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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, 21 Nov 2014 20:35:45 +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/2014/Nov/21/t1416602177f9v2rosciwewi6m.htm/, Retrieved Sun, 19 May 2024 16:11:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=257751, Retrieved Sun, 19 May 2024 16:11:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact66

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] [] [2014-11-21 20:35:45] [9c8c71143ae36c30e98dcd90d9bfe9d4] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
560576
548854
531673
525919
511038
498662
555362
564591
541657
527070
509846
514258
516922
507561
492622
490243
469357
477580
528379
533590
517945
506174
501866
516141
528222
532638
536322
536535
523597
536214
586570
596594
580523
564478
557560
575093
580112
574761
563250
551531
537034
544686
600991
604378
586111
563668
548604
551174
555654
547970
540324
530577
520579
518654
572273
581302
563280
547612
538712
540735
561649
558685
545732
536352
527676
530455
581744
598714
583775
571477
563278
564872
577537
572399
565430
560619
551227
553397
610893
621668
613148
598778
590623
595902

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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=257751&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=257751&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=257751&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1532458.83333333321778.072975246365929
250486519560.160730888264233
3554528.83333333325444.42511483172997
4567191.66666666722153.710230336167344
5546472.66666666719252.037338862962648
6560367.41666666722128.569293843371038
7584301.7524258.117153664470441

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 532458.833333333 & 21778.0729752463 & 65929 \tabularnewline
2 & 504865 & 19560.1607308882 & 64233 \tabularnewline
3 & 554528.833333333 & 25444.425114831 & 72997 \tabularnewline
4 & 567191.666666667 & 22153.7102303361 & 67344 \tabularnewline
5 & 546472.666666667 & 19252.0373388629 & 62648 \tabularnewline
6 & 560367.416666667 & 22128.5692938433 & 71038 \tabularnewline
7 & 584301.75 & 24258.1171536644 & 70441 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=257751&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]532458.833333333[/C][C]21778.0729752463[/C][C]65929[/C][/ROW]
[ROW][C]2[/C][C]504865[/C][C]19560.1607308882[/C][C]64233[/C][/ROW]
[ROW][C]3[/C][C]554528.833333333[/C][C]25444.425114831[/C][C]72997[/C][/ROW]
[ROW][C]4[/C][C]567191.666666667[/C][C]22153.7102303361[/C][C]67344[/C][/ROW]
[ROW][C]5[/C][C]546472.666666667[/C][C]19252.0373388629[/C][C]62648[/C][/ROW]
[ROW][C]6[/C][C]560367.416666667[/C][C]22128.5692938433[/C][C]71038[/C][/ROW]
[ROW][C]7[/C][C]584301.75[/C][C]24258.1171536644[/C][C]70441[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=257751&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=257751&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
1532458.83333333321778.072975246365929
250486519560.160730888264233
3554528.83333333325444.42511483172997
4567191.66666666722153.710230336167344
5546472.66666666719252.037338862962648
6560367.41666666722128.569293843371038
7584301.7524258.117153664470441






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-8595.25773531982
beta0.0557744191291471
S.D.0.0303267903783878
T-STAT1.83911381432881
p-value0.125290309655849

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -8595.25773531982 \tabularnewline
beta & 0.0557744191291471 \tabularnewline
S.D. & 0.0303267903783878 \tabularnewline
T-STAT & 1.83911381432881 \tabularnewline
p-value & 0.125290309655849 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=257751&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-8595.25773531982[/C][/ROW]
[ROW][C]beta[/C][C]0.0557744191291471[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0303267903783878[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.83911381432881[/C][/ROW]
[ROW][C]p-value[/C][C]0.125290309655849[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=257751&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=257751&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-8595.25773531982
beta0.0557744191291471
S.D.0.0303267903783878
T-STAT1.83911381432881
p-value0.125290309655849






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-8.36425561231428
beta1.38931943778652
S.D.0.737544376774212
T-STAT1.88370962010851
p-value0.118311721842694
Lambda-0.389319437786521

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -8.36425561231428 \tabularnewline
beta & 1.38931943778652 \tabularnewline
S.D. & 0.737544376774212 \tabularnewline
T-STAT & 1.88370962010851 \tabularnewline
p-value & 0.118311721842694 \tabularnewline
Lambda & -0.389319437786521 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=257751&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-8.36425561231428[/C][/ROW]
[ROW][C]beta[/C][C]1.38931943778652[/C][/ROW]
[ROW][C]S.D.[/C][C]0.737544376774212[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.88370962010851[/C][/ROW]
[ROW][C]p-value[/C][C]0.118311721842694[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.389319437786521[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=257751&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=257751&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-8.36425561231428
beta1.38931943778652
S.D.0.737544376774212
T-STAT1.88370962010851
p-value0.118311721842694
Lambda-0.389319437786521


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')