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Author

*Unverified author*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Wed, 19 Aug 2009 04:15:59 -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/2009/Aug/19/t1250677010mux2k5aejxp8zge.htm/, Retrieved Tue, 07 May 2024 21:50:44 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=42917, Retrieved Tue, 07 May 2024 21:50:44 +0000

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No (this computation is public)

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Estimated Impact

165

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

-     [Variability] [Opgave 8 oefening...] [2008-12-26 20:06:20] [61fbc7ea9bd73829dc055ddb9178936d]
- RMPD  [Standard Deviation Plot] [dennis volkaerts ...] [2009-08-18 19:14:16] [65364f12da24daf6c8f7985fc762862c]
- RMP       [Standard Deviation-Mean Plot] [dennis volkaerts ...] [2009-08-19 10:15:59] [9e20205489828c19845a9d736cd20362] [Current]

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Boxplots

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=42917&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=42917&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42917&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	17.3175	0.0718215380880508	0.16
2	17.4325	0.118145390656315	0.259999999999998
3	17.54	0.132413493773607	0.279999999999998
4	17.6125	0.128160056179763	0.300000000000001
5	17.8575	0.225000000000000	0.530000000000001
6	18.51	0.221810730128189	0.460000000000001
7	19.025	0.0435889894354064	0.0899999999999999
8	19.395	0.292403830344269	0.66
9	19.52	0.130894359440479	0.300000000000001
10	19.225	0.0675771164423776	0.16
11	19.2675	0.180254449783263	0.390000000000001
12	19.2475	0.129196233175223	0.309999999999999
13	19.33	0.181659021245850	0.420000000000002
14	19.515	0.130256157883866	0.289999999999999
15	19.5625	0.0917877987534288	0.180000000000000
16	19.5725	0.195682566077478	0.41
17	19.61	0.0605530070819499	0.140000000000001
18	19.845	0.101159939369956	0.239999999999998
19	20.125	0.151107026088574	0.369999999999997
20	20.345	0.0929157324317765	0.220000000000002
21	19.9775	0.130735101126923	0.32

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 17.3175 & 0.0718215380880508 & 0.16 \tabularnewline
2 & 17.4325 & 0.118145390656315 & 0.259999999999998 \tabularnewline
3 & 17.54 & 0.132413493773607 & 0.279999999999998 \tabularnewline
4 & 17.6125 & 0.128160056179763 & 0.300000000000001 \tabularnewline
5 & 17.8575 & 0.225000000000000 & 0.530000000000001 \tabularnewline
6 & 18.51 & 0.221810730128189 & 0.460000000000001 \tabularnewline
7 & 19.025 & 0.0435889894354064 & 0.0899999999999999 \tabularnewline
8 & 19.395 & 0.292403830344269 & 0.66 \tabularnewline
9 & 19.52 & 0.130894359440479 & 0.300000000000001 \tabularnewline
10 & 19.225 & 0.0675771164423776 & 0.16 \tabularnewline
11 & 19.2675 & 0.180254449783263 & 0.390000000000001 \tabularnewline
12 & 19.2475 & 0.129196233175223 & 0.309999999999999 \tabularnewline
13 & 19.33 & 0.181659021245850 & 0.420000000000002 \tabularnewline
14 & 19.515 & 0.130256157883866 & 0.289999999999999 \tabularnewline
15 & 19.5625 & 0.0917877987534288 & 0.180000000000000 \tabularnewline
16 & 19.5725 & 0.195682566077478 & 0.41 \tabularnewline
17 & 19.61 & 0.0605530070819499 & 0.140000000000001 \tabularnewline
18 & 19.845 & 0.101159939369956 & 0.239999999999998 \tabularnewline
19 & 20.125 & 0.151107026088574 & 0.369999999999997 \tabularnewline
20 & 20.345 & 0.0929157324317765 & 0.220000000000002 \tabularnewline
21 & 19.9775 & 0.130735101126923 & 0.32 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42917&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]17.3175[/C][C]0.0718215380880508[/C][C]0.16[/C][/ROW]
[ROW][C]2[/C][C]17.4325[/C][C]0.118145390656315[/C][C]0.259999999999998[/C][/ROW]
[ROW][C]3[/C][C]17.54[/C][C]0.132413493773607[/C][C]0.279999999999998[/C][/ROW]
[ROW][C]4[/C][C]17.6125[/C][C]0.128160056179763[/C][C]0.300000000000001[/C][/ROW]
[ROW][C]5[/C][C]17.8575[/C][C]0.225000000000000[/C][C]0.530000000000001[/C][/ROW]
[ROW][C]6[/C][C]18.51[/C][C]0.221810730128189[/C][C]0.460000000000001[/C][/ROW]
[ROW][C]7[/C][C]19.025[/C][C]0.0435889894354064[/C][C]0.0899999999999999[/C][/ROW]
[ROW][C]8[/C][C]19.395[/C][C]0.292403830344269[/C][C]0.66[/C][/ROW]
[ROW][C]9[/C][C]19.52[/C][C]0.130894359440479[/C][C]0.300000000000001[/C][/ROW]
[ROW][C]10[/C][C]19.225[/C][C]0.0675771164423776[/C][C]0.16[/C][/ROW]
[ROW][C]11[/C][C]19.2675[/C][C]0.180254449783263[/C][C]0.390000000000001[/C][/ROW]
[ROW][C]12[/C][C]19.2475[/C][C]0.129196233175223[/C][C]0.309999999999999[/C][/ROW]
[ROW][C]13[/C][C]19.33[/C][C]0.181659021245850[/C][C]0.420000000000002[/C][/ROW]
[ROW][C]14[/C][C]19.515[/C][C]0.130256157883866[/C][C]0.289999999999999[/C][/ROW]
[ROW][C]15[/C][C]19.5625[/C][C]0.0917877987534288[/C][C]0.180000000000000[/C][/ROW]
[ROW][C]16[/C][C]19.5725[/C][C]0.195682566077478[/C][C]0.41[/C][/ROW]
[ROW][C]17[/C][C]19.61[/C][C]0.0605530070819499[/C][C]0.140000000000001[/C][/ROW]
[ROW][C]18[/C][C]19.845[/C][C]0.101159939369956[/C][C]0.239999999999998[/C][/ROW]
[ROW][C]19[/C][C]20.125[/C][C]0.151107026088574[/C][C]0.369999999999997[/C][/ROW]
[ROW][C]20[/C][C]20.345[/C][C]0.0929157324317765[/C][C]0.220000000000002[/C][/ROW]
[ROW][C]21[/C][C]19.9775[/C][C]0.130735101126923[/C][C]0.32[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42917&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42917&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	17.3175	0.0718215380880508	0.16
2	17.4325	0.118145390656315	0.259999999999998
3	17.54	0.132413493773607	0.279999999999998
4	17.6125	0.128160056179763	0.300000000000001
5	17.8575	0.225000000000000	0.530000000000001
6	18.51	0.221810730128189	0.460000000000001
7	19.025	0.0435889894354064	0.0899999999999999
8	19.395	0.292403830344269	0.66
9	19.52	0.130894359440479	0.300000000000001
10	19.225	0.0675771164423776	0.16
11	19.2675	0.180254449783263	0.390000000000001
12	19.2475	0.129196233175223	0.309999999999999
13	19.33	0.181659021245850	0.420000000000002
14	19.515	0.130256157883866	0.289999999999999
15	19.5625	0.0917877987534288	0.180000000000000
16	19.5725	0.195682566077478	0.41
17	19.61	0.0605530070819499	0.140000000000001
18	19.845	0.101159939369956	0.239999999999998
19	20.125	0.151107026088574	0.369999999999997
20	20.345	0.0929157324317765	0.220000000000002
21	19.9775	0.130735101126923	0.32

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	0.181425517439645
beta	-0.00233301026986499
S.D.	0.0150792996469490
T-STAT	-0.154716089240725
p-value	0.878676843071928

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.181425517439645 \tabularnewline
beta & -0.00233301026986499 \tabularnewline
S.D. & 0.0150792996469490 \tabularnewline
T-STAT & -0.154716089240725 \tabularnewline
p-value & 0.878676843071928 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42917&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.181425517439645[/C][/ROW]
[ROW][C]beta[/C][C]-0.00233301026986499[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0150792996469490[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.154716089240725[/C][/ROW]
[ROW][C]p-value[/C][C]0.878676843071928[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42917&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42917&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	0.181425517439645
beta	-0.00233301026986499
S.D.	0.0150792996469490
T-STAT	-0.154716089240725
p-value	0.878676843071928

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-1.31245953750420
beta	-0.263386281844197
S.D.	2.15796642109322
T-STAT	-0.122053002896480
p-value	0.904138728891683
Lambda	1.26338628184420

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.31245953750420 \tabularnewline
beta & -0.263386281844197 \tabularnewline
S.D. & 2.15796642109322 \tabularnewline
T-STAT & -0.122053002896480 \tabularnewline
p-value & 0.904138728891683 \tabularnewline
Lambda & 1.26338628184420 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42917&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.31245953750420[/C][/ROW]
[ROW][C]beta[/C][C]-0.263386281844197[/C][/ROW]
[ROW][C]S.D.[/C][C]2.15796642109322[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.122053002896480[/C][/ROW]
[ROW][C]p-value[/C][C]0.904138728891683[/C][/ROW]
[ROW][C]Lambda[/C][C]1.26338628184420[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42917&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42917&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	-1.31245953750420
beta	-0.263386281844197
S.D.	2.15796642109322
T-STAT	-0.122053002896480
p-value	0.904138728891683
Lambda	1.26338628184420

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

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code