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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

Mon, 12 May 2008 01:26:58 -0600

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/2008/May/12/t12105772885e9gffwroj83688.htm/, Retrieved Mon, 20 May 2024 07:29:15 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=12298, Retrieved Mon, 20 May 2024 07:29:15 +0000

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No (this computation is public)

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Estimated Impact

176

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

-       [Standard Deviation-Mean Plot] [Ruts Wouter: kaas...] [2008-05-12 07:26:58] [01e9b7c485def8aabed90073ada23605] [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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12298&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12298&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12298&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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	6.53	0.0141421356237311	0.0300000000000002
2	6.48	0.0244948974278317	0.0499999999999998
3	6.4925	0.0189296944860005	0.0399999999999991
4	6.5175	0.0411298755975102	0.0899999999999999
5	6.555	0.0191485421551268	0.04
6	6.605	0.0387298334620745	0.0900000000000007
7	6.755	0.0580229839517642	0.140000000000001
8	6.8675	0.0419324854180306	0.100000000000001
9	7.0225	0.0464578662158877	0.0999999999999996
10	7.07	0.0535412613473633	0.110000000000000
11	7.085	0.0450924975282292	0.100000000000001
12	7.0625	0.0340342964277703	0.08
13	7.0775	0.0275378527364308	0.0600000000000005
14	7.0825	0.0457347424467075	0.0999999999999996
15	7.0575	0.0590903263374528	0.13
16	6.995	0.0299999999999997	0.0599999999999996
17	6.9975	0.0531507290636729	0.119999999999999
18	6.96	0.0316227766016838	0.0700000000000003
19	6.96	0.0270801280154533	0.0600000000000005
20	6.96	0.0316227766016838	0.0700000000000003
21	6.87	0.0346410161513775	0.08

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 6.53 & 0.0141421356237311 & 0.0300000000000002 \tabularnewline
2 & 6.48 & 0.0244948974278317 & 0.0499999999999998 \tabularnewline
3 & 6.4925 & 0.0189296944860005 & 0.0399999999999991 \tabularnewline
4 & 6.5175 & 0.0411298755975102 & 0.0899999999999999 \tabularnewline
5 & 6.555 & 0.0191485421551268 & 0.04 \tabularnewline
6 & 6.605 & 0.0387298334620745 & 0.0900000000000007 \tabularnewline
7 & 6.755 & 0.0580229839517642 & 0.140000000000001 \tabularnewline
8 & 6.8675 & 0.0419324854180306 & 0.100000000000001 \tabularnewline
9 & 7.0225 & 0.0464578662158877 & 0.0999999999999996 \tabularnewline
10 & 7.07 & 0.0535412613473633 & 0.110000000000000 \tabularnewline
11 & 7.085 & 0.0450924975282292 & 0.100000000000001 \tabularnewline
12 & 7.0625 & 0.0340342964277703 & 0.08 \tabularnewline
13 & 7.0775 & 0.0275378527364308 & 0.0600000000000005 \tabularnewline
14 & 7.0825 & 0.0457347424467075 & 0.0999999999999996 \tabularnewline
15 & 7.0575 & 0.0590903263374528 & 0.13 \tabularnewline
16 & 6.995 & 0.0299999999999997 & 0.0599999999999996 \tabularnewline
17 & 6.9975 & 0.0531507290636729 & 0.119999999999999 \tabularnewline
18 & 6.96 & 0.0316227766016838 & 0.0700000000000003 \tabularnewline
19 & 6.96 & 0.0270801280154533 & 0.0600000000000005 \tabularnewline
20 & 6.96 & 0.0316227766016838 & 0.0700000000000003 \tabularnewline
21 & 6.87 & 0.0346410161513775 & 0.08 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12298&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]6.53[/C][C]0.0141421356237311[/C][C]0.0300000000000002[/C][/ROW]
[ROW][C]2[/C][C]6.48[/C][C]0.0244948974278317[/C][C]0.0499999999999998[/C][/ROW]
[ROW][C]3[/C][C]6.4925[/C][C]0.0189296944860005[/C][C]0.0399999999999991[/C][/ROW]
[ROW][C]4[/C][C]6.5175[/C][C]0.0411298755975102[/C][C]0.0899999999999999[/C][/ROW]
[ROW][C]5[/C][C]6.555[/C][C]0.0191485421551268[/C][C]0.04[/C][/ROW]
[ROW][C]6[/C][C]6.605[/C][C]0.0387298334620745[/C][C]0.0900000000000007[/C][/ROW]
[ROW][C]7[/C][C]6.755[/C][C]0.0580229839517642[/C][C]0.140000000000001[/C][/ROW]
[ROW][C]8[/C][C]6.8675[/C][C]0.0419324854180306[/C][C]0.100000000000001[/C][/ROW]
[ROW][C]9[/C][C]7.0225[/C][C]0.0464578662158877[/C][C]0.0999999999999996[/C][/ROW]
[ROW][C]10[/C][C]7.07[/C][C]0.0535412613473633[/C][C]0.110000000000000[/C][/ROW]
[ROW][C]11[/C][C]7.085[/C][C]0.0450924975282292[/C][C]0.100000000000001[/C][/ROW]
[ROW][C]12[/C][C]7.0625[/C][C]0.0340342964277703[/C][C]0.08[/C][/ROW]
[ROW][C]13[/C][C]7.0775[/C][C]0.0275378527364308[/C][C]0.0600000000000005[/C][/ROW]
[ROW][C]14[/C][C]7.0825[/C][C]0.0457347424467075[/C][C]0.0999999999999996[/C][/ROW]
[ROW][C]15[/C][C]7.0575[/C][C]0.0590903263374528[/C][C]0.13[/C][/ROW]
[ROW][C]16[/C][C]6.995[/C][C]0.0299999999999997[/C][C]0.0599999999999996[/C][/ROW]
[ROW][C]17[/C][C]6.9975[/C][C]0.0531507290636729[/C][C]0.119999999999999[/C][/ROW]
[ROW][C]18[/C][C]6.96[/C][C]0.0316227766016838[/C][C]0.0700000000000003[/C][/ROW]
[ROW][C]19[/C][C]6.96[/C][C]0.0270801280154533[/C][C]0.0600000000000005[/C][/ROW]
[ROW][C]20[/C][C]6.96[/C][C]0.0316227766016838[/C][C]0.0700000000000003[/C][/ROW]
[ROW][C]21[/C][C]6.87[/C][C]0.0346410161513775[/C][C]0.08[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12298&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12298&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	6.53	0.0141421356237311	0.0300000000000002
2	6.48	0.0244948974278317	0.0499999999999998
3	6.4925	0.0189296944860005	0.0399999999999991
4	6.5175	0.0411298755975102	0.0899999999999999
5	6.555	0.0191485421551268	0.04
6	6.605	0.0387298334620745	0.0900000000000007
7	6.755	0.0580229839517642	0.140000000000001
8	6.8675	0.0419324854180306	0.100000000000001
9	7.0225	0.0464578662158877	0.0999999999999996
10	7.07	0.0535412613473633	0.110000000000000
11	7.085	0.0450924975282292	0.100000000000001
12	7.0625	0.0340342964277703	0.08
13	7.0775	0.0275378527364308	0.0600000000000005
14	7.0825	0.0457347424467075	0.0999999999999996
15	7.0575	0.0590903263374528	0.13
16	6.995	0.0299999999999997	0.0599999999999996
17	6.9975	0.0531507290636729	0.119999999999999
18	6.96	0.0316227766016838	0.0700000000000003
19	6.96	0.0270801280154533	0.0600000000000005
20	6.96	0.0316227766016838	0.0700000000000003
21	6.87	0.0346410161513775	0.08

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-0.160985930081978
beta	0.0288664519665792
S.D.	0.0112641035579584
T-STAT	2.56269412102345
p-value	0.0190390098289210

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.160985930081978 \tabularnewline
beta & 0.0288664519665792 \tabularnewline
S.D. & 0.0112641035579584 \tabularnewline
T-STAT & 2.56269412102345 \tabularnewline
p-value & 0.0190390098289210 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12298&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.160985930081978[/C][/ROW]
[ROW][C]beta[/C][C]0.0288664519665792[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0112641035579584[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.56269412102345[/C][/ROW]
[ROW][C]p-value[/C][C]0.0190390098289210[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12298&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12298&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	-0.160985930081978
beta	0.0288664519665792
S.D.	0.0112641035579584
T-STAT	2.56269412102345
p-value	0.0190390098289210

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-15.9408327938656
beta	6.53395095920199
S.D.	2.19031579400085
T-STAT	2.98310909189355
p-value	0.007642083475524
Lambda	-5.53395095920199

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -15.9408327938656 \tabularnewline
beta & 6.53395095920199 \tabularnewline
S.D. & 2.19031579400085 \tabularnewline
T-STAT & 2.98310909189355 \tabularnewline
p-value & 0.007642083475524 \tabularnewline
Lambda & -5.53395095920199 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12298&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-15.9408327938656[/C][/ROW]
[ROW][C]beta[/C][C]6.53395095920199[/C][/ROW]
[ROW][C]S.D.[/C][C]2.19031579400085[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.98310909189355[/C][/ROW]
[ROW][C]p-value[/C][C]0.007642083475524[/C][/ROW]
[ROW][C]Lambda[/C][C]-5.53395095920199[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12298&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12298&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	-15.9408327938656
beta	6.53395095920199
S.D.	2.19031579400085
T-STAT	2.98310909189355
p-value	0.007642083475524
Lambda	-5.53395095920199

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