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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 computationWed, 30 Dec 2009 16:26:05 -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/31/t1262215627tdyq6ygbe4p6lg1.htm/, Retrieved Thu, 02 May 2024 05:10:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=71399, Retrieved Thu, 02 May 2024 05:10:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact141

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Standard Deviation-Mean Plot] [Identifying Integ...] [2009-11-22 12:50:05] [b98453cac15ba1066b407e146608df68]
- R  D        [Standard Deviation-Mean Plot] [WS08 - Heteroskel...] [2009-11-25 22:14:53] [df6326eec97a6ca984a853b142930499]
-    D            [Standard Deviation-Mean Plot] [CaseStatistiek - ...] [2009-12-30 23:26:05] [0cc924834281808eda7297686c82928f] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
15
14.4
13.5
12.8
12.3
12.2
14.5
17.2
18
18.1
18
18.3
18.7
18.6
18.3
17.9
17.4
17.4
20.1
23.2
24.2
24.2
23.9
23.8
23.8
23.3
22.4
21.5
20.5
19.9
22
24.9
25.7
25.3
24.4
23.8
23.5
23
22.2
21.4
20.3
19.5
21.7
24.7
25.3
24.9
24.1
23.4
23.1
22.4
21.3
20.3
19.3
18.7
21
24
24.8
24.2
23.3
22.7
22.3
21.8
21.2
20.5
19.7
19.2
21.2
23.9
24.8
24.2
23
22.2
21.8
21.2
20.5
19.7
19
18.4
20.7
24.5
26
25.2
24.1
23.7
23.5
23.1
22.7
22.5
21.7
20.5
21.9
22.9
21.5
19
17
16.1
15.9
15.7
15.1
14.8
14.3
14.5
18.9
21.6
20.4
17.9
15.7
14.5
14
13.9
14.4
15.8
15.6
14.7
16.7
17.9
18.7
20.1
19.5
19.4
18.6
17.8
17.1
16.5
15.5
14.9
18.6
19.1
18.8
18.2
18
19
20.7
21.2
20.7
19.6
18.6
18.7
23.8
24.9
24.8
23.8
22.3
21.7
20.7
19.7
18.4
17.4
17
18
23.8
25.5
25.6
23.7
22
21.3
20.7
20.4
20.3
20.4
19.8
19.5
23.1
23.5
23.5
22.9
21.9
21.5
20.5
20.2
19.4
19.2
18.8
18.8
22.6
23.3
23
21.4
19.9
18.8
18.6
18.4
18.6
19.9
19.2
18.4
21.1
20.5
19.1
18.1
17
17.1
17.4
16.8
15.3
14.3
13.4
15.3
22.1
23.7
22.2
19.5
16.6
17.3
19.8
21.2
21.5
20.6
19.1
19.6
23.5
24
23.2
21.2

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=71399&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=71399&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71399&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
115.35833333333332.423918065421936.1
220.64166666666672.934267241139476.8
323.1251.878163997099295.8
422.83333333333331.84653647938435.8
522.09166666666671.969983079453566.1
6221.761197939420265.6
722.06666666666672.551410780273727.6
821.03333333333332.434723554713927.4
916.60833333333332.488686522256397.3
1016.7252.307349916324716.2
1117.6751.391614497298344.2
1221.73333333333332.221520091097886.3
1321.09166666666673.075255594206278.6
1421.45833333333331.478610117234384
1520.49166666666671.687633271953974.5
1618.83333333333331.230176139149734.1
1717.8253.3371531144211710.3

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 15.3583333333333 & 2.42391806542193 & 6.1 \tabularnewline
2 & 20.6416666666667 & 2.93426724113947 & 6.8 \tabularnewline
3 & 23.125 & 1.87816399709929 & 5.8 \tabularnewline
4 & 22.8333333333333 & 1.8465364793843 & 5.8 \tabularnewline
5 & 22.0916666666667 & 1.96998307945356 & 6.1 \tabularnewline
6 & 22 & 1.76119793942026 & 5.6 \tabularnewline
7 & 22.0666666666667 & 2.55141078027372 & 7.6 \tabularnewline
8 & 21.0333333333333 & 2.43472355471392 & 7.4 \tabularnewline
9 & 16.6083333333333 & 2.48868652225639 & 7.3 \tabularnewline
10 & 16.725 & 2.30734991632471 & 6.2 \tabularnewline
11 & 17.675 & 1.39161449729834 & 4.2 \tabularnewline
12 & 21.7333333333333 & 2.22152009109788 & 6.3 \tabularnewline
13 & 21.0916666666667 & 3.07525559420627 & 8.6 \tabularnewline
14 & 21.4583333333333 & 1.47861011723438 & 4 \tabularnewline
15 & 20.4916666666667 & 1.68763327195397 & 4.5 \tabularnewline
16 & 18.8333333333333 & 1.23017613914973 & 4.1 \tabularnewline
17 & 17.825 & 3.33715311442117 & 10.3 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71399&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]15.3583333333333[/C][C]2.42391806542193[/C][C]6.1[/C][/ROW]
[ROW][C]2[/C][C]20.6416666666667[/C][C]2.93426724113947[/C][C]6.8[/C][/ROW]
[ROW][C]3[/C][C]23.125[/C][C]1.87816399709929[/C][C]5.8[/C][/ROW]
[ROW][C]4[/C][C]22.8333333333333[/C][C]1.8465364793843[/C][C]5.8[/C][/ROW]
[ROW][C]5[/C][C]22.0916666666667[/C][C]1.96998307945356[/C][C]6.1[/C][/ROW]
[ROW][C]6[/C][C]22[/C][C]1.76119793942026[/C][C]5.6[/C][/ROW]
[ROW][C]7[/C][C]22.0666666666667[/C][C]2.55141078027372[/C][C]7.6[/C][/ROW]
[ROW][C]8[/C][C]21.0333333333333[/C][C]2.43472355471392[/C][C]7.4[/C][/ROW]
[ROW][C]9[/C][C]16.6083333333333[/C][C]2.48868652225639[/C][C]7.3[/C][/ROW]
[ROW][C]10[/C][C]16.725[/C][C]2.30734991632471[/C][C]6.2[/C][/ROW]
[ROW][C]11[/C][C]17.675[/C][C]1.39161449729834[/C][C]4.2[/C][/ROW]
[ROW][C]12[/C][C]21.7333333333333[/C][C]2.22152009109788[/C][C]6.3[/C][/ROW]
[ROW][C]13[/C][C]21.0916666666667[/C][C]3.07525559420627[/C][C]8.6[/C][/ROW]
[ROW][C]14[/C][C]21.4583333333333[/C][C]1.47861011723438[/C][C]4[/C][/ROW]
[ROW][C]15[/C][C]20.4916666666667[/C][C]1.68763327195397[/C][C]4.5[/C][/ROW]
[ROW][C]16[/C][C]18.8333333333333[/C][C]1.23017613914973[/C][C]4.1[/C][/ROW]
[ROW][C]17[/C][C]17.825[/C][C]3.33715311442117[/C][C]10.3[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71399&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71399&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
115.35833333333332.423918065421936.1
220.64166666666672.934267241139476.8
323.1251.878163997099295.8
422.83333333333331.84653647938435.8
522.09166666666671.969983079453566.1
6221.761197939420265.6
722.06666666666672.551410780273727.6
821.03333333333332.434723554713927.4
916.60833333333332.488686522256397.3
1016.7252.307349916324716.2
1117.6751.391614497298344.2
1221.73333333333332.221520091097886.3
1321.09166666666673.075255594206278.6
1421.45833333333331.478610117234384
1520.49166666666671.687633271953974.5
1618.83333333333331.230176139149734.1
1717.8253.3371531144211710.3






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha3.0434413350614
beta-0.0430932710942241
S.D.0.063102106437619
T-STAT-0.682913353087901
p-value0.505073104873551

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 3.0434413350614 \tabularnewline
beta & -0.0430932710942241 \tabularnewline
S.D. & 0.063102106437619 \tabularnewline
T-STAT & -0.682913353087901 \tabularnewline
p-value & 0.505073104873551 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71399&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.0434413350614[/C][/ROW]
[ROW][C]beta[/C][C]-0.0430932710942241[/C][/ROW]
[ROW][C]S.D.[/C][C]0.063102106437619[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.682913353087901[/C][/ROW]
[ROW][C]p-value[/C][C]0.505073104873551[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71399&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71399&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)
alpha3.0434413350614
beta-0.0430932710942241
S.D.0.063102106437619
T-STAT-0.682913353087901
p-value0.505073104873551






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha1.6933578483235
beta-0.318069864964684
S.D.0.574128755178128
T-STAT-0.554004414682209
p-value0.58774045477702
Lambda1.31806986496468

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.6933578483235 \tabularnewline
beta & -0.318069864964684 \tabularnewline
S.D. & 0.574128755178128 \tabularnewline
T-STAT & -0.554004414682209 \tabularnewline
p-value & 0.58774045477702 \tabularnewline
Lambda & 1.31806986496468 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71399&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.6933578483235[/C][/ROW]
[ROW][C]beta[/C][C]-0.318069864964684[/C][/ROW]
[ROW][C]S.D.[/C][C]0.574128755178128[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.554004414682209[/C][/ROW]
[ROW][C]p-value[/C][C]0.58774045477702[/C][/ROW]
[ROW][C]Lambda[/C][C]1.31806986496468[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71399&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71399&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)
alpha1.6933578483235
beta-0.318069864964684
S.D.0.574128755178128
T-STAT-0.554004414682209
p-value0.58774045477702
Lambda1.31806986496468


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')