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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 computationTue, 01 Dec 2009 12:37:41 -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/01/t12596963304lqe6nut63c01fo.htm/, Retrieved Fri, 26 Apr 2024 20:44:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=62210, Retrieved Fri, 26 Apr 2024 20:44:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact158

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   [ARIMA Backward Selection] [] [2009-11-27 14:53:14] [b98453cac15ba1066b407e146608df68]
- RMPD      [Standard Deviation-Mean Plot] [Workshop 9 - opga...] [2009-12-01 19:37:41] [d41d8cd98f00b204e9800998ecf8427e] [Current]
-    D        [Standard Deviation-Mean Plot] [] [2009-12-07 14:15:47] [3af9fa3d2c04a43d660a9a466bdfbaa0]
- R  D          [Standard Deviation-Mean Plot] [Workshop9 R3 blog 1] [2009-12-11 10:40:37] [143cbdcaf7333bdd9926a1dde50d1082]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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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=62210&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=62210&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62210&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
10.0575815165020320.7829586181335922.85604141920762
2-0.2703122056324300.59514219995411.72640113808987
3-0.1537620198709210.752893835050862.47133844116357
4-0.02682169154699510.3883983639857721.07880568401176
50.2668604150599840.6193959893608931.91026385412779
6-0.04904095032911840.6336327871377472.34989284691035
7-0.05404313537444370.439113707028251.34565267956362
80.00743014287568020.6947118504202152.01471924040206
90.1042049137560080.5412240737583531.55965754758747
10-0.01981137188009240.6628788280819592.21440852115091
11-0.1038654363376910.5325256960528461.72958061696699
120.1539158473609000.7309925322504442.17132614408817
13-0.1770998918514990.2806012508465851.01790129622526
14-0.01960395103658750.5620760592961941.77003127409635
15-0.006845398992363120.4155649373529291.29014079107386
16-0.05587504110812210.5644738949056592.24986399457946
17-0.08508890269964560.4292356207122191.25615087181410
180.04019087786979660.3928457937899761.09754721270227
190.001937303965221990.6534580587150862.49123793576910
20-0.01021033286825920.667673581159972.58525481769413
210.05799712327836840.4675464100389551.63295346510947
220.3171602564278150.3463172988033871.15338758495194
23-0.08923153805114340.3597987601950061.10863584643172
24-0.1510514091003890.2960948895773121.0923623570916
250.02617068303922700.3300548491549901.24099780132598
260.2620162245274880.4530245706345751.34912469403316
27-0.06552803387844870.6892586320558972.94240160932535
28-0.07480233365957780.3553453964580961.16972454038064
29-0.1954437124141750.4712704864662221.38292917996791
300.02855238661860130.4019716275568041.42878854373818

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 0.057581516502032 & 0.782958618133592 & 2.85604141920762 \tabularnewline
2 & -0.270312205632430 & 0.5951421999541 & 1.72640113808987 \tabularnewline
3 & -0.153762019870921 & 0.75289383505086 & 2.47133844116357 \tabularnewline
4 & -0.0268216915469951 & 0.388398363985772 & 1.07880568401176 \tabularnewline
5 & 0.266860415059984 & 0.619395989360893 & 1.91026385412779 \tabularnewline
6 & -0.0490409503291184 & 0.633632787137747 & 2.34989284691035 \tabularnewline
7 & -0.0540431353744437 & 0.43911370702825 & 1.34565267956362 \tabularnewline
8 & 0.0074301428756802 & 0.694711850420215 & 2.01471924040206 \tabularnewline
9 & 0.104204913756008 & 0.541224073758353 & 1.55965754758747 \tabularnewline
10 & -0.0198113718800924 & 0.662878828081959 & 2.21440852115091 \tabularnewline
11 & -0.103865436337691 & 0.532525696052846 & 1.72958061696699 \tabularnewline
12 & 0.153915847360900 & 0.730992532250444 & 2.17132614408817 \tabularnewline
13 & -0.177099891851499 & 0.280601250846585 & 1.01790129622526 \tabularnewline
14 & -0.0196039510365875 & 0.562076059296194 & 1.77003127409635 \tabularnewline
15 & -0.00684539899236312 & 0.415564937352929 & 1.29014079107386 \tabularnewline
16 & -0.0558750411081221 & 0.564473894905659 & 2.24986399457946 \tabularnewline
17 & -0.0850889026996456 & 0.429235620712219 & 1.25615087181410 \tabularnewline
18 & 0.0401908778697966 & 0.392845793789976 & 1.09754721270227 \tabularnewline
19 & 0.00193730396522199 & 0.653458058715086 & 2.49123793576910 \tabularnewline
20 & -0.0102103328682592 & 0.66767358115997 & 2.58525481769413 \tabularnewline
21 & 0.0579971232783684 & 0.467546410038955 & 1.63295346510947 \tabularnewline
22 & 0.317160256427815 & 0.346317298803387 & 1.15338758495194 \tabularnewline
23 & -0.0892315380511434 & 0.359798760195006 & 1.10863584643172 \tabularnewline
24 & -0.151051409100389 & 0.296094889577312 & 1.0923623570916 \tabularnewline
25 & 0.0261706830392270 & 0.330054849154990 & 1.24099780132598 \tabularnewline
26 & 0.262016224527488 & 0.453024570634575 & 1.34912469403316 \tabularnewline
27 & -0.0655280338784487 & 0.689258632055897 & 2.94240160932535 \tabularnewline
28 & -0.0748023336595778 & 0.355345396458096 & 1.16972454038064 \tabularnewline
29 & -0.195443712414175 & 0.471270486466222 & 1.38292917996791 \tabularnewline
30 & 0.0285523866186013 & 0.401971627556804 & 1.42878854373818 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62210&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]0.057581516502032[/C][C]0.782958618133592[/C][C]2.85604141920762[/C][/ROW]
[ROW][C]2[/C][C]-0.270312205632430[/C][C]0.5951421999541[/C][C]1.72640113808987[/C][/ROW]
[ROW][C]3[/C][C]-0.153762019870921[/C][C]0.75289383505086[/C][C]2.47133844116357[/C][/ROW]
[ROW][C]4[/C][C]-0.0268216915469951[/C][C]0.388398363985772[/C][C]1.07880568401176[/C][/ROW]
[ROW][C]5[/C][C]0.266860415059984[/C][C]0.619395989360893[/C][C]1.91026385412779[/C][/ROW]
[ROW][C]6[/C][C]-0.0490409503291184[/C][C]0.633632787137747[/C][C]2.34989284691035[/C][/ROW]
[ROW][C]7[/C][C]-0.0540431353744437[/C][C]0.43911370702825[/C][C]1.34565267956362[/C][/ROW]
[ROW][C]8[/C][C]0.0074301428756802[/C][C]0.694711850420215[/C][C]2.01471924040206[/C][/ROW]
[ROW][C]9[/C][C]0.104204913756008[/C][C]0.541224073758353[/C][C]1.55965754758747[/C][/ROW]
[ROW][C]10[/C][C]-0.0198113718800924[/C][C]0.662878828081959[/C][C]2.21440852115091[/C][/ROW]
[ROW][C]11[/C][C]-0.103865436337691[/C][C]0.532525696052846[/C][C]1.72958061696699[/C][/ROW]
[ROW][C]12[/C][C]0.153915847360900[/C][C]0.730992532250444[/C][C]2.17132614408817[/C][/ROW]
[ROW][C]13[/C][C]-0.177099891851499[/C][C]0.280601250846585[/C][C]1.01790129622526[/C][/ROW]
[ROW][C]14[/C][C]-0.0196039510365875[/C][C]0.562076059296194[/C][C]1.77003127409635[/C][/ROW]
[ROW][C]15[/C][C]-0.00684539899236312[/C][C]0.415564937352929[/C][C]1.29014079107386[/C][/ROW]
[ROW][C]16[/C][C]-0.0558750411081221[/C][C]0.564473894905659[/C][C]2.24986399457946[/C][/ROW]
[ROW][C]17[/C][C]-0.0850889026996456[/C][C]0.429235620712219[/C][C]1.25615087181410[/C][/ROW]
[ROW][C]18[/C][C]0.0401908778697966[/C][C]0.392845793789976[/C][C]1.09754721270227[/C][/ROW]
[ROW][C]19[/C][C]0.00193730396522199[/C][C]0.653458058715086[/C][C]2.49123793576910[/C][/ROW]
[ROW][C]20[/C][C]-0.0102103328682592[/C][C]0.66767358115997[/C][C]2.58525481769413[/C][/ROW]
[ROW][C]21[/C][C]0.0579971232783684[/C][C]0.467546410038955[/C][C]1.63295346510947[/C][/ROW]
[ROW][C]22[/C][C]0.317160256427815[/C][C]0.346317298803387[/C][C]1.15338758495194[/C][/ROW]
[ROW][C]23[/C][C]-0.0892315380511434[/C][C]0.359798760195006[/C][C]1.10863584643172[/C][/ROW]
[ROW][C]24[/C][C]-0.151051409100389[/C][C]0.296094889577312[/C][C]1.0923623570916[/C][/ROW]
[ROW][C]25[/C][C]0.0261706830392270[/C][C]0.330054849154990[/C][C]1.24099780132598[/C][/ROW]
[ROW][C]26[/C][C]0.262016224527488[/C][C]0.453024570634575[/C][C]1.34912469403316[/C][/ROW]
[ROW][C]27[/C][C]-0.0655280338784487[/C][C]0.689258632055897[/C][C]2.94240160932535[/C][/ROW]
[ROW][C]28[/C][C]-0.0748023336595778[/C][C]0.355345396458096[/C][C]1.16972454038064[/C][/ROW]
[ROW][C]29[/C][C]-0.195443712414175[/C][C]0.471270486466222[/C][C]1.38292917996791[/C][/ROW]
[ROW][C]30[/C][C]0.0285523866186013[/C][C]0.401971627556804[/C][C]1.42878854373818[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62210&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62210&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
10.0575815165020320.7829586181335922.85604141920762
2-0.2703122056324300.59514219995411.72640113808987
3-0.1537620198709210.752893835050862.47133844116357
4-0.02682169154699510.3883983639857721.07880568401176
50.2668604150599840.6193959893608931.91026385412779
6-0.04904095032911840.6336327871377472.34989284691035
7-0.05404313537444370.439113707028251.34565267956362
80.00743014287568020.6947118504202152.01471924040206
90.1042049137560080.5412240737583531.55965754758747
10-0.01981137188009240.6628788280819592.21440852115091
11-0.1038654363376910.5325256960528461.72958061696699
120.1539158473609000.7309925322504442.17132614408817
13-0.1770998918514990.2806012508465851.01790129622526
14-0.01960395103658750.5620760592961941.77003127409635
15-0.006845398992363120.4155649373529291.29014079107386
16-0.05587504110812210.5644738949056592.24986399457946
17-0.08508890269964560.4292356207122191.25615087181410
180.04019087786979660.3928457937899761.09754721270227
190.001937303965221990.6534580587150862.49123793576910
20-0.01021033286825920.667673581159972.58525481769413
210.05799712327836840.4675464100389551.63295346510947
220.3171602564278150.3463172988033871.15338758495194
23-0.08923153805114340.3597987601950061.10863584643172
24-0.1510514091003890.2960948895773121.0923623570916
250.02617068303922700.3300548491549901.24099780132598
260.2620162245274880.4530245706345751.34912469403316
27-0.06552803387844870.6892586320558972.94240160932535
28-0.07480233365957780.3553453964580961.16972454038064
29-0.1954437124141750.4712704864662221.38292917996791
300.02855238661860130.4019716275568041.42878854373818






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.517655573868784
beta0.0674588274511613
S.D.0.207983241425307
T-STAT0.324347418517312
p-value0.748085708605218

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.517655573868784 \tabularnewline
beta & 0.0674588274511613 \tabularnewline
S.D. & 0.207983241425307 \tabularnewline
T-STAT & 0.324347418517312 \tabularnewline
p-value & 0.748085708605218 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62210&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.517655573868784[/C][/ROW]
[ROW][C]beta[/C][C]0.0674588274511613[/C][/ROW]
[ROW][C]S.D.[/C][C]0.207983241425307[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.324347418517312[/C][/ROW]
[ROW][C]p-value[/C][C]0.748085708605218[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62210&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62210&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)
alpha0.517655573868784
beta0.0674588274511613
S.D.0.207983241425307
T-STAT0.324347418517312
p-value0.748085708605218






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-0.783208846586725
beta-0.0395150001825585
S.D.0.0609559926686875
T-STAT-0.648254559602258
p-value0.531422691411516
Lambda1.03951500018256

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -0.783208846586725 \tabularnewline
beta & -0.0395150001825585 \tabularnewline
S.D. & 0.0609559926686875 \tabularnewline
T-STAT & -0.648254559602258 \tabularnewline
p-value & 0.531422691411516 \tabularnewline
Lambda & 1.03951500018256 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62210&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.783208846586725[/C][/ROW]
[ROW][C]beta[/C][C]-0.0395150001825585[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0609559926686875[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.648254559602258[/C][/ROW]
[ROW][C]p-value[/C][C]0.531422691411516[/C][/ROW]
[ROW][C]Lambda[/C][C]1.03951500018256[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62210&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62210&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-0.783208846586725
beta-0.0395150001825585
S.D.0.0609559926686875
T-STAT-0.648254559602258
p-value0.531422691411516
Lambda1.03951500018256


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')