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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, 29 Dec 2010 13:18:25 +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/29/t1293628565845pkmqaifbn908.htm/, Retrieved Fri, 03 May 2024 04:51:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116800, Retrieved Fri, 03 May 2024 04:51:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact107

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] [] [2010-12-22 22:30:51] [29e492448d11757ae0fad5ef6e7f8e86]
-    D    [Standard Deviation-Mean Plot] [] [2010-12-29 13:18:25] [e180d4cd19004beeddc12e67012247dc] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
09,166456
07,970589
07,104091
06,621064
07,529215
08,170938
08,157450
07,378962
07,921496
08,156740
08,856365
08,817177
08,734347
09,345927
08,992970
10,785120
08,886867
08,818847
08,823744
09,165298
08,652657
08,173054
07,563416
07,595809
08,381467
07,216432
06,540178
06,238914
05,487288
05,759462
05,993215
07,474726
07,348907
07,303379
07,119314
06,993780
06,958153
07,595706
08,088153
07,555753
07,315433
07,893427
08,858794
08,839367
08,014733
07,873465
08,930377
10,500550
12,611440
11,417870
11,872490
11,060820
12,043310
09,776299
09,557194
09,202590
10,224020
09,350807
08,300913
08,365779
08,133595
07,660470
08,074839
07,848597
07,998220
07,396895
07,900419
08,100500
07,899453
07,599783
08,100929
09,002175
10,298900
10,101520
10,699150
09,698140
09,800951
10,900470
10,697850
09,297252
10,397440
10,900720
12,901270
13,099060
11,698280
11,099870
11,301570
10,702110
10,099310
09,591119

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=116800&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=116800&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116800&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
17.987545250.7481460218339882.545392
28.7948380.8429310538855153.221704
36.821421833333330.8343512712089372.894179
48.201992583333330.9544654297605983.542397
510.31529433333331.457111559362654.310527
67.976322916666670.3958311064195891.60528
710.73272691666671.170043688283433.801808

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 7.98754525 & 0.748146021833988 & 2.545392 \tabularnewline
2 & 8.794838 & 0.842931053885515 & 3.221704 \tabularnewline
3 & 6.82142183333333 & 0.834351271208937 & 2.894179 \tabularnewline
4 & 8.20199258333333 & 0.954465429760598 & 3.542397 \tabularnewline
5 & 10.3152943333333 & 1.45711155936265 & 4.310527 \tabularnewline
6 & 7.97632291666667 & 0.395831106419589 & 1.60528 \tabularnewline
7 & 10.7327269166667 & 1.17004368828343 & 3.801808 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116800&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]7.98754525[/C][C]0.748146021833988[/C][C]2.545392[/C][/ROW]
[ROW][C]2[/C][C]8.794838[/C][C]0.842931053885515[/C][C]3.221704[/C][/ROW]
[ROW][C]3[/C][C]6.82142183333333[/C][C]0.834351271208937[/C][C]2.894179[/C][/ROW]
[ROW][C]4[/C][C]8.20199258333333[/C][C]0.954465429760598[/C][C]3.542397[/C][/ROW]
[ROW][C]5[/C][C]10.3152943333333[/C][C]1.45711155936265[/C][C]4.310527[/C][/ROW]
[ROW][C]6[/C][C]7.97632291666667[/C][C]0.395831106419589[/C][C]1.60528[/C][/ROW]
[ROW][C]7[/C][C]10.7327269166667[/C][C]1.17004368828343[/C][C]3.801808[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116800&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116800&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
17.987545250.7481460218339882.545392
28.7948380.8429310538855153.221704
36.821421833333330.8343512712089372.894179
48.201992583333330.9544654297605983.542397
510.31529433333331.457111559362654.310527
67.976322916666670.3958311064195891.60528
710.73272691666671.170043688283433.801808






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.599339833323904
beta0.174227096051492
S.D.0.0742651946613059
T-STAT2.34601278359361
p-value0.0658857936092111

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.599339833323904 \tabularnewline
beta & 0.174227096051492 \tabularnewline
S.D. & 0.0742651946613059 \tabularnewline
T-STAT & 2.34601278359361 \tabularnewline
p-value & 0.0658857936092111 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116800&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.599339833323904[/C][/ROW]
[ROW][C]beta[/C][C]0.174227096051492[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0742651946613059[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.34601278359361[/C][/ROW]
[ROW][C]p-value[/C][C]0.0658857936092111[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116800&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116800&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-0.599339833323904
beta0.174227096051492
S.D.0.0742651946613059
T-STAT2.34601278359361
p-value0.0658857936092111






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.52345353235084
beta1.56589207801908
S.D.0.924159640781895
T-STAT1.69439565300021
p-value0.15096356681979
Lambda-0.565892078019076

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.52345353235084 \tabularnewline
beta & 1.56589207801908 \tabularnewline
S.D. & 0.924159640781895 \tabularnewline
T-STAT & 1.69439565300021 \tabularnewline
p-value & 0.15096356681979 \tabularnewline
Lambda & -0.565892078019076 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116800&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.52345353235084[/C][/ROW]
[ROW][C]beta[/C][C]1.56589207801908[/C][/ROW]
[ROW][C]S.D.[/C][C]0.924159640781895[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.69439565300021[/C][/ROW]
[ROW][C]p-value[/C][C]0.15096356681979[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.565892078019076[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116800&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116800&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-3.52345353235084
beta1.56589207801908
S.D.0.924159640781895
T-STAT1.69439565300021
p-value0.15096356681979
Lambda-0.565892078019076


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')