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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 computationThu, 15 Jan 2009 11:50:44 -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/2009/Jan/15/t1232045471wgn9zprhe4dmsey.htm/, Retrieved Tue, 07 May 2024 10:40:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36897, Retrieved Tue, 07 May 2024 10:40:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact222

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] [Opgave 8-Oefening...] [2009-01-06 20:46:46] [ca4e42c3236d1c0cb4de680f9dd82ba0]
-   P     [Standard Deviation-Mean Plot] [Opgave 8-Oefening...] [2009-01-15 18:50:44] [59eb7d50a05a673a4523845c066501a9] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
101.6
101.8
102.1
102.1
101.9
102.1
102
102.1
102.2
102.3
102.7
102.8
103.1
103.1
103.3
103.5
103.3
103.5
103.8
103.9
103.9
104.2
104.6
104.9
105.2
105.2
105.6
105.6
106.2
106.3
106.4
106.9
107.2
107.3
107.3
107.4
107.55
107.87
108.37
108.38
107.92
108.03
108.14
108.3
108.64
108.66
109.04
109.03
109.03
109.54
109.75
109.83
109.65
109.82
109.95
110.12
110.15
110.2
109.99
110.14
110.14
110.81
110.97
110.99
109.73
109.81
110.02
110.18
110.21
110.25
110.36
110.51
110.64
110.95
111.18
111.19
111.69
111.7
111.83
111.77
111.73
112.01
111.86
112.04

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=36897&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=36897&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36897&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
1102.1416666666670.3396745322787511.20000000000000
2103.7583333333330.5775470596069281.80000000000001
3106.3833333333330.8375650133065212.20000000000000
4108.32750.4590726819063931.49000000000001
5109.84750.3328697533980411.17000000000000
6110.3316666666670.417216606776021.25999999999999
7111.5491666666670.4475886572072691.40000000000001

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 102.141666666667 & 0.339674532278751 & 1.20000000000000 \tabularnewline
2 & 103.758333333333 & 0.577547059606928 & 1.80000000000001 \tabularnewline
3 & 106.383333333333 & 0.837565013306521 & 2.20000000000000 \tabularnewline
4 & 108.3275 & 0.459072681906393 & 1.49000000000001 \tabularnewline
5 & 109.8475 & 0.332869753398041 & 1.17000000000000 \tabularnewline
6 & 110.331666666667 & 0.41721660677602 & 1.25999999999999 \tabularnewline
7 & 111.549166666667 & 0.447588657207269 & 1.40000000000001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36897&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]102.141666666667[/C][C]0.339674532278751[/C][C]1.20000000000000[/C][/ROW]
[ROW][C]2[/C][C]103.758333333333[/C][C]0.577547059606928[/C][C]1.80000000000001[/C][/ROW]
[ROW][C]3[/C][C]106.383333333333[/C][C]0.837565013306521[/C][C]2.20000000000000[/C][/ROW]
[ROW][C]4[/C][C]108.3275[/C][C]0.459072681906393[/C][C]1.49000000000001[/C][/ROW]
[ROW][C]5[/C][C]109.8475[/C][C]0.332869753398041[/C][C]1.17000000000000[/C][/ROW]
[ROW][C]6[/C][C]110.331666666667[/C][C]0.41721660677602[/C][C]1.25999999999999[/C][/ROW]
[ROW][C]7[/C][C]111.549166666667[/C][C]0.447588657207269[/C][C]1.40000000000001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36897&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36897&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
1102.1416666666670.3396745322787511.20000000000000
2103.7583333333330.5775470596069281.80000000000001
3106.3833333333330.8375650133065212.20000000000000
4108.32750.4590726819063931.49000000000001
5109.84750.3328697533980411.17000000000000
6110.3316666666670.417216606776021.25999999999999
7111.5491666666670.4475886572072691.40000000000001






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha1.47169125483320
beta-0.0091585082694562
S.D.0.0218198390995092
T-STAT-0.41973307995943
p-value0.692105686126182

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.47169125483320 \tabularnewline
beta & -0.0091585082694562 \tabularnewline
S.D. & 0.0218198390995092 \tabularnewline
T-STAT & -0.41973307995943 \tabularnewline
p-value & 0.692105686126182 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36897&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.47169125483320[/C][/ROW]
[ROW][C]beta[/C][C]-0.0091585082694562[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0218198390995092[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.41973307995943[/C][/ROW]
[ROW][C]p-value[/C][C]0.692105686126182[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36897&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36897&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)
alpha1.47169125483320
beta-0.0091585082694562
S.D.0.0218198390995092
T-STAT-0.41973307995943
p-value0.692105686126182






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha5.89335191013362
beta-1.42392588092272
S.D.4.295686874911
T-STAT-0.331478043532263
p-value0.75372573394922
Lambda2.42392588092272

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 5.89335191013362 \tabularnewline
beta & -1.42392588092272 \tabularnewline
S.D. & 4.295686874911 \tabularnewline
T-STAT & -0.331478043532263 \tabularnewline
p-value & 0.75372573394922 \tabularnewline
Lambda & 2.42392588092272 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36897&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]5.89335191013362[/C][/ROW]
[ROW][C]beta[/C][C]-1.42392588092272[/C][/ROW]
[ROW][C]S.D.[/C][C]4.295686874911[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.331478043532263[/C][/ROW]
[ROW][C]p-value[/C][C]0.75372573394922[/C][/ROW]
[ROW][C]Lambda[/C][C]2.42392588092272[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36897&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36897&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)
alpha5.89335191013362
beta-1.42392588092272
S.D.4.295686874911
T-STAT-0.331478043532263
p-value0.75372573394922
Lambda2.42392588092272


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')