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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, 19 May 2008 10:27:43 -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/19/t12112145675xexbhpzj9ra3lu.htm/, Retrieved Tue, 14 May 2024 02:45:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=12895, Retrieved Tue, 14 May 2024 02:45:18 +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] [BlueJeans Dames -...] [2008-05-19 16:27:43] [c804036083fecabefcdec45121c2ee7a] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
44.13
44.13
44.14
44.14
44.14
44.14
44.15
44.17
44.19
44.26
44.27
44.29
44.29
44.29
44.29
44.32
44.33
44.34
44.34
44.34
44.37
44.47
44.51
44.51
44.51
44.52
44.7
44.84
44.9
44.91
44.94
44.94
44.95
45.28
45.34
45.34
45.34
45.36
45.44
45.62
45.75
45.77
45.77
45.77
46.09
46.25
46.28
46.29
46.29
46.29
46.3
46.34
46.34
46.35
46.42
46.52
46.59
46.66
46.67
46.72
46.72
46.72
46.76
46.89
47.02
47.02
47.04
47.18
47.22
47.8
47.88
47.91

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12895&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12895&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12895&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
144.17916666666670.05961365513695520.159999999999997
244.36666666666670.08260897302498250.219999999999999
344.93083333333330.2805986565552420.830000000000005
445.81083333333330.3474702952204780.949999999999996
546.45750.1646000662763590.43
647.180.4434779896147351.19000000000000

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 44.1791666666667 & 0.0596136551369552 & 0.159999999999997 \tabularnewline
2 & 44.3666666666667 & 0.0826089730249825 & 0.219999999999999 \tabularnewline
3 & 44.9308333333333 & 0.280598656555242 & 0.830000000000005 \tabularnewline
4 & 45.8108333333333 & 0.347470295220478 & 0.949999999999996 \tabularnewline
5 & 46.4575 & 0.164600066276359 & 0.43 \tabularnewline
6 & 47.18 & 0.443477989614735 & 1.19000000000000 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12895&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]44.1791666666667[/C][C]0.0596136551369552[/C][C]0.159999999999997[/C][/ROW]
[ROW][C]2[/C][C]44.3666666666667[/C][C]0.0826089730249825[/C][C]0.219999999999999[/C][/ROW]
[ROW][C]3[/C][C]44.9308333333333[/C][C]0.280598656555242[/C][C]0.830000000000005[/C][/ROW]
[ROW][C]4[/C][C]45.8108333333333[/C][C]0.347470295220478[/C][C]0.949999999999996[/C][/ROW]
[ROW][C]5[/C][C]46.4575[/C][C]0.164600066276359[/C][C]0.43[/C][/ROW]
[ROW][C]6[/C][C]47.18[/C][C]0.443477989614735[/C][C]1.19000000000000[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12895&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12895&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
144.17916666666670.05961365513695520.159999999999997
244.36666666666670.08260897302498250.219999999999999
344.93083333333330.2805986565552420.830000000000005
445.81083333333330.3474702952204780.949999999999996
546.45750.1646000662763590.43
647.180.4434779896147351.19000000000000






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-4.17361978905108
beta0.096803474837905
S.D.0.0415378404796447
T-STAT2.33048886798395
p-value0.080209125618142

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -4.17361978905108 \tabularnewline
beta & 0.096803474837905 \tabularnewline
S.D. & 0.0415378404796447 \tabularnewline
T-STAT & 2.33048886798395 \tabularnewline
p-value & 0.080209125618142 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12895&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.17361978905108[/C][/ROW]
[ROW][C]beta[/C][C]0.096803474837905[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0415378404796447[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.33048886798395[/C][/ROW]
[ROW][C]p-value[/C][C]0.080209125618142[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12895&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12895&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-4.17361978905108
beta0.096803474837905
S.D.0.0415378404796447
T-STAT2.33048886798395
p-value0.080209125618142






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-92.2265507717555
beta23.7131836863362
S.D.9.82951533247692
T-STAT2.41244688921613
p-value0.0733601657258687
Lambda-22.7131836863362

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -92.2265507717555 \tabularnewline
beta & 23.7131836863362 \tabularnewline
S.D. & 9.82951533247692 \tabularnewline
T-STAT & 2.41244688921613 \tabularnewline
p-value & 0.0733601657258687 \tabularnewline
Lambda & -22.7131836863362 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12895&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-92.2265507717555[/C][/ROW]
[ROW][C]beta[/C][C]23.7131836863362[/C][/ROW]
[ROW][C]S.D.[/C][C]9.82951533247692[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.41244688921613[/C][/ROW]
[ROW][C]p-value[/C][C]0.0733601657258687[/C][/ROW]
[ROW][C]Lambda[/C][C]-22.7131836863362[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12895&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12895&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-92.2265507717555
beta23.7131836863362
S.D.9.82951533247692
T-STAT2.41244688921613
p-value0.0733601657258687
Lambda-22.7131836863362


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')