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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, 18 Dec 2009 12:32:26 -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/18/t1261164798tmalhdpi6z72ya1.htm/, Retrieved Sat, 27 Apr 2024 06:58:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=69443, Retrieved Sat, 27 Apr 2024 06:58:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact136

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Standard Deviation-Mean Plot] [Standard deviatio...] [2008-12-11 16:40:34] [12d343c4448a5f9e527bb31caeac580b]
-  M D    [Standard Deviation-Mean Plot] [Standard Deviatio...] [2009-12-18 19:32:26] [d45d8d97b86162be82506c3c0ea6e4a6] [Current]
-    D      [Standard Deviation-Mean Plot] [Standard Deviatio...] [2009-12-21 13:17:50] [976efdaed7598845c859b86bc2e467ce]
-    D      [Standard Deviation-Mean Plot] [Standard Deviatio...] [2009-12-21 14:42:25] [ae69f4b008b5eaa8ebe185637a6eee4e]
- RMPD      [(Partial) Autocorrelation Function] [Autocorrelatie fu...] [2009-12-21 15:27:36] [ae69f4b008b5eaa8ebe185637a6eee4e]
-   P         [(Partial) Autocorrelation Function] [Autocorrelatie en...] [2009-12-21 16:53:21] [ae69f4b008b5eaa8ebe185637a6eee4e]
-   P           [(Partial) Autocorrelation Function] [Autocorrelatie fu...] [2009-12-21 17:00:29] [ae69f4b008b5eaa8ebe185637a6eee4e]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
12.1
12
11.8
12.7
12.3
11.9
12
12.3
12.8
12.4
12.3
12.7
12.7
12.9
13
12.2
12.3
12.8
12.8
12.8
12.2
12.6
12.8
12.5
12.4
12.3
11.9
11.7
12
12.1
11.7
11.8
11.8
11.8
11.3
11.3
11.3
11.2
11.4
12.2
12.9
13.1
13.5
13.6
14.4
14.1
15.1
15.8
15.9
15.4
15.5
14.8
13.2
12.7
12.1
11.9
10.6
10.7
9.8
9
8.3
9.3
9
9.1
10

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69443&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]2 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=69443&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69443&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
112.2750.3306330017076061
212.63333333333330.2741377667369370.8
311.84166666666670.3369875458538581.1
413.21666666666671.502018843443924.6
512.63333333333332.364253998557896.9

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 12.275 & 0.330633001707606 & 1 \tabularnewline
2 & 12.6333333333333 & 0.274137766736937 & 0.8 \tabularnewline
3 & 11.8416666666667 & 0.336987545853858 & 1.1 \tabularnewline
4 & 13.2166666666667 & 1.50201884344392 & 4.6 \tabularnewline
5 & 12.6333333333333 & 2.36425399855789 & 6.9 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69443&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]12.275[/C][C]0.330633001707606[/C][C]1[/C][/ROW]
[ROW][C]2[/C][C]12.6333333333333[/C][C]0.274137766736937[/C][C]0.8[/C][/ROW]
[ROW][C]3[/C][C]11.8416666666667[/C][C]0.336987545853858[/C][C]1.1[/C][/ROW]
[ROW][C]4[/C][C]13.2166666666667[/C][C]1.50201884344392[/C][C]4.6[/C][/ROW]
[ROW][C]5[/C][C]12.6333333333333[/C][C]2.36425399855789[/C][C]6.9[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69443&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69443&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
112.2750.3306330017076061
212.63333333333330.2741377667369370.8
311.84166666666670.3369875458538581.1
413.21666666666671.502018843443924.6
512.63333333333332.364253998557896.9






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-11.6146658286644
beta1.00449457347639
S.D.0.89533090592947
T-STAT1.12192549907969
p-value0.343592290628115

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -11.6146658286644 \tabularnewline
beta & 1.00449457347639 \tabularnewline
S.D. & 0.89533090592947 \tabularnewline
T-STAT & 1.12192549907969 \tabularnewline
p-value & 0.343592290628115 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69443&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-11.6146658286644[/C][/ROW]
[ROW][C]beta[/C][C]1.00449457347639[/C][/ROW]
[ROW][C]S.D.[/C][C]0.89533090592947[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.12192549907969[/C][/ROW]
[ROW][C]p-value[/C][C]0.343592290628115[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69443&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69443&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-11.6146658286644
beta1.00449457347639
S.D.0.89533090592947
T-STAT1.12192549907969
p-value0.343592290628115






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-38.4709429813567
beta15.0501234602525
S.D.11.2711639921533
T-STAT1.33527677094664
p-value0.274062345359740
Lambda-14.0501234602525

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -38.4709429813567 \tabularnewline
beta & 15.0501234602525 \tabularnewline
S.D. & 11.2711639921533 \tabularnewline
T-STAT & 1.33527677094664 \tabularnewline
p-value & 0.274062345359740 \tabularnewline
Lambda & -14.0501234602525 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69443&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-38.4709429813567[/C][/ROW]
[ROW][C]beta[/C][C]15.0501234602525[/C][/ROW]
[ROW][C]S.D.[/C][C]11.2711639921533[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.33527677094664[/C][/ROW]
[ROW][C]p-value[/C][C]0.274062345359740[/C][/ROW]
[ROW][C]Lambda[/C][C]-14.0501234602525[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69443&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69443&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-38.4709429813567
beta15.0501234602525
S.D.11.2711639921533
T-STAT1.33527677094664
p-value0.274062345359740
Lambda-14.0501234602525


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')