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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 computationFri, 04 Dec 2009 07:35:33 -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/04/t1259937391ximbcfnwby2v86p.htm/, Retrieved Sun, 28 Apr 2024 00:02:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63621, Retrieved Sun, 28 Apr 2024 00:02:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact106

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] [] [2009-12-04 14:35:33] [27b6e36591879260e4dc6bb7e89a38fd] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
455
456
517
525
523
519
509
512
519
517
510
509
501
507
569
580
578
565
547
555
562
561
555
544
537
543
594
611
613
611
594
595
591
589
584
573
567
569
621
629
628
612
595
597
593
590
580
574
573
573
620
626
620
588
566
557
561
549
532
526
511
499
555
565
542
527
510
514
517
508
493
490
469
478
528
534
518
506
502
516
528
533
536
537
524
536
587
597
581
564

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=63621&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=63621&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63621&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
1505.91666666666724.122634913116770
255224.921695550080679
3586.2524.576873830345676
4596.2522.054168849366462
5574.2533.5047486457992100
6519.2523.77211888670575
7515.41666666666722.745462417943168

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 505.916666666667 & 24.1226349131167 & 70 \tabularnewline
2 & 552 & 24.9216955500806 & 79 \tabularnewline
3 & 586.25 & 24.5768738303456 & 76 \tabularnewline
4 & 596.25 & 22.0541688493664 & 62 \tabularnewline
5 & 574.25 & 33.5047486457992 & 100 \tabularnewline
6 & 519.25 & 23.772118886705 & 75 \tabularnewline
7 & 515.416666666667 & 22.7454624179431 & 68 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63621&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]505.916666666667[/C][C]24.1226349131167[/C][C]70[/C][/ROW]
[ROW][C]2[/C][C]552[/C][C]24.9216955500806[/C][C]79[/C][/ROW]
[ROW][C]3[/C][C]586.25[/C][C]24.5768738303456[/C][C]76[/C][/ROW]
[ROW][C]4[/C][C]596.25[/C][C]22.0541688493664[/C][C]62[/C][/ROW]
[ROW][C]5[/C][C]574.25[/C][C]33.5047486457992[/C][C]100[/C][/ROW]
[ROW][C]6[/C][C]519.25[/C][C]23.772118886705[/C][C]75[/C][/ROW]
[ROW][C]7[/C][C]515.416666666667[/C][C]22.7454624179431[/C][C]68[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63621&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63621&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
1505.91666666666724.122634913116770
255224.921695550080679
3586.2524.576873830345676
4596.2522.054168849366462
5574.2533.5047486457992100
6519.2523.77211888670575
7515.41666666666722.745462417943168






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha10.9651539791571
beta0.0257035742741402
S.D.0.0452172705802337
T-STAT0.568445948733939
p-value0.59431081272287

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 10.9651539791571 \tabularnewline
beta & 0.0257035742741402 \tabularnewline
S.D. & 0.0452172705802337 \tabularnewline
T-STAT & 0.568445948733939 \tabularnewline
p-value & 0.59431081272287 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63621&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]10.9651539791571[/C][/ROW]
[ROW][C]beta[/C][C]0.0257035742741402[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0452172705802337[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.568445948733939[/C][/ROW]
[ROW][C]p-value[/C][C]0.59431081272287[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63621&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63621&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)
alpha10.9651539791571
beta0.0257035742741402
S.D.0.0452172705802337
T-STAT0.568445948733939
p-value0.59431081272287






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha0.0865325405698563
beta0.495825120461428
S.D.0.894180735941505
T-STAT0.554502127513809
p-value0.603122959811236
Lambda0.504174879538572

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.0865325405698563 \tabularnewline
beta & 0.495825120461428 \tabularnewline
S.D. & 0.894180735941505 \tabularnewline
T-STAT & 0.554502127513809 \tabularnewline
p-value & 0.603122959811236 \tabularnewline
Lambda & 0.504174879538572 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63621&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.0865325405698563[/C][/ROW]
[ROW][C]beta[/C][C]0.495825120461428[/C][/ROW]
[ROW][C]S.D.[/C][C]0.894180735941505[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.554502127513809[/C][/ROW]
[ROW][C]p-value[/C][C]0.603122959811236[/C][/ROW]
[ROW][C]Lambda[/C][C]0.504174879538572[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63621&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63621&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)
alpha0.0865325405698563
beta0.495825120461428
S.D.0.894180735941505
T-STAT0.554502127513809
p-value0.603122959811236
Lambda0.504174879538572


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')