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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 computationSun, 07 Dec 2008 10:37:06 -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/2008/Dec/07/t1228671699941m2r8s3y9t4q7.htm/, Retrieved Sun, 19 May 2024 12:34:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30192, Retrieved Sun, 19 May 2024 12:34:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact187

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]
- RMPD    [Standard Deviation-Mean Plot] [S1] [2008-12-07 17:37:06] [5f3e73ccf1ddc75508eed47fa51813d3] [Current]
-    D      [Standard Deviation-Mean Plot] [S1] [2008-12-07 17:58:18] [a0d819c22534897f04a2f0b92f1eb36a]
- RM          [Variance Reduction Matrix] [s2] [2008-12-07 18:02:35] [a0d819c22534897f04a2f0b92f1eb36a]
- RMP           [(Partial) Autocorrelation Function] [S2 ACF] [2008-12-07 18:10:24] [a0d819c22534897f04a2f0b92f1eb36a]
-   P             [(Partial) Autocorrelation Function] [s2] [2008-12-07 18:12:59] [a0d819c22534897f04a2f0b92f1eb36a]
-   P               [(Partial) Autocorrelation Function] [s2 ACF] [2008-12-07 18:25:03] [a0d819c22534897f04a2f0b92f1eb36a]
-                     [(Partial) Autocorrelation Function] [s2 acf d1D1] [2008-12-07 18:26:56] [a0d819c22534897f04a2f0b92f1eb36a]
- RM                    [Spectral Analysis] [S2 SA - d0 D0 L1] [2008-12-07 18:29:54] [a0d819c22534897f04a2f0b92f1eb36a]
-                         [Spectral Analysis] [s2 SA d1D1 L1] [2008-12-07 18:32:14] [a0d819c22534897f04a2f0b92f1eb36a]
-                           [Spectral Analysis] [s3] [2008-12-07 18:39:13] [a0d819c22534897f04a2f0b92f1eb36a]
-                             [Spectral Analysis] [s3 sa] [2008-12-07 18:42:05] [a0d819c22534897f04a2f0b92f1eb36a]
- RM                            [(Partial) Autocorrelation Function] [s4] [2008-12-07 18:48:27] [a0d819c22534897f04a2f0b92f1eb36a]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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

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=30192&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=30192&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30192&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
1573.33333333333329.10586736641876
2596.08333333333321.977088620707362
3591.66666666666720.526405757787560
4536.16666666666722.032345368213666
5504.7519.484842593900865

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 573.333333333333 & 29.105867366418 & 76 \tabularnewline
2 & 596.083333333333 & 21.9770886207073 & 62 \tabularnewline
3 & 591.666666666667 & 20.5264057577875 & 60 \tabularnewline
4 & 536.166666666667 & 22.0323453682136 & 66 \tabularnewline
5 & 504.75 & 19.4848425939008 & 65 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30192&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]573.333333333333[/C][C]29.105867366418[/C][C]76[/C][/ROW]
[ROW][C]2[/C][C]596.083333333333[/C][C]21.9770886207073[/C][C]62[/C][/ROW]
[ROW][C]3[/C][C]591.666666666667[/C][C]20.5264057577875[/C][C]60[/C][/ROW]
[ROW][C]4[/C][C]536.166666666667[/C][C]22.0323453682136[/C][C]66[/C][/ROW]
[ROW][C]5[/C][C]504.75[/C][C]19.4848425939008[/C][C]65[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30192&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30192&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
1573.33333333333329.10586736641876
2596.08333333333321.977088620707362
3591.66666666666720.526405757787560
4536.16666666666722.032345368213666
5504.7519.484842593900865






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha5.71002422443165
beta0.0301843071323587
S.D.0.0530273163011595
T-STAT0.569221850884025
p-value0.609034852307422

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 5.71002422443165 \tabularnewline
beta & 0.0301843071323587 \tabularnewline
S.D. & 0.0530273163011595 \tabularnewline
T-STAT & 0.569221850884025 \tabularnewline
p-value & 0.609034852307422 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30192&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]5.71002422443165[/C][/ROW]
[ROW][C]beta[/C][C]0.0301843071323587[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0530273163011595[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.569221850884025[/C][/ROW]
[ROW][C]p-value[/C][C]0.609034852307422[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30192&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30192&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)
alpha5.71002422443165
beta0.0301843071323587
S.D.0.0530273163011595
T-STAT0.569221850884025
p-value0.609034852307422






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.71608301267087
beta0.762652532012433
S.D.1.18271477628692
T-STAT0.644832166895508
p-value0.564952738901996
Lambda0.237347467987567

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.71608301267087 \tabularnewline
beta & 0.762652532012433 \tabularnewline
S.D. & 1.18271477628692 \tabularnewline
T-STAT & 0.644832166895508 \tabularnewline
p-value & 0.564952738901996 \tabularnewline
Lambda & 0.237347467987567 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30192&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.71608301267087[/C][/ROW]
[ROW][C]beta[/C][C]0.762652532012433[/C][/ROW]
[ROW][C]S.D.[/C][C]1.18271477628692[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.644832166895508[/C][/ROW]
[ROW][C]p-value[/C][C]0.564952738901996[/C][/ROW]
[ROW][C]Lambda[/C][C]0.237347467987567[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30192&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30192&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-1.71608301267087
beta0.762652532012433
S.D.1.18271477628692
T-STAT0.644832166895508
p-value0.564952738901996
Lambda0.237347467987567


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')