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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationSat, 17 May 2008 02:42:48 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/17/t1211013830w2sipam4spmh9rs.htm/, Retrieved Tue, 14 May 2024 09:03:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=12623, Retrieved Tue, 14 May 2024 09:03:58 +0000
QR Codes:

Original text written by user:bron: belgostat
IsPrivate?No (this computation is public)
User-defined keywordsperiode: januari 2000 tot januari 2008
Estimated Impact207

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] [Laurane Potié -Go...] [2008-05-17 08:42:48] [8c9b3412c86ca5b785d4e204c3e8d338] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9026
9787
9536
9490
9736
9694
9647
9753
10070
10137
9984
9732
9103
9155
9308
9394
9948
10177
10002
9728
10002
10063
10018
9960
10236
10893
10756
10940
10997
10827
10166
10186
10457
10368
10244
10511
10812
10738
10171
9721
9897
9828
9924
10371
10846
10413
10709
10662
10570
10297
10635
10872
10296
10383
10431
10574
10653
10805
10872
10625
10407
10463
10556
10646
10702
11353
11346
11451
11964
12574
13031
13812
14544
14931
14886
16005
17064
15168
16050
15839
15137
14954
15648
15305
15579
16348
15928
16171
15937
15713
15594
15683
16438
17032
17696
17745
19394

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12623&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]3 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=12623&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12623&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 time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
19716293.2991026859161111
29738.16666666667387.9985551363291074
310548.4166666667316.826725896702831
410341418.4949223108931125
510584.4166666667202.975349301935576
611525.41666666671112.953683454603405
715460.9166666667695.1090768993592520
816322775.6835109056462166

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 9716 & 293.299102685916 & 1111 \tabularnewline
2 & 9738.16666666667 & 387.998555136329 & 1074 \tabularnewline
3 & 10548.4166666667 & 316.826725896702 & 831 \tabularnewline
4 & 10341 & 418.494922310893 & 1125 \tabularnewline
5 & 10584.4166666667 & 202.975349301935 & 576 \tabularnewline
6 & 11525.4166666667 & 1112.95368345460 & 3405 \tabularnewline
7 & 15460.9166666667 & 695.109076899359 & 2520 \tabularnewline
8 & 16322 & 775.683510905646 & 2166 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12623&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]9716[/C][C]293.299102685916[/C][C]1111[/C][/ROW]
[ROW][C]2[/C][C]9738.16666666667[/C][C]387.998555136329[/C][C]1074[/C][/ROW]
[ROW][C]3[/C][C]10548.4166666667[/C][C]316.826725896702[/C][C]831[/C][/ROW]
[ROW][C]4[/C][C]10341[/C][C]418.494922310893[/C][C]1125[/C][/ROW]
[ROW][C]5[/C][C]10584.4166666667[/C][C]202.975349301935[/C][C]576[/C][/ROW]
[ROW][C]6[/C][C]11525.4166666667[/C][C]1112.95368345460[/C][C]3405[/C][/ROW]
[ROW][C]7[/C][C]15460.9166666667[/C][C]695.109076899359[/C][C]2520[/C][/ROW]
[ROW][C]8[/C][C]16322[/C][C]775.683510905646[/C][C]2166[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12623&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12623&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
19716293.2991026859161111
29738.16666666667387.9985551363291074
310548.4166666667316.826725896702831
410341418.4949223108931125
510584.4166666667202.975349301935576
611525.41666666671112.953683454603405
715460.9166666667695.1090768993592520
816322775.6835109056462166






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-257.013286469029
beta0.0664228646949012
S.D.0.0400031272586681
T-STAT1.66044180159711
p-value0.147892956018625

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -257.013286469029 \tabularnewline
beta & 0.0664228646949012 \tabularnewline
S.D. & 0.0400031272586681 \tabularnewline
T-STAT & 1.66044180159711 \tabularnewline
p-value & 0.147892956018625 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12623&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-257.013286469029[/C][/ROW]
[ROW][C]beta[/C][C]0.0664228646949012[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0400031272586681[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.66044180159711[/C][/ROW]
[ROW][C]p-value[/C][C]0.147892956018625[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12623&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12623&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-257.013286469029
beta0.0664228646949012
S.D.0.0400031272586681
T-STAT1.66044180159711
p-value0.147892956018625






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-10.6121917526551
beta1.78865170685891
S.D.0.87450719601605
T-STAT2.04532531579773
p-value0.0868019956680664
Lambda-0.78865170685891

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -10.6121917526551 \tabularnewline
beta & 1.78865170685891 \tabularnewline
S.D. & 0.87450719601605 \tabularnewline
T-STAT & 2.04532531579773 \tabularnewline
p-value & 0.0868019956680664 \tabularnewline
Lambda & -0.78865170685891 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12623&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-10.6121917526551[/C][/ROW]
[ROW][C]beta[/C][C]1.78865170685891[/C][/ROW]
[ROW][C]S.D.[/C][C]0.87450719601605[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.04532531579773[/C][/ROW]
[ROW][C]p-value[/C][C]0.0868019956680664[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.78865170685891[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12623&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12623&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-10.6121917526551
beta1.78865170685891
S.D.0.87450719601605
T-STAT2.04532531579773
p-value0.0868019956680664
Lambda-0.78865170685891


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')