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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 computationThu, 10 Dec 2009 05:13:58 -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/10/t126044732586737s07s043fmq.htm/, Retrieved Tue, 16 Apr 2024 15:08:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=65300, Retrieved Tue, 16 Apr 2024 15:08:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact129

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]
-    D        [Standard Deviation-Mean Plot] [W8] [2009-11-25 19:03:18] [315ba876df544ad397193b5931d5f354]
-                 [Standard Deviation-Mean Plot] [Standaard deviati...] [2009-12-10 12:13:58] [950726a732ba3ca782ecb1a5307d0f6f] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
13132.1
17665.9
16913
17318.8
16224.2
15469.6
16557.5
19414.8
17335
16525.2
18160.4
15553.8
15262.2
18581
17564.1
18948.6
17187.8
17564.8
17668.4
20811.7
17257.8
18984.2
20532.6
17082.3
16894.9
20274.9
20078.6
19900.9
17012.2
19642.9
19024
21691
18835.9
19873.4
21468.2
19406.8
18385.3
20739.3
22268.3
21569
17514.8
21124.7
21251
21393
22145.2
20310.5
23466.9
21264.6
18388.1
22635.4
22014.3
18422.7
16120.2
16037.7
16410.7
17749.8
16349.8
15662.3
17782.3
16398.9

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=65300&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=65300&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65300&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
116689.19166666671569.620439039816282.7
218120.45833333331548.878419700905549.5
319508.64166666671464.153455356834796.1
420952.71666666671627.386613747965952.1
517831.01666666672303.353875560726973.1

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 16689.1916666667 & 1569.62043903981 & 6282.7 \tabularnewline
2 & 18120.4583333333 & 1548.87841970090 & 5549.5 \tabularnewline
3 & 19508.6416666667 & 1464.15345535683 & 4796.1 \tabularnewline
4 & 20952.7166666667 & 1627.38661374796 & 5952.1 \tabularnewline
5 & 17831.0166666667 & 2303.35387556072 & 6973.1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65300&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]16689.1916666667[/C][C]1569.62043903981[/C][C]6282.7[/C][/ROW]
[ROW][C]2[/C][C]18120.4583333333[/C][C]1548.87841970090[/C][C]5549.5[/C][/ROW]
[ROW][C]3[/C][C]19508.6416666667[/C][C]1464.15345535683[/C][C]4796.1[/C][/ROW]
[ROW][C]4[/C][C]20952.7166666667[/C][C]1627.38661374796[/C][C]5952.1[/C][/ROW]
[ROW][C]5[/C][C]17831.0166666667[/C][C]2303.35387556072[/C][C]6973.1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65300&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65300&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
116689.19166666671569.620439039816282.7
218120.45833333331548.878419700905549.5
319508.64166666671464.153455356834796.1
420952.71666666671627.386613747965952.1
517831.01666666672303.353875560726973.1






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha2610.00277599822
beta-0.0487274157203871
S.D.0.116235510925212
T-STAT-0.419212814849149
p-value0.703268324339009

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 2610.00277599822 \tabularnewline
beta & -0.0487274157203871 \tabularnewline
S.D. & 0.116235510925212 \tabularnewline
T-STAT & -0.419212814849149 \tabularnewline
p-value & 0.703268324339009 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65300&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2610.00277599822[/C][/ROW]
[ROW][C]beta[/C][C]-0.0487274157203871[/C][/ROW]
[ROW][C]S.D.[/C][C]0.116235510925212[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.419212814849149[/C][/ROW]
[ROW][C]p-value[/C][C]0.703268324339009[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65300&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65300&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)
alpha2610.00277599822
beta-0.0487274157203871
S.D.0.116235510925212
T-STAT-0.419212814849149
p-value0.703268324339009






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha11.9751835360959
beta-0.462841020754767
S.D.1.16189857480545
T-STAT-0.398348901350763
p-value0.717029544137025
Lambda1.46284102075477

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 11.9751835360959 \tabularnewline
beta & -0.462841020754767 \tabularnewline
S.D. & 1.16189857480545 \tabularnewline
T-STAT & -0.398348901350763 \tabularnewline
p-value & 0.717029544137025 \tabularnewline
Lambda & 1.46284102075477 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65300&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]11.9751835360959[/C][/ROW]
[ROW][C]beta[/C][C]-0.462841020754767[/C][/ROW]
[ROW][C]S.D.[/C][C]1.16189857480545[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.398348901350763[/C][/ROW]
[ROW][C]p-value[/C][C]0.717029544137025[/C][/ROW]
[ROW][C]Lambda[/C][C]1.46284102075477[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65300&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65300&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)
alpha11.9751835360959
beta-0.462841020754767
S.D.1.16189857480545
T-STAT-0.398348901350763
p-value0.717029544137025
Lambda1.46284102075477


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')