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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, 02 Dec 2009 06:53:55 -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/02/t1259762209jq6lao72tswtqwt.htm/, Retrieved Sat, 27 Apr 2024 16:48:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=62356, Retrieved Sat, 27 Apr 2024 16:48:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact170

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] [] [2009-11-27 14:40:44] [b98453cac15ba1066b407e146608df68]
-    D      [Standard Deviation-Mean Plot] [St dev - mean plot] [2009-12-02 13:53:55] [a93df6747c5c78315f2ee9914aea3ec6] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2.085
2.053
2.077
2.058
2.057
2.076
2.07
2.062
2.073
2.061
2.094
2.067
2.086
2.276
2.326
2.349
2.52
2.628
2.577
2.698
2.814
2.968
3.041
3.278
3.328
3.5
3.563
3.569
3.69
3.819
3.79
3.956
4.063
4.047
4.029
3.941
4.022
3.879
4.022
4.028
4.091
3.987
4.01
4.007
4.191
4.299
4.273
3.82
3.15
2.486
1.812
1.257
1.062
0.842
0.782
0.698
0.358
0.347
0.363
0.359
0.355

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=62356&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=62356&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62356&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
12.069416666666670.01223600003962480.0409999999999999
22.630083333333330.3502065516061611.192
33.774583333333330.2438253690780770.735
44.052416666666670.1429662759555770.479000000000001
51.126333333333330.9138990727380762.803

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 2.06941666666667 & 0.0122360000396248 & 0.0409999999999999 \tabularnewline
2 & 2.63008333333333 & 0.350206551606161 & 1.192 \tabularnewline
3 & 3.77458333333333 & 0.243825369078077 & 0.735 \tabularnewline
4 & 4.05241666666667 & 0.142966275955577 & 0.479000000000001 \tabularnewline
5 & 1.12633333333333 & 0.913899072738076 & 2.803 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62356&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]2.06941666666667[/C][C]0.0122360000396248[/C][C]0.0409999999999999[/C][/ROW]
[ROW][C]2[/C][C]2.63008333333333[/C][C]0.350206551606161[/C][C]1.192[/C][/ROW]
[ROW][C]3[/C][C]3.77458333333333[/C][C]0.243825369078077[/C][C]0.735[/C][/ROW]
[ROW][C]4[/C][C]4.05241666666667[/C][C]0.142966275955577[/C][C]0.479000000000001[/C][/ROW]
[ROW][C]5[/C][C]1.12633333333333[/C][C]0.913899072738076[/C][C]2.803[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62356&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62356&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
12.069416666666670.01223600003962480.0409999999999999
22.630083333333330.3502065516061611.192
33.774583333333330.2438253690780770.735
44.052416666666670.1429662759555770.479000000000001
51.126333333333330.9138990727380762.803






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.829443556913396
beta-0.181946446902313
S.D.0.12862787739395
T-STAT-1.41451799243382
p-value0.252134946505349

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.829443556913396 \tabularnewline
beta & -0.181946446902313 \tabularnewline
S.D. & 0.12862787739395 \tabularnewline
T-STAT & -1.41451799243382 \tabularnewline
p-value & 0.252134946505349 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62356&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.829443556913396[/C][/ROW]
[ROW][C]beta[/C][C]-0.181946446902313[/C][/ROW]
[ROW][C]S.D.[/C][C]0.12862787739395[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.41451799243382[/C][/ROW]
[ROW][C]p-value[/C][C]0.252134946505349[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62356&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62356&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)
alpha0.829443556913396
beta-0.181946446902313
S.D.0.12862787739395
T-STAT-1.41451799243382
p-value0.252134946505349






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.15368610935228
beta-0.689442920578763
S.D.1.75272437625738
T-STAT-0.393355013439672
p-value0.720345159221468
Lambda1.68944292057876

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.15368610935228 \tabularnewline
beta & -0.689442920578763 \tabularnewline
S.D. & 1.75272437625738 \tabularnewline
T-STAT & -0.393355013439672 \tabularnewline
p-value & 0.720345159221468 \tabularnewline
Lambda & 1.68944292057876 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62356&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.15368610935228[/C][/ROW]
[ROW][C]beta[/C][C]-0.689442920578763[/C][/ROW]
[ROW][C]S.D.[/C][C]1.75272437625738[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.393355013439672[/C][/ROW]
[ROW][C]p-value[/C][C]0.720345159221468[/C][/ROW]
[ROW][C]Lambda[/C][C]1.68944292057876[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62356&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62356&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-1.15368610935228
beta-0.689442920578763
S.D.1.75272437625738
T-STAT-0.393355013439672
p-value0.720345159221468
Lambda1.68944292057876


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')