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Author's title

Author

*Unverified author*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Tue, 05 Jul 2016 15:02:02 +0100

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Jul/05/t1467727361ujx5pr0tgn3dnam.htm/, Retrieved Fri, 03 May 2024 04:48:52 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=295797, Retrieved Fri, 03 May 2024 04:48:52 +0000

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IsPrivate?

No (this computation is public)

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Estimated Impact

142

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Standard Deviation-Mean Plot] [Standard Deviatio...] [2016-07-05 14:02:02] [fcb50c3fd850be3d4e9c7b78a2663ee0] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295797&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' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295797&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295797&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'George Udny Yule' @ yule.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	2090	174.460206455122	520
2	2543.33333333333	306.752293711016	780
3	3343.33333333333	274.998622586082	720
4	4108.33333333333	290.761799833514	760
5	4948.33333333333	415.382262792267	1100
6	6230	487.852436706019	1400
7	7811.66666666667	564.943011338848	1560
8	9476.66666666667	619.374073096576	1640
9	11283.3333333333	712.987738429992	1980
10	13093.3333333333	787.508537712257	2120

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 2090 & 174.460206455122 & 520 \tabularnewline
2 & 2543.33333333333 & 306.752293711016 & 780 \tabularnewline
3 & 3343.33333333333 & 274.998622586082 & 720 \tabularnewline
4 & 4108.33333333333 & 290.761799833514 & 760 \tabularnewline
5 & 4948.33333333333 & 415.382262792267 & 1100 \tabularnewline
6 & 6230 & 487.852436706019 & 1400 \tabularnewline
7 & 7811.66666666667 & 564.943011338848 & 1560 \tabularnewline
8 & 9476.66666666667 & 619.374073096576 & 1640 \tabularnewline
9 & 11283.3333333333 & 712.987738429992 & 1980 \tabularnewline
10 & 13093.3333333333 & 787.508537712257 & 2120 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295797&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]2090[/C][C]174.460206455122[/C][C]520[/C][/ROW]
[ROW][C]2[/C][C]2543.33333333333[/C][C]306.752293711016[/C][C]780[/C][/ROW]
[ROW][C]3[/C][C]3343.33333333333[/C][C]274.998622586082[/C][C]720[/C][/ROW]
[ROW][C]4[/C][C]4108.33333333333[/C][C]290.761799833514[/C][C]760[/C][/ROW]
[ROW][C]5[/C][C]4948.33333333333[/C][C]415.382262792267[/C][C]1100[/C][/ROW]
[ROW][C]6[/C][C]6230[/C][C]487.852436706019[/C][C]1400[/C][/ROW]
[ROW][C]7[/C][C]7811.66666666667[/C][C]564.943011338848[/C][C]1560[/C][/ROW]
[ROW][C]8[/C][C]9476.66666666667[/C][C]619.374073096576[/C][C]1640[/C][/ROW]
[ROW][C]9[/C][C]11283.3333333333[/C][C]712.987738429992[/C][C]1980[/C][/ROW]
[ROW][C]10[/C][C]13093.3333333333[/C][C]787.508537712257[/C][C]2120[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295797&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295797&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	2090	174.460206455122	520
2	2543.33333333333	306.752293711016	780
3	3343.33333333333	274.998622586082	720
4	4108.33333333333	290.761799833514	760
5	4948.33333333333	415.382262792267	1100
6	6230	487.852436706019	1400
7	7811.66666666667	564.943011338848	1560
8	9476.66666666667	619.374073096576	1640
9	11283.3333333333	712.987738429992	1980
10	13093.3333333333	787.508537712257	2120

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	119.522863101141
beta	0.0529782942985899
S.D.	0.0035014825453213
T-STAT	15.1302465778045
p-value	3.60355203347099e-07

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 119.522863101141 \tabularnewline
beta & 0.0529782942985899 \tabularnewline
S.D. & 0.0035014825453213 \tabularnewline
T-STAT & 15.1302465778045 \tabularnewline
p-value & 3.60355203347099e-07 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295797&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]119.522863101141[/C][/ROW]
[ROW][C]beta[/C][C]0.0529782942985899[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0035014825453213[/C][/ROW]
[ROW][C]T-STAT[/C][C]15.1302465778045[/C][/ROW]
[ROW][C]p-value[/C][C]3.60355203347099e-07[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295797&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295797&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	119.522863101141
beta	0.0529782942985899
S.D.	0.0035014825453213
T-STAT	15.1302465778045
p-value	3.60355203347099e-07

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-0.386999526589626
beta	0.746487931115478
S.D.	0.0667905728846016
T-STAT	11.1765463129839
p-value	3.67834766631995e-06
Lambda	0.253512068884522

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -0.386999526589626 \tabularnewline
beta & 0.746487931115478 \tabularnewline
S.D. & 0.0667905728846016 \tabularnewline
T-STAT & 11.1765463129839 \tabularnewline
p-value & 3.67834766631995e-06 \tabularnewline
Lambda & 0.253512068884522 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295797&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.386999526589626[/C][/ROW]
[ROW][C]beta[/C][C]0.746487931115478[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0667905728846016[/C][/ROW]
[ROW][C]T-STAT[/C][C]11.1765463129839[/C][/ROW]
[ROW][C]p-value[/C][C]3.67834766631995e-06[/C][/ROW]
[ROW][C]Lambda[/C][C]0.253512068884522[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295797&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295797&T=3

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-0.386999526589626
beta	0.746487931115478
S.D.	0.0667905728846016
T-STAT	11.1765463129839
p-value	3.67834766631995e-06
Lambda	0.253512068884522

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 0 ; par2 = no ; par3 = 512 ;

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code