
Lambda-10.8321718036283

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -55.9213166109517 \tabularnewline
beta & 11.8321718036283 \tabularnewline
S.D. & 7.04285878955506 \tabularnewline
T-STAT & 1.68002400121610 \tabularnewline
p-value & 0.168250148364649 \tabularnewline
Lambda & -10.8321718036283 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34201&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-55.9213166109517[/C][/ROW]
[ROW][C]beta[/C][C]11.8321718036283[/C][/ROW]
[ROW][C]S.D.[/C][C]7.04285878955506[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.68002400121610[/C][/ROW]
[ROW][C]p-value[/C][C]0.168250148364649[/C][/ROW]
[ROW][C]Lambda[/C][C]-10.8321718036283[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34201&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34201&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-55.9213166109517
beta11.8321718036283
S.D.7.04285878955506
T-STAT1.68002400121610
p-value0.168250148364649
Lambda-10.8321718036283


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')