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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 computationFri, 19 Dec 2008 05:53:43 -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/19/t1229691261mx36y9nspwcpz8k.htm/, Retrieved Wed, 15 May 2024 18:02:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35091, Retrieved Wed, 15 May 2024 18:02:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact196

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] [Paper1] [2008-12-19 12:53:43] [acca1d0ee7cc95ffc080d0867a313954] [Current]
-         [Standard Deviation-Mean Plot] [Paper 1] [2008-12-24 11:43:12] [74be16979710d4c4e7c6647856088456]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
528
478
469
490
493
508
517
514
510
527
542
565
555
499
511
526
532
549
561
557
566
588
620
626
620
573
573
574
580
590
593
597
595
612
628
629
621
569
567
573
584
589
591
595
594
611
613
611
594
543
537
544
555
561
562
555
547
565
578
580

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'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35091&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35091&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35091&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'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1511.7527.116331878509296
2557.539.2185021270689127
359720.841392380636156
4593.16666666666718.064698539785654
5560.08333333333317.063828480861057

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 511.75 & 27.1163318785092 & 96 \tabularnewline
2 & 557.5 & 39.2185021270689 & 127 \tabularnewline
3 & 597 & 20.8413923806361 & 56 \tabularnewline
4 & 593.166666666667 & 18.0646985397856 & 54 \tabularnewline
5 & 560.083333333333 & 17.0638284808610 & 57 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35091&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]511.75[/C][C]27.1163318785092[/C][C]96[/C][/ROW]
[ROW][C]2[/C][C]557.5[/C][C]39.2185021270689[/C][C]127[/C][/ROW]
[ROW][C]3[/C][C]597[/C][C]20.8413923806361[/C][C]56[/C][/ROW]
[ROW][C]4[/C][C]593.166666666667[/C][C]18.0646985397856[/C][C]54[/C][/ROW]
[ROW][C]5[/C][C]560.083333333333[/C][C]17.0638284808610[/C][C]57[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35091&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35091&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
1511.7527.116331878509296
2557.539.2185021270689127
359720.841392380636156
4593.16666666666718.064698539785654
5560.08333333333317.063828480861057






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha85.4993733928976
beta-0.108243345826433
S.D.0.140053882218057
T-STAT-0.772869299387953
p-value0.495907806090671

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 85.4993733928976 \tabularnewline
beta & -0.108243345826433 \tabularnewline
S.D. & 0.140053882218057 \tabularnewline
T-STAT & -0.772869299387953 \tabularnewline
p-value & 0.495907806090671 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35091&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]85.4993733928976[/C][/ROW]
[ROW][C]beta[/C][C]-0.108243345826433[/C][/ROW]
[ROW][C]S.D.[/C][C]0.140053882218057[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.772869299387953[/C][/ROW]
[ROW][C]p-value[/C][C]0.495907806090671[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35091&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35091&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)
alpha85.4993733928976
beta-0.108243345826433
S.D.0.140053882218057
T-STAT-0.772869299387953
p-value0.495907806090671






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha18.6945223669926
beta-2.45479562909501
S.D.2.85163816110698
T-STAT-0.860836996283596
p-value0.452631683863145
Lambda3.45479562909501

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 18.6945223669926 \tabularnewline
beta & -2.45479562909501 \tabularnewline
S.D. & 2.85163816110698 \tabularnewline
T-STAT & -0.860836996283596 \tabularnewline
p-value & 0.452631683863145 \tabularnewline
Lambda & 3.45479562909501 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35091&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]18.6945223669926[/C][/ROW]
[ROW][C]beta[/C][C]-2.45479562909501[/C][/ROW]
[ROW][C]S.D.[/C][C]2.85163816110698[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.860836996283596[/C][/ROW]
[ROW][C]p-value[/C][C]0.452631683863145[/C][/ROW]
[ROW][C]Lambda[/C][C]3.45479562909501[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35091&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35091&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)
alpha18.6945223669926
beta-2.45479562909501
S.D.2.85163816110698
T-STAT-0.860836996283596
p-value0.452631683863145
Lambda3.45479562909501


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')