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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 03:01:29 -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/t12599209448rzslq8djwcwblk.htm/, Retrieved Sun, 28 Apr 2024 03:22:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63225, Retrieved Sun, 28 Apr 2024 03:22:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsSHW WS 9 Standard Deviation - Mean Plot
Estimated Impact103

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]
-    D      [Standard Deviation-Mean Plot] [WS 9 Standard Dev...] [2009-12-04 10:01:29] [a45cc820faa25ce30779915639528ec2] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
14.2
13.5
11.9
14.6
15.6
14.1
14.9
14.2
14.6
17.2
15.4
14.3
17.5
14.5
14.4
16.6
16.7
16.6
16.9
15.7
16.4
18.4
16.9
16.5
18.3
15.1
15.7
18.1
16.8
18.9
19
18.1
17.8
21.5
17.1
18.7
19
16.4
16.9
18.6
19.3
19.4
17.6
18.6
18.1
20.4
18.1
19.6
19.9
19.2
17.8
19.2
22
21.1
19.5
22.2
20.9
22.2
23.5
21.5
24.3
22.8
20.3
23.7
23.3
19.6
18
17.3
16.8
18.2
16.5
16
18.4

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=63225&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=63225&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63225&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
114.54166666666671.265240425110325.3
216.4251.127446834061974
317.9251.667401353222216.4
418.51.153650333033844
520.751.646759904120265.7
619.73333333333333.064854537059368.3

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 14.5416666666667 & 1.26524042511032 & 5.3 \tabularnewline
2 & 16.425 & 1.12744683406197 & 4 \tabularnewline
3 & 17.925 & 1.66740135322221 & 6.4 \tabularnewline
4 & 18.5 & 1.15365033303384 & 4 \tabularnewline
5 & 20.75 & 1.64675990412026 & 5.7 \tabularnewline
6 & 19.7333333333333 & 3.06485453705936 & 8.3 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63225&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]14.5416666666667[/C][C]1.26524042511032[/C][C]5.3[/C][/ROW]
[ROW][C]2[/C][C]16.425[/C][C]1.12744683406197[/C][C]4[/C][/ROW]
[ROW][C]3[/C][C]17.925[/C][C]1.66740135322221[/C][C]6.4[/C][/ROW]
[ROW][C]4[/C][C]18.5[/C][C]1.15365033303384[/C][C]4[/C][/ROW]
[ROW][C]5[/C][C]20.75[/C][C]1.64675990412026[/C][C]5.7[/C][/ROW]
[ROW][C]6[/C][C]19.7333333333333[/C][C]3.06485453705936[/C][C]8.3[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63225&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63225&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
114.54166666666671.265240425110325.3
216.4251.127446834061974
317.9251.667401353222216.4
418.51.153650333033844
520.751.646759904120265.7
619.73333333333333.064854537059368.3






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-1.44058766049552
beta0.172133296403996
S.D.0.137883704520514
T-STAT1.24839477589164
p-value0.279968044197974

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -1.44058766049552 \tabularnewline
beta & 0.172133296403996 \tabularnewline
S.D. & 0.137883704520514 \tabularnewline
T-STAT & 1.24839477589164 \tabularnewline
p-value & 0.279968044197974 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63225&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.44058766049552[/C][/ROW]
[ROW][C]beta[/C][C]0.172133296403996[/C][/ROW]
[ROW][C]S.D.[/C][C]0.137883704520514[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.24839477589164[/C][/ROW]
[ROW][C]p-value[/C][C]0.279968044197974[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63225&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63225&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-1.44058766049552
beta0.172133296403996
S.D.0.137883704520514
T-STAT1.24839477589164
p-value0.279968044197974






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-4.26412246335470
beta1.63131185180003
S.D.1.20611128790692
T-STAT1.35253841677495
p-value0.247607344103516
Lambda-0.631311851800026

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -4.26412246335470 \tabularnewline
beta & 1.63131185180003 \tabularnewline
S.D. & 1.20611128790692 \tabularnewline
T-STAT & 1.35253841677495 \tabularnewline
p-value & 0.247607344103516 \tabularnewline
Lambda & -0.631311851800026 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63225&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.26412246335470[/C][/ROW]
[ROW][C]beta[/C][C]1.63131185180003[/C][/ROW]
[ROW][C]S.D.[/C][C]1.20611128790692[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.35253841677495[/C][/ROW]
[ROW][C]p-value[/C][C]0.247607344103516[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.631311851800026[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63225&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63225&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-4.26412246335470
beta1.63131185180003
S.D.1.20611128790692
T-STAT1.35253841677495
p-value0.247607344103516
Lambda-0.631311851800026


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')