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*Unverified author*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Mon, 01 Jun 2009 11:38:54 -0600

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/01/t1243877954ygxyo250g40hp01.htm/, Retrieved Mon, 13 May 2024 12:54:06 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41022, Retrieved Mon, 13 May 2024 12:54:06 +0000

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

-       [Standard Deviation-Mean Plot] [] [2009-06-01 17:38:54] [738a25b0d97c8f3fa6714f905e8e3fd3] [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' @ 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=41022&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=41022&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41022&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' @ 72.249.76.132

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	27.02	0.251396101799530	0.559999999999999
2	26.2925	0.493853892023406	1.15000000000000
3	25.475	0.281602556806573	0.619999999999997
4	26.3725	0.188745860881769	0.43
5	20.765	0.380219235003527	0.8
6	20.8575	0.316372670543248	0.77
7	22.455	0.409104713571803	0.91
8	23.4725	0.395	0.95
9	22.3525	0.326228447563973	0.629999999999999
10	21.985	0.107548438699345	0.260000000000002
11	21.965	0.274408454680246	0.600000000000001
12	20.2925	0.324384031666172	0.75
13	18.3025	0.72967458500348	1.75
14	18.37	0.182938969786830	0.440000000000001
15	16.655	0.448144321991625	0.969999999999999
16	17.9425	0.792396155131173	1.7
17	18.19	0.254950975679638	0.539999999999999
18	18.9575	0.330088372005640	0.740000000000002
19	18.565	0.234591844132173	0.560000000000002
20	17.8375	0.130989821487522	0.319999999999997
21	18.25	0.164924225024707	0.32

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 27.02 & 0.251396101799530 & 0.559999999999999 \tabularnewline
2 & 26.2925 & 0.493853892023406 & 1.15000000000000 \tabularnewline
3 & 25.475 & 0.281602556806573 & 0.619999999999997 \tabularnewline
4 & 26.3725 & 0.188745860881769 & 0.43 \tabularnewline
5 & 20.765 & 0.380219235003527 & 0.8 \tabularnewline
6 & 20.8575 & 0.316372670543248 & 0.77 \tabularnewline
7 & 22.455 & 0.409104713571803 & 0.91 \tabularnewline
8 & 23.4725 & 0.395 & 0.95 \tabularnewline
9 & 22.3525 & 0.326228447563973 & 0.629999999999999 \tabularnewline
10 & 21.985 & 0.107548438699345 & 0.260000000000002 \tabularnewline
11 & 21.965 & 0.274408454680246 & 0.600000000000001 \tabularnewline
12 & 20.2925 & 0.324384031666172 & 0.75 \tabularnewline
13 & 18.3025 & 0.72967458500348 & 1.75 \tabularnewline
14 & 18.37 & 0.182938969786830 & 0.440000000000001 \tabularnewline
15 & 16.655 & 0.448144321991625 & 0.969999999999999 \tabularnewline
16 & 17.9425 & 0.792396155131173 & 1.7 \tabularnewline
17 & 18.19 & 0.254950975679638 & 0.539999999999999 \tabularnewline
18 & 18.9575 & 0.330088372005640 & 0.740000000000002 \tabularnewline
19 & 18.565 & 0.234591844132173 & 0.560000000000002 \tabularnewline
20 & 17.8375 & 0.130989821487522 & 0.319999999999997 \tabularnewline
21 & 18.25 & 0.164924225024707 & 0.32 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41022&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]27.02[/C][C]0.251396101799530[/C][C]0.559999999999999[/C][/ROW]
[ROW][C]2[/C][C]26.2925[/C][C]0.493853892023406[/C][C]1.15000000000000[/C][/ROW]
[ROW][C]3[/C][C]25.475[/C][C]0.281602556806573[/C][C]0.619999999999997[/C][/ROW]
[ROW][C]4[/C][C]26.3725[/C][C]0.188745860881769[/C][C]0.43[/C][/ROW]
[ROW][C]5[/C][C]20.765[/C][C]0.380219235003527[/C][C]0.8[/C][/ROW]
[ROW][C]6[/C][C]20.8575[/C][C]0.316372670543248[/C][C]0.77[/C][/ROW]
[ROW][C]7[/C][C]22.455[/C][C]0.409104713571803[/C][C]0.91[/C][/ROW]
[ROW][C]8[/C][C]23.4725[/C][C]0.395[/C][C]0.95[/C][/ROW]
[ROW][C]9[/C][C]22.3525[/C][C]0.326228447563973[/C][C]0.629999999999999[/C][/ROW]
[ROW][C]10[/C][C]21.985[/C][C]0.107548438699345[/C][C]0.260000000000002[/C][/ROW]
[ROW][C]11[/C][C]21.965[/C][C]0.274408454680246[/C][C]0.600000000000001[/C][/ROW]
[ROW][C]12[/C][C]20.2925[/C][C]0.324384031666172[/C][C]0.75[/C][/ROW]
[ROW][C]13[/C][C]18.3025[/C][C]0.72967458500348[/C][C]1.75[/C][/ROW]
[ROW][C]14[/C][C]18.37[/C][C]0.182938969786830[/C][C]0.440000000000001[/C][/ROW]
[ROW][C]15[/C][C]16.655[/C][C]0.448144321991625[/C][C]0.969999999999999[/C][/ROW]
[ROW][C]16[/C][C]17.9425[/C][C]0.792396155131173[/C][C]1.7[/C][/ROW]
[ROW][C]17[/C][C]18.19[/C][C]0.254950975679638[/C][C]0.539999999999999[/C][/ROW]
[ROW][C]18[/C][C]18.9575[/C][C]0.330088372005640[/C][C]0.740000000000002[/C][/ROW]
[ROW][C]19[/C][C]18.565[/C][C]0.234591844132173[/C][C]0.560000000000002[/C][/ROW]
[ROW][C]20[/C][C]17.8375[/C][C]0.130989821487522[/C][C]0.319999999999997[/C][/ROW]
[ROW][C]21[/C][C]18.25[/C][C]0.164924225024707[/C][C]0.32[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41022&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41022&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	27.02	0.251396101799530	0.559999999999999
2	26.2925	0.493853892023406	1.15000000000000
3	25.475	0.281602556806573	0.619999999999997
4	26.3725	0.188745860881769	0.43
5	20.765	0.380219235003527	0.8
6	20.8575	0.316372670543248	0.77
7	22.455	0.409104713571803	0.91
8	23.4725	0.395	0.95
9	22.3525	0.326228447563973	0.629999999999999
10	21.985	0.107548438699345	0.260000000000002
11	21.965	0.274408454680246	0.600000000000001
12	20.2925	0.324384031666172	0.75
13	18.3025	0.72967458500348	1.75
14	18.37	0.182938969786830	0.440000000000001
15	16.655	0.448144321991625	0.969999999999999
16	17.9425	0.792396155131173	1.7
17	18.19	0.254950975679638	0.539999999999999
18	18.9575	0.330088372005640	0.740000000000002
19	18.565	0.234591844132173	0.560000000000002
20	17.8375	0.130989821487522	0.319999999999997
21	18.25	0.164924225024707	0.32

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	0.508767222308945
beta	-0.00828832550439212
S.D.	0.0124290867480402
T-STAT	-0.666849115499095
p-value	0.512886038330861

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.508767222308945 \tabularnewline
beta & -0.00828832550439212 \tabularnewline
S.D. & 0.0124290867480402 \tabularnewline
T-STAT & -0.666849115499095 \tabularnewline
p-value & 0.512886038330861 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41022&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.508767222308945[/C][/ROW]
[ROW][C]beta[/C][C]-0.00828832550439212[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0124290867480402[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.666849115499095[/C][/ROW]
[ROW][C]p-value[/C][C]0.512886038330861[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41022&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41022&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	0.508767222308945
beta	-0.00828832550439212
S.D.	0.0124290867480402
T-STAT	-0.666849115499095
p-value	0.512886038330861

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-0.582281726175017
beta	-0.208711704646226
S.D.	0.78133883078245
T-STAT	-0.267120609425258
p-value	0.79225417232154
Lambda	1.20871170464623

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -0.582281726175017 \tabularnewline
beta & -0.208711704646226 \tabularnewline
S.D. & 0.78133883078245 \tabularnewline
T-STAT & -0.267120609425258 \tabularnewline
p-value & 0.79225417232154 \tabularnewline
Lambda & 1.20871170464623 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41022&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.582281726175017[/C][/ROW]
[ROW][C]beta[/C][C]-0.208711704646226[/C][/ROW]
[ROW][C]S.D.[/C][C]0.78133883078245[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.267120609425258[/C][/ROW]
[ROW][C]p-value[/C][C]0.79225417232154[/C][/ROW]
[ROW][C]Lambda[/C][C]1.20871170464623[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41022&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41022&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	-0.582281726175017
beta	-0.208711704646226
S.D.	0.78133883078245
T-STAT	-0.267120609425258
p-value	0.79225417232154
Lambda	1.20871170464623

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 4 ;

Parameters (R input):

par1 = 4 ;

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

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code