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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 computationSun, 12 Jan 2014 06:37:57 -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/2014/Jan/12/t13895268864qr017f8omo3jg0.htm/, Retrieved Sun, 19 May 2024 06:07:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232980, Retrieved Sun, 19 May 2024 06:07:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact116

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] [] [2014-01-12 11:37:57] [62a6597007cd6653b71a687b26797f80] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
103,43
103,49
103,5
103,5
103,5
103,5
103,54
103,71
103,76
103,76
103,76
103,82
105,11
105,58
105,91
105,92
105,92
105,92
105,96
105,98
105,98
105,98
106,01
106,01
106,91
107,11
107,18
107,2
107,35
107,35
107,35
107,52
107,56
107,55
107,6
107,6
110,04
110,27
110,33
110,33
110,33
110,33
110,33
110,35
110,38
110,54
110,54
110,54
110,54
106,74
106,78
106,75
106,75
106,75
106,82
107,08
107,25
107,28
107,28
107,28
108,44
109,33
109,44
109,44
109,45
109,45
109,45
109,45
109,46
109,46
109,46
109,46
110,95
110,95
110,95
110,95
110,95
110,95
110,95
110,95
110,97
110,97
110,97
111

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'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232980&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232980&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232980&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'Gertrude Mary Cox' @ cox.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1103.6058333333330.1418999861191180.389999999999986
2105.8566666666670.261510762279260.900000000000006
3107.3566666666670.221578360173030.689999999999998
4110.3591666666670.1390525298605040.5
5107.2751.055896861354453.80000000000001
6109.35750.2911458553558841.02
7110.9591666666670.01564279289950890.0499999999999972

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 103.605833333333 & 0.141899986119118 & 0.389999999999986 \tabularnewline
2 & 105.856666666667 & 0.26151076227926 & 0.900000000000006 \tabularnewline
3 & 107.356666666667 & 0.22157836017303 & 0.689999999999998 \tabularnewline
4 & 110.359166666667 & 0.139052529860504 & 0.5 \tabularnewline
5 & 107.275 & 1.05589686135445 & 3.80000000000001 \tabularnewline
6 & 109.3575 & 0.291145855355884 & 1.02 \tabularnewline
7 & 110.959166666667 & 0.0156427928995089 & 0.0499999999999972 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232980&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]103.605833333333[/C][C]0.141899986119118[/C][C]0.389999999999986[/C][/ROW]
[ROW][C]2[/C][C]105.856666666667[/C][C]0.26151076227926[/C][C]0.900000000000006[/C][/ROW]
[ROW][C]3[/C][C]107.356666666667[/C][C]0.22157836017303[/C][C]0.689999999999998[/C][/ROW]
[ROW][C]4[/C][C]110.359166666667[/C][C]0.139052529860504[/C][C]0.5[/C][/ROW]
[ROW][C]5[/C][C]107.275[/C][C]1.05589686135445[/C][C]3.80000000000001[/C][/ROW]
[ROW][C]6[/C][C]109.3575[/C][C]0.291145855355884[/C][C]1.02[/C][/ROW]
[ROW][C]7[/C][C]110.959166666667[/C][C]0.0156427928995089[/C][C]0.0499999999999972[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232980&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232980&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
1103.6058333333330.1418999861191180.389999999999986
2105.8566666666670.261510762279260.900000000000006
3107.3566666666670.221578360173030.689999999999998
4110.3591666666670.1390525298605040.5
5107.2751.055896861354453.80000000000001
6109.35750.2911458553558841.02
7110.9591666666670.01564279289950890.0499999999999972






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha2.81193129205385
beta-0.0232611151693035
S.D.0.0581084876633587
T-STAT-0.4003049486344
p-value0.705462484629456

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 2.81193129205385 \tabularnewline
beta & -0.0232611151693035 \tabularnewline
S.D. & 0.0581084876633587 \tabularnewline
T-STAT & -0.4003049486344 \tabularnewline
p-value & 0.705462484629456 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232980&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.81193129205385[/C][/ROW]
[ROW][C]beta[/C][C]-0.0232611151693035[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0581084876633587[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.4003049486344[/C][/ROW]
[ROW][C]p-value[/C][C]0.705462484629456[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232980&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232980&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)
alpha2.81193129205385
beta-0.0232611151693035
S.D.0.0581084876633587
T-STAT-0.4003049486344
p-value0.705462484629456






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha99.5911387604474
beta-21.648688106479
S.D.21.2360536546416
T-STAT-1.01943084428717
p-value0.354763097919884
Lambda22.648688106479

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 99.5911387604474 \tabularnewline
beta & -21.648688106479 \tabularnewline
S.D. & 21.2360536546416 \tabularnewline
T-STAT & -1.01943084428717 \tabularnewline
p-value & 0.354763097919884 \tabularnewline
Lambda & 22.648688106479 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232980&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]99.5911387604474[/C][/ROW]
[ROW][C]beta[/C][C]-21.648688106479[/C][/ROW]
[ROW][C]S.D.[/C][C]21.2360536546416[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.01943084428717[/C][/ROW]
[ROW][C]p-value[/C][C]0.354763097919884[/C][/ROW]
[ROW][C]Lambda[/C][C]22.648688106479[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232980&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232980&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)
alpha99.5911387604474
beta-21.648688106479
S.D.21.2360536546416
T-STAT-1.01943084428717
p-value0.354763097919884
Lambda22.648688106479


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')