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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, 18 Aug 2010 08:21:55 +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/Aug/18/t1282119813q2gpoermxwci285.htm/, Retrieved Thu, 16 May 2024 16:34:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79177, Retrieved Thu, 16 May 2024 16:34:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsVanhille Olivier
Estimated Impact144

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] [tijdreeks 1 - sta...] [2010-08-18 08:21:55] [ddb1c76c3acba5bf82e5ed3b5a08f68d] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
568
567
566
564
584
583
568
558
559
559
560
562
563
552
552
555
575
567
548
541
544
546
551
550
546
532
523
528
555
543
525
517
519
521
520
516
509
494
484
482
508
500
480
467
471
482
481
477
471
455
441
434
459
448
432
414
415
423
425
427
415
399
386
377
397
379
361
350
348
363
367
365
354
327
312
307
335
317
298
286
288
303
310
301
293
264
255
251
279
253
233
226
232
245
250
242
230
196
188
181
212
186
166
155
157
173
182
182
168
131
114
106
134
103
83
74
83
96
95
100

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'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79177&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79177&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79177&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'RServer@AstonUniversity' @ vre.aston.ac.uk






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1566.58.7230103227560826
2553.6666666666679.966610925150734
3528.7512.721670845093839
4486.2513.605647223253942
543718.060504372298657
6375.58333333333320.571199343359767
7311.519.58431654527368
8251.91666666666719.435012142257567
918421.523771214002675
10107.2526.365007801319594

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 566.5 & 8.72301032275608 & 26 \tabularnewline
2 & 553.666666666667 & 9.9666109251507 & 34 \tabularnewline
3 & 528.75 & 12.7216708450938 & 39 \tabularnewline
4 & 486.25 & 13.6056472232539 & 42 \tabularnewline
5 & 437 & 18.0605043722986 & 57 \tabularnewline
6 & 375.583333333333 & 20.5711993433597 & 67 \tabularnewline
7 & 311.5 & 19.584316545273 & 68 \tabularnewline
8 & 251.916666666667 & 19.4350121422575 & 67 \tabularnewline
9 & 184 & 21.5237712140026 & 75 \tabularnewline
10 & 107.25 & 26.3650078013195 & 94 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79177&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]566.5[/C][C]8.72301032275608[/C][C]26[/C][/ROW]
[ROW][C]2[/C][C]553.666666666667[/C][C]9.9666109251507[/C][C]34[/C][/ROW]
[ROW][C]3[/C][C]528.75[/C][C]12.7216708450938[/C][C]39[/C][/ROW]
[ROW][C]4[/C][C]486.25[/C][C]13.6056472232539[/C][C]42[/C][/ROW]
[ROW][C]5[/C][C]437[/C][C]18.0605043722986[/C][C]57[/C][/ROW]
[ROW][C]6[/C][C]375.583333333333[/C][C]20.5711993433597[/C][C]67[/C][/ROW]
[ROW][C]7[/C][C]311.5[/C][C]19.584316545273[/C][C]68[/C][/ROW]
[ROW][C]8[/C][C]251.916666666667[/C][C]19.4350121422575[/C][C]67[/C][/ROW]
[ROW][C]9[/C][C]184[/C][C]21.5237712140026[/C][C]75[/C][/ROW]
[ROW][C]10[/C][C]107.25[/C][C]26.3650078013195[/C][C]94[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79177&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79177&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
1566.58.7230103227560826
2553.6666666666679.966610925150734
3528.7512.721670845093839
4486.2513.605647223253942
543718.060504372298657
6375.58333333333320.571199343359767
7311.519.58431654527368
8251.91666666666719.435012142257567
918421.523771214002675
10107.2526.365007801319594






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha29.401771658893
beta-0.0324690786615962
S.D.0.00425523435086716
T-STAT-7.63038554033563
p-value6.12822886779461e-05

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 29.401771658893 \tabularnewline
beta & -0.0324690786615962 \tabularnewline
S.D. & 0.00425523435086716 \tabularnewline
T-STAT & -7.63038554033563 \tabularnewline
p-value & 6.12822886779461e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79177&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]29.401771658893[/C][/ROW]
[ROW][C]beta[/C][C]-0.0324690786615962[/C][/ROW]
[ROW][C]S.D.[/C][C]0.00425523435086716[/C][/ROW]
[ROW][C]T-STAT[/C][C]-7.63038554033563[/C][/ROW]
[ROW][C]p-value[/C][C]6.12822886779461e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79177&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79177&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)
alpha29.401771658893
beta-0.0324690786615962
S.D.0.00425523435086716
T-STAT-7.63038554033563
p-value6.12822886779461e-05






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha5.97363609417048
beta-0.547623382111924
S.D.0.128053423969672
T-STAT-4.27652276007567
p-value0.0027001977174771
Lambda1.54762338211192

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 5.97363609417048 \tabularnewline
beta & -0.547623382111924 \tabularnewline
S.D. & 0.128053423969672 \tabularnewline
T-STAT & -4.27652276007567 \tabularnewline
p-value & 0.0027001977174771 \tabularnewline
Lambda & 1.54762338211192 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79177&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]5.97363609417048[/C][/ROW]
[ROW][C]beta[/C][C]-0.547623382111924[/C][/ROW]
[ROW][C]S.D.[/C][C]0.128053423969672[/C][/ROW]
[ROW][C]T-STAT[/C][C]-4.27652276007567[/C][/ROW]
[ROW][C]p-value[/C][C]0.0027001977174771[/C][/ROW]
[ROW][C]Lambda[/C][C]1.54762338211192[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79177&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79177&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)
alpha5.97363609417048
beta-0.547623382111924
S.D.0.128053423969672
T-STAT-4.27652276007567
p-value0.0027001977174771
Lambda1.54762338211192


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')