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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 computationTue, 03 Dec 2013 15:44:43 -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/2013/Dec/03/t1386103526ipllzvx6ebr8rjs.htm/, Retrieved Fri, 29 Mar 2024 01:27:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=230402, Retrieved Fri, 29 Mar 2024 01:27:39 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact57
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Standard Deviation-Mean Plot] [stat vd var] [2013-12-03 20:44:43] [b86744663ec671173a5f381479557f00] [Current]
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Dataseries X:
4
5
7
5
6
5
3
7
7
11
13
13
9
7
6
3
5
1
5
2
9
4
4
10
8
6
7
0
7
4
5
11
2
4
5
12
10
6
6
8
3
10
2
5
4
3
8
5
7
1
7
4
8
7
10
2
6
6
11
8
8
6
11
15
9
5
10
4
9
3
7
7
9
15
11
10
6
5
6
6
14
11
1
9
13
10
11
7
6
4
6
8
6
7
12
20
10
14
11
13
7
9
8
7
9
10
12
13
11
11
14
10
9
12
8
13
14
15
14
14
15
14
21
10
8
12
13
6
12
12




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 5 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230402&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230402&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230402&T=0

As an alternative you can also use a 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 time5 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
17.166666666666673.3799766898963110
25.416666666666672.874917653629679
35.916666666666673.4234042953903312
45.833333333333332.691175253012018
56.416666666666672.9374798516394810
67.833333333333333.2983007562664612
78.583333333333333.9876703915337814
89.166666666666674.3866187710381516
910.252.378884383296287
1012.08333333333332.274696116900557

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 7.16666666666667 & 3.37997668989631 & 10 \tabularnewline
2 & 5.41666666666667 & 2.87491765362967 & 9 \tabularnewline
3 & 5.91666666666667 & 3.42340429539033 & 12 \tabularnewline
4 & 5.83333333333333 & 2.69117525301201 & 8 \tabularnewline
5 & 6.41666666666667 & 2.93747985163948 & 10 \tabularnewline
6 & 7.83333333333333 & 3.29830075626646 & 12 \tabularnewline
7 & 8.58333333333333 & 3.98767039153378 & 14 \tabularnewline
8 & 9.16666666666667 & 4.38661877103815 & 16 \tabularnewline
9 & 10.25 & 2.37888438329628 & 7 \tabularnewline
10 & 12.0833333333333 & 2.27469611690055 & 7 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230402&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]7.16666666666667[/C][C]3.37997668989631[/C][C]10[/C][/ROW]
[ROW][C]2[/C][C]5.41666666666667[/C][C]2.87491765362967[/C][C]9[/C][/ROW]
[ROW][C]3[/C][C]5.91666666666667[/C][C]3.42340429539033[/C][C]12[/C][/ROW]
[ROW][C]4[/C][C]5.83333333333333[/C][C]2.69117525301201[/C][C]8[/C][/ROW]
[ROW][C]5[/C][C]6.41666666666667[/C][C]2.93747985163948[/C][C]10[/C][/ROW]
[ROW][C]6[/C][C]7.83333333333333[/C][C]3.29830075626646[/C][C]12[/C][/ROW]
[ROW][C]7[/C][C]8.58333333333333[/C][C]3.98767039153378[/C][C]14[/C][/ROW]
[ROW][C]8[/C][C]9.16666666666667[/C][C]4.38661877103815[/C][C]16[/C][/ROW]
[ROW][C]9[/C][C]10.25[/C][C]2.37888438329628[/C][C]7[/C][/ROW]
[ROW][C]10[/C][C]12.0833333333333[/C][C]2.27469611690055[/C][C]7[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230402&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230402&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
17.166666666666673.3799766898963110
25.416666666666672.874917653629679
35.916666666666673.4234042953903312
45.833333333333332.691175253012018
56.416666666666672.9374798516394810
67.833333333333333.2983007562664612
78.583333333333333.9876703915337814
89.166666666666674.3866187710381516
910.252.378884383296287
1012.08333333333332.274696116900557







Regression: S.E.(k) = alpha + beta * Mean(k)
alpha3.55569685920541
beta-0.0498793783404806
S.D.0.108389022004547
T-STAT-0.460188471286217
p-value0.657630469318565

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 3.55569685920541 \tabularnewline
beta & -0.0498793783404806 \tabularnewline
S.D. & 0.108389022004547 \tabularnewline
T-STAT & -0.460188471286217 \tabularnewline
p-value & 0.657630469318565 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230402&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.55569685920541[/C][/ROW]
[ROW][C]beta[/C][C]-0.0498793783404806[/C][/ROW]
[ROW][C]S.D.[/C][C]0.108389022004547[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.460188471286217[/C][/ROW]
[ROW][C]p-value[/C][C]0.657630469318565[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230402&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230402&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha3.55569685920541
beta-0.0498793783404806
S.D.0.108389022004547
T-STAT-0.460188471286217
p-value0.657630469318565







Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha1.39711791498858
beta-0.130797957287463
S.D.0.276684815233291
T-STAT-0.472732691084543
p-value0.649032410349209
Lambda1.13079795728746

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.39711791498858 \tabularnewline
beta & -0.130797957287463 \tabularnewline
S.D. & 0.276684815233291 \tabularnewline
T-STAT & -0.472732691084543 \tabularnewline
p-value & 0.649032410349209 \tabularnewline
Lambda & 1.13079795728746 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230402&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.39711791498858[/C][/ROW]
[ROW][C]beta[/C][C]-0.130797957287463[/C][/ROW]
[ROW][C]S.D.[/C][C]0.276684815233291[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.472732691084543[/C][/ROW]
[ROW][C]p-value[/C][C]0.649032410349209[/C][/ROW]
[ROW][C]Lambda[/C][C]1.13079795728746[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230402&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230402&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha1.39711791498858
beta-0.130797957287463
S.D.0.276684815233291
T-STAT-0.472732691084543
p-value0.649032410349209
Lambda1.13079795728746



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')