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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, 03 Dec 2012 04:17:19 -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/2012/Dec/03/t1354526277w0ok8ou0ebh8ief.htm/, Retrieved Sat, 04 May 2024 22:05:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=195652, Retrieved Sat, 04 May 2024 22:05:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact115

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] [standaard deviati...] [2012-12-03 09:17:19] [a4dec8ecbe2562b1daf91a8f6c837985] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
97.51
96.65
95.91
95.86
95.7
95.57
95.57
95.57
94.87
95.07
95.13
95.48
95.38
95.38
95.48
95.77
94.78
92.51
92.17
91.75
90.43
90.55
90.37
90.4
90.41
90.41
90.41
89.77
89.77
89.77
89.37
89.81
89.07
89.84
89.73
90.02
88.39
90.13
90.13
90.37
89.73
89.73
89.73
89.73
89.6
89.63
86.42
86.8
86.51
86.41
86.39
86.62
85.85
87.36
87.28
87.35
87.35
87.35
87.38
88.17
88.37
87.44
87.44
87.47
87.47
87.48
87.11
87.11
86.26
86.28
86.28
86.28

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'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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=195652&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=195652&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=195652&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'Gwilym Jenkins' @ jenkins.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
195.74083333333330.722249746950252.64
292.91416666666672.276518307868535.39999999999999
389.8650.4091121206622051.34
489.19916666666671.30424801275983.95
587.00166666666670.6407358459165712.32000000000001
687.08250.6729598799334172.11

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 95.7408333333333 & 0.72224974695025 & 2.64 \tabularnewline
2 & 92.9141666666667 & 2.27651830786853 & 5.39999999999999 \tabularnewline
3 & 89.865 & 0.409112120662205 & 1.34 \tabularnewline
4 & 89.1991666666667 & 1.3042480127598 & 3.95 \tabularnewline
5 & 87.0016666666667 & 0.640735845916571 & 2.32000000000001 \tabularnewline
6 & 87.0825 & 0.672959879933417 & 2.11 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=195652&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]95.7408333333333[/C][C]0.72224974695025[/C][C]2.64[/C][/ROW]
[ROW][C]2[/C][C]92.9141666666667[/C][C]2.27651830786853[/C][C]5.39999999999999[/C][/ROW]
[ROW][C]3[/C][C]89.865[/C][C]0.409112120662205[/C][C]1.34[/C][/ROW]
[ROW][C]4[/C][C]89.1991666666667[/C][C]1.3042480127598[/C][C]3.95[/C][/ROW]
[ROW][C]5[/C][C]87.0016666666667[/C][C]0.640735845916571[/C][C]2.32000000000001[/C][/ROW]
[ROW][C]6[/C][C]87.0825[/C][C]0.672959879933417[/C][C]2.11[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=195652&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=195652&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
195.74083333333330.722249746950252.64
292.91416666666672.276518307868535.39999999999999
389.8650.4091121206622051.34
489.19916666666671.30424801275983.95
587.00166666666670.6407358459165712.32000000000001
687.08250.6729598799334172.11






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-5.08793829458334
beta0.0674662768438563
S.D.0.0946210777157594
T-STAT0.713015307715308
p-value0.515225081799142

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -5.08793829458334 \tabularnewline
beta & 0.0674662768438563 \tabularnewline
S.D. & 0.0946210777157594 \tabularnewline
T-STAT & 0.713015307715308 \tabularnewline
p-value & 0.515225081799142 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=195652&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-5.08793829458334[/C][/ROW]
[ROW][C]beta[/C][C]0.0674662768438563[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0946210777157594[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.713015307715308[/C][/ROW]
[ROW][C]p-value[/C][C]0.515225081799142[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=195652&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=195652&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-5.08793829458334
beta0.0674662768438563
S.D.0.0946210777157594
T-STAT0.713015307715308
p-value0.515225081799142






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-22.8690104387093
beta5.0431443249812
S.D.7.65979256718177
T-STAT0.658391762015651
p-value0.546253554649172
Lambda-4.0431443249812

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -22.8690104387093 \tabularnewline
beta & 5.0431443249812 \tabularnewline
S.D. & 7.65979256718177 \tabularnewline
T-STAT & 0.658391762015651 \tabularnewline
p-value & 0.546253554649172 \tabularnewline
Lambda & -4.0431443249812 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=195652&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-22.8690104387093[/C][/ROW]
[ROW][C]beta[/C][C]5.0431443249812[/C][/ROW]
[ROW][C]S.D.[/C][C]7.65979256718177[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.658391762015651[/C][/ROW]
[ROW][C]p-value[/C][C]0.546253554649172[/C][/ROW]
[ROW][C]Lambda[/C][C]-4.0431443249812[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=195652&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=195652&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-22.8690104387093
beta5.0431443249812
S.D.7.65979256718177
T-STAT0.658391762015651
p-value0.546253554649172
Lambda-4.0431443249812


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')