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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 computationMon, 20 Dec 2010 14:52:00 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/20/t1292856603qm2tkvpb0fac3tz.htm/, Retrieved Sat, 04 May 2024 04:14:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112979, Retrieved Sat, 04 May 2024 04:14:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact108

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] [Unemployment] [2010-11-29 10:34:47] [b98453cac15ba1066b407e146608df68]
-   PD    [Standard Deviation-Mean Plot] [test 4] [2010-12-05 10:51:45] [74be16979710d4c4e7c6647856088456]
-           [Standard Deviation-Mean Plot] [W9 - Blog 7] [2010-12-06 15:54:04] [1aa8d85d6b335d32b1f6be940e33a166]
-   PD          [Standard Deviation-Mean Plot] [SMP Whisky] [2010-12-20 14:52:00] [47bfda5353cd53c1cf7ea7aa9038654a] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
16,46
16,49
16,59
16,58
16,60
16,55
16,57
16,51
16,50
16,49
16,44
16,26
16,33
16,72
16,75
16,74
16,84
16,79
16,66
16,69
16,84
16,86
16,76
16,72
16,29
16,29
16,46
16,54
16,70
16,82
16,88
16,89
16,92
16,88
16,91
16,80
16,78
17,03
17,18
17,12
17,11
17,14
17,17
17,21
17,22
17,19
17,15
17,10
17,21
17,33
17,30
17,33
17,35
17,43
17,46
17,50
17,54
17,56
17,44
17,41
17,72
17,79
17,83
17,76
17,95
17,91
17,96
17,98
17,89
17,88
17,91
17,51
17,63

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'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112979&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112979&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112979&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'RServer@AstonUniversity' @ vre.aston.ac.uk






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
116.50333333333330.09286679936469410.34
216.7250.1389898622856430.530000000000001
316.69833333333330.2406745570770670.630000000000003
417.11666666666670.1185007351978210.439999999999998
517.4050.104228769366410.349999999999998
617.84083333333330.1322159619942330.469999999999999

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 16.5033333333333 & 0.0928667993646941 & 0.34 \tabularnewline
2 & 16.725 & 0.138989862285643 & 0.530000000000001 \tabularnewline
3 & 16.6983333333333 & 0.240674557077067 & 0.630000000000003 \tabularnewline
4 & 17.1166666666667 & 0.118500735197821 & 0.439999999999998 \tabularnewline
5 & 17.405 & 0.10422876936641 & 0.349999999999998 \tabularnewline
6 & 17.8408333333333 & 0.132215961994233 & 0.469999999999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112979&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]16.5033333333333[/C][C]0.0928667993646941[/C][C]0.34[/C][/ROW]
[ROW][C]2[/C][C]16.725[/C][C]0.138989862285643[/C][C]0.530000000000001[/C][/ROW]
[ROW][C]3[/C][C]16.6983333333333[/C][C]0.240674557077067[/C][C]0.630000000000003[/C][/ROW]
[ROW][C]4[/C][C]17.1166666666667[/C][C]0.118500735197821[/C][C]0.439999999999998[/C][/ROW]
[ROW][C]5[/C][C]17.405[/C][C]0.10422876936641[/C][C]0.349999999999998[/C][/ROW]
[ROW][C]6[/C][C]17.8408333333333[/C][C]0.132215961994233[/C][C]0.469999999999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112979&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112979&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
116.50333333333330.09286679936469410.34
216.7250.1389898622856430.530000000000001
316.69833333333330.2406745570770670.630000000000003
417.11666666666670.1185007351978210.439999999999998
517.4050.104228769366410.349999999999998
617.84083333333330.1322159619942330.469999999999999






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.531187798623266
beta-0.0230684263382769
S.D.0.0511754853530387
T-STAT-0.45077103185514
p-value0.675509366826076

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.531187798623266 \tabularnewline
beta & -0.0230684263382769 \tabularnewline
S.D. & 0.0511754853530387 \tabularnewline
T-STAT & -0.45077103185514 \tabularnewline
p-value & 0.675509366826076 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112979&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.531187798623266[/C][/ROW]
[ROW][C]beta[/C][C]-0.0230684263382769[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0511754853530387[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.45077103185514[/C][/ROW]
[ROW][C]p-value[/C][C]0.675509366826076[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112979&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112979&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)
alpha0.531187798623266
beta-0.0230684263382769
S.D.0.0511754853530387
T-STAT-0.45077103185514
p-value0.675509366826076






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha2.70607744961407
beta-1.67085416083444
S.D.5.5744293116352
T-STAT-0.299735464820938
p-value0.779309103728253
Lambda2.67085416083444

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 2.70607744961407 \tabularnewline
beta & -1.67085416083444 \tabularnewline
S.D. & 5.5744293116352 \tabularnewline
T-STAT & -0.299735464820938 \tabularnewline
p-value & 0.779309103728253 \tabularnewline
Lambda & 2.67085416083444 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112979&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.70607744961407[/C][/ROW]
[ROW][C]beta[/C][C]-1.67085416083444[/C][/ROW]
[ROW][C]S.D.[/C][C]5.5744293116352[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.299735464820938[/C][/ROW]
[ROW][C]p-value[/C][C]0.779309103728253[/C][/ROW]
[ROW][C]Lambda[/C][C]2.67085416083444[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112979&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112979&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)
alpha2.70607744961407
beta-1.67085416083444
S.D.5.5744293116352
T-STAT-0.299735464820938
p-value0.779309103728253
Lambda2.67085416083444


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')