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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationWed, 28 Nov 2007 03:35:50 -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/2007/Nov/28/t1196245831odwss9mh92f8er9.htm/, Retrieved Sun, 26 Oct 2025 03:33:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7000, Retrieved Sun, 26 Oct 2025 03:33:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsbridome
Estimated Impact383

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] [workshop 3] [2007-11-28 10:35:50] [ff60737d3854dcb913eacf6907ce202b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
540
522
526
527
516
503
489
479
475
524
552
532
511
492
492
493
481
462
457
442
439
488
521
501
485
464
460
467
460
448
443
436
431
484
510
513
503
471
471
476
475
470
461
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

Tables (Output of Computation)





Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7000&T=0

[TABLE]
[ROW][C]Summary of compuational 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]3 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=7000&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7000&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1515.41666666666724.107555712353867
2481.58333333333326.203602574432257
3466.7526.761998158854853
4483.58333333333326.081893173524658
5527.529.5988329008241120
6565.58333333333326.1376020786958165
7595.91666666666721.9191005677005186
8596.08333333333319.4303339854949190

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 515.416666666667 & 24.1075557123538 & 67 \tabularnewline
2 & 481.583333333333 & 26.2036025744322 & 57 \tabularnewline
3 & 466.75 & 26.7619981588548 & 53 \tabularnewline
4 & 483.583333333333 & 26.0818931735246 & 58 \tabularnewline
5 & 527.5 & 29.5988329008241 & 120 \tabularnewline
6 & 565.583333333333 & 26.1376020786958 & 165 \tabularnewline
7 & 595.916666666667 & 21.9191005677005 & 186 \tabularnewline
8 & 596.083333333333 & 19.4303339854949 & 190 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7000&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]515.416666666667[/C][C]24.1075557123538[/C][C]67[/C][/ROW]
[ROW][C]2[/C][C]481.583333333333[/C][C]26.2036025744322[/C][C]57[/C][/ROW]
[ROW][C]3[/C][C]466.75[/C][C]26.7619981588548[/C][C]53[/C][/ROW]
[ROW][C]4[/C][C]483.583333333333[/C][C]26.0818931735246[/C][C]58[/C][/ROW]
[ROW][C]5[/C][C]527.5[/C][C]29.5988329008241[/C][C]120[/C][/ROW]
[ROW][C]6[/C][C]565.583333333333[/C][C]26.1376020786958[/C][C]165[/C][/ROW]
[ROW][C]7[/C][C]595.916666666667[/C][C]21.9191005677005[/C][C]186[/C][/ROW]
[ROW][C]8[/C][C]596.083333333333[/C][C]19.4303339854949[/C][C]190[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7000&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7000&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
1515.41666666666724.107555712353867
2481.58333333333326.203602574432257
3466.7526.761998158854853
4483.58333333333326.081893173524658
5527.529.5988329008241120
6565.58333333333326.1376020786958165
7595.91666666666721.9191005677005186
8596.08333333333319.4303339854949190






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha46.2287435787144
beta-0.0400690770390047
S.D.0.0187597527252338
T-STAT-2.13590646027587
p-value0.0765820616233245

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 46.2287435787144 \tabularnewline
beta & -0.0400690770390047 \tabularnewline
S.D. & 0.0187597527252338 \tabularnewline
T-STAT & -2.13590646027587 \tabularnewline
p-value & 0.0765820616233245 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7000&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]46.2287435787144[/C][/ROW]
[ROW][C]beta[/C][C]-0.0400690770390047[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0187597527252338[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.13590646027587[/C][/ROW]
[ROW][C]p-value[/C][C]0.0765820616233245[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7000&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7000&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)
alpha46.2287435787144
beta-0.0400690770390047
S.D.0.0187597527252338
T-STAT-2.13590646027587
p-value0.0765820616233245






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha8.83806152633017
beta-0.897617216670617
S.D.0.413684491099942
T-STAT-2.16981113863841
p-value0.0730809829187061
Lambda1.89761721667062

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 8.83806152633017 \tabularnewline
beta & -0.897617216670617 \tabularnewline
S.D. & 0.413684491099942 \tabularnewline
T-STAT & -2.16981113863841 \tabularnewline
p-value & 0.0730809829187061 \tabularnewline
Lambda & 1.89761721667062 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7000&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]8.83806152633017[/C][/ROW]
[ROW][C]beta[/C][C]-0.897617216670617[/C][/ROW]
[ROW][C]S.D.[/C][C]0.413684491099942[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.16981113863841[/C][/ROW]
[ROW][C]p-value[/C][C]0.0730809829187061[/C][/ROW]
[ROW][C]Lambda[/C][C]1.89761721667062[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7000&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7000&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)
alpha8.83806152633017
beta-0.897617216670617
S.D.0.413684491099942
T-STAT-2.16981113863841
p-value0.0730809829187061
Lambda1.89761721667062


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')