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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationFri, 04 Dec 2009 07:47:17 -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/Dec/04/t1259938114fq7g6qibf1p1au5.htm/, Retrieved Sat, 27 Apr 2024 20:49:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63658, Retrieved Sat, 27 Apr 2024 20:49:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact124

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Standard Deviation-Mean Plot] [] [2009-11-27 14:40:44] [b98453cac15ba1066b407e146608df68]
- R  D    [Standard Deviation-Mean Plot] [] [2009-12-01 16:51:24] [ee35698a38947a6c6c039b1e3deafc05]
- R  D        [Standard Deviation-Mean Plot] [] [2009-12-04 14:47:17] [18c0746232b29e9668aa6bedcb8dd698] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
12,6
15,7
13,2
20,3
12,8
8
0,9
3,6
14,1
21,7
24,5
18,9
13,9
11
5,8
15,5
22,4
31,7
30,3
31,4
20,2
19,7
10,8
13,2
15,1
15,6
15,5
12,7
10,9
10
9,1
10,3
16,9
22
27,6
28,9
31
32,9
38,1
28,8
29
21,8
28,8
25,6
28,2
20,2
17,9
16,3
13,2
8,1
4,5
-0,1
0
2,3
2,8
2,9
0,1
3,5
8,6
13,8

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time0 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 & 0 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63658&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]0 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=63658&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63658&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 time0 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
113.85833333333337.1076729772489623.6
218.8258.7034084232453525.9
316.21666666666676.684015305642319.8
426.556.4388734192474221.8
54.9754.8738868192924513.9

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 13.8583333333333 & 7.10767297724896 & 23.6 \tabularnewline
2 & 18.825 & 8.70340842324535 & 25.9 \tabularnewline
3 & 16.2166666666667 & 6.6840153056423 & 19.8 \tabularnewline
4 & 26.55 & 6.43887341924742 & 21.8 \tabularnewline
5 & 4.975 & 4.87388681929245 & 13.9 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63658&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]13.8583333333333[/C][C]7.10767297724896[/C][C]23.6[/C][/ROW]
[ROW][C]2[/C][C]18.825[/C][C]8.70340842324535[/C][C]25.9[/C][/ROW]
[ROW][C]3[/C][C]16.2166666666667[/C][C]6.6840153056423[/C][C]19.8[/C][/ROW]
[ROW][C]4[/C][C]26.55[/C][C]6.43887341924742[/C][C]21.8[/C][/ROW]
[ROW][C]5[/C][C]4.975[/C][C]4.87388681929245[/C][C]13.9[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63658&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63658&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
113.85833333333337.1076729772489623.6
218.8258.7034084232453525.9
316.21666666666676.684015305642319.8
426.556.4388734192474221.8
54.9754.8738868192924513.9






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha5.3109005689287
beta0.090187803544084
S.D.0.0869587127585983
T-STAT1.03713360838781
p-value0.375930869701041

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 5.3109005689287 \tabularnewline
beta & 0.090187803544084 \tabularnewline
S.D. & 0.0869587127585983 \tabularnewline
T-STAT & 1.03713360838781 \tabularnewline
p-value & 0.375930869701041 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63658&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]5.3109005689287[/C][/ROW]
[ROW][C]beta[/C][C]0.090187803544084[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0869587127585983[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.03713360838781[/C][/ROW]
[ROW][C]p-value[/C][C]0.375930869701041[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63658&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63658&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)
alpha5.3109005689287
beta0.090187803544084
S.D.0.0869587127585983
T-STAT1.03713360838781
p-value0.375930869701041






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha1.26025210440533
beta0.239511636571379
S.D.0.132182996815569
T-STAT1.81197008950827
p-value0.167660052586525
Lambda0.760488363428621

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.26025210440533 \tabularnewline
beta & 0.239511636571379 \tabularnewline
S.D. & 0.132182996815569 \tabularnewline
T-STAT & 1.81197008950827 \tabularnewline
p-value & 0.167660052586525 \tabularnewline
Lambda & 0.760488363428621 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63658&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.26025210440533[/C][/ROW]
[ROW][C]beta[/C][C]0.239511636571379[/C][/ROW]
[ROW][C]S.D.[/C][C]0.132182996815569[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.81197008950827[/C][/ROW]
[ROW][C]p-value[/C][C]0.167660052586525[/C][/ROW]
[ROW][C]Lambda[/C][C]0.760488363428621[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63658&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63658&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)
alpha1.26025210440533
beta0.239511636571379
S.D.0.132182996815569
T-STAT1.81197008950827
p-value0.167660052586525
Lambda0.760488363428621


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')