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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, 19 Dec 2010 14:23:46 +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/19/t1292768541zcov5jt68m8kwqh.htm/, Retrieved Sat, 04 May 2024 20:14:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112423, Retrieved Sat, 04 May 2024 20:14:23 +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] [] [2008-12-08 19:22:39] [d2d412c7f4d35ffbf5ee5ee89db327d4]
- RMP   [Standard Deviation-Mean Plot] [] [2010-12-14 14:15:51] [c91278f1cd2d8b4eeb874e50bb706c21]
-    D      [Standard Deviation-Mean Plot] [] [2010-12-19 14:23:46] [c1585b71a1b15294a02e0a160577aa4f] [Current]
-    D        [Standard Deviation-Mean Plot] [] [2010-12-21 16:16:49] [c91278f1cd2d8b4eeb874e50bb706c21]
-    D        [Standard Deviation-Mean Plot] [] [2010-12-21 16:16:49] [c91278f1cd2d8b4eeb874e50bb706c21]
-               [Standard Deviation-Mean Plot] [] [2010-12-27 23:46:33] [2e1e44f0ae3cb9513dc28781dfdb387b]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
364
351
380
319
322
386
221
187
343
342
365
313
356
337
389
326
343
357
220
218
391
425
332
298
360
336
325
393
301
426
265
210
429
440
357
431
442
422
544
420
396
482
261
211
448
468
464
425
415
433
531
457
380
481
302
216
509
417
370

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=112423&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=112423&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112423&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
1324.41666666666761.2007996580754199
2332.66666666666762.8509540440113207
3356.08333333333372.7879339817619230
4415.2592.4535509913442333

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 324.416666666667 & 61.2007996580754 & 199 \tabularnewline
2 & 332.666666666667 & 62.8509540440113 & 207 \tabularnewline
3 & 356.083333333333 & 72.7879339817619 & 230 \tabularnewline
4 & 415.25 & 92.4535509913442 & 333 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112423&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]324.416666666667[/C][C]61.2007996580754[/C][C]199[/C][/ROW]
[ROW][C]2[/C][C]332.666666666667[/C][C]62.8509540440113[/C][C]207[/C][/ROW]
[ROW][C]3[/C][C]356.083333333333[/C][C]72.7879339817619[/C][C]230[/C][/ROW]
[ROW][C]4[/C][C]415.25[/C][C]92.4535509913442[/C][C]333[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112423&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112423&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
1324.41666666666761.2007996580754199
2332.66666666666762.8509540440113207
3356.08333333333372.7879339817619230
4415.2592.4535509913442333






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-52.5490806065714
beta0.349680574833308
S.D.0.0128615828384180
T-STAT27.1879891632622
p-value0.00135009901229898

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -52.5490806065714 \tabularnewline
beta & 0.349680574833308 \tabularnewline
S.D. & 0.0128615828384180 \tabularnewline
T-STAT & 27.1879891632622 \tabularnewline
p-value & 0.00135009901229898 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112423&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-52.5490806065714[/C][/ROW]
[ROW][C]beta[/C][C]0.349680574833308[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0128615828384180[/C][/ROW]
[ROW][C]T-STAT[/C][C]27.1879891632622[/C][/ROW]
[ROW][C]p-value[/C][C]0.00135009901229898[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112423&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112423&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-52.5490806065714
beta0.349680574833308
S.D.0.0128615828384180
T-STAT27.1879891632622
p-value0.00135009901229898






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-5.71529846232004
beta1.69965568409605
S.D.0.083874664754815
T-STAT20.2642322215479
p-value0.00242636880445572
Lambda-0.699655684096048

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -5.71529846232004 \tabularnewline
beta & 1.69965568409605 \tabularnewline
S.D. & 0.083874664754815 \tabularnewline
T-STAT & 20.2642322215479 \tabularnewline
p-value & 0.00242636880445572 \tabularnewline
Lambda & -0.699655684096048 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112423&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-5.71529846232004[/C][/ROW]
[ROW][C]beta[/C][C]1.69965568409605[/C][/ROW]
[ROW][C]S.D.[/C][C]0.083874664754815[/C][/ROW]
[ROW][C]T-STAT[/C][C]20.2642322215479[/C][/ROW]
[ROW][C]p-value[/C][C]0.00242636880445572[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.699655684096048[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112423&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112423&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-5.71529846232004
beta1.69965568409605
S.D.0.083874664754815
T-STAT20.2642322215479
p-value0.00242636880445572
Lambda-0.699655684096048


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')