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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, 09 May 2011 21:46:33 +0000

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/2011/May/09/t1304977691wf4i3b2hd1t8943.htm/, Retrieved Tue, 14 May 2024 20:00:13 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=121366, Retrieved Tue, 14 May 2024 20:00:13 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W83

Estimated Impact

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

-       [Standard Deviation-Mean Plot] [Alexander De Raey...] [2011-05-09 21:46:33] [67591050a6cb6cfbed77a59a4d2c72eb] [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	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121366&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121366&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121366&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	1836.5	485.626399611883	1056
2	1448.5	386.689798158679	810
3	1535.75	987.901943514638	2301
4	2225.25	662.795783028227	1492
5	1349	363.166628422822	794
6	997.25	716.737690279133	1733
7	1745.75	406.746747579703	896
8	1236.25	412.697932310465	1002
9	1096.75	668.331940979431	1509
10	2111.25	574.583544839217	1278
11	1519.25	395.230207178888	940
12	1235.75	828.370840867784	1989
13	1866.75	778.860866907563	1746
14	1088.5	292.427198917383	609
15	1177	735.978713460292	1642
16	1409.25	600.012985970582	1325
17	1140	438.545322629258	1038
18	912	570.668029593388	1295
19	1337	495.450636626227	1147
20	1203.75	420.221667694563	942
21	938.75	536.802493163609	1250

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 1836.5 & 485.626399611883 & 1056 \tabularnewline
2 & 1448.5 & 386.689798158679 & 810 \tabularnewline
3 & 1535.75 & 987.901943514638 & 2301 \tabularnewline
4 & 2225.25 & 662.795783028227 & 1492 \tabularnewline
5 & 1349 & 363.166628422822 & 794 \tabularnewline
6 & 997.25 & 716.737690279133 & 1733 \tabularnewline
7 & 1745.75 & 406.746747579703 & 896 \tabularnewline
8 & 1236.25 & 412.697932310465 & 1002 \tabularnewline
9 & 1096.75 & 668.331940979431 & 1509 \tabularnewline
10 & 2111.25 & 574.583544839217 & 1278 \tabularnewline
11 & 1519.25 & 395.230207178888 & 940 \tabularnewline
12 & 1235.75 & 828.370840867784 & 1989 \tabularnewline
13 & 1866.75 & 778.860866907563 & 1746 \tabularnewline
14 & 1088.5 & 292.427198917383 & 609 \tabularnewline
15 & 1177 & 735.978713460292 & 1642 \tabularnewline
16 & 1409.25 & 600.012985970582 & 1325 \tabularnewline
17 & 1140 & 438.545322629258 & 1038 \tabularnewline
18 & 912 & 570.668029593388 & 1295 \tabularnewline
19 & 1337 & 495.450636626227 & 1147 \tabularnewline
20 & 1203.75 & 420.221667694563 & 942 \tabularnewline
21 & 938.75 & 536.802493163609 & 1250 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121366&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]1836.5[/C][C]485.626399611883[/C][C]1056[/C][/ROW]
[ROW][C]2[/C][C]1448.5[/C][C]386.689798158679[/C][C]810[/C][/ROW]
[ROW][C]3[/C][C]1535.75[/C][C]987.901943514638[/C][C]2301[/C][/ROW]
[ROW][C]4[/C][C]2225.25[/C][C]662.795783028227[/C][C]1492[/C][/ROW]
[ROW][C]5[/C][C]1349[/C][C]363.166628422822[/C][C]794[/C][/ROW]
[ROW][C]6[/C][C]997.25[/C][C]716.737690279133[/C][C]1733[/C][/ROW]
[ROW][C]7[/C][C]1745.75[/C][C]406.746747579703[/C][C]896[/C][/ROW]
[ROW][C]8[/C][C]1236.25[/C][C]412.697932310465[/C][C]1002[/C][/ROW]
[ROW][C]9[/C][C]1096.75[/C][C]668.331940979431[/C][C]1509[/C][/ROW]
[ROW][C]10[/C][C]2111.25[/C][C]574.583544839217[/C][C]1278[/C][/ROW]
[ROW][C]11[/C][C]1519.25[/C][C]395.230207178888[/C][C]940[/C][/ROW]
[ROW][C]12[/C][C]1235.75[/C][C]828.370840867784[/C][C]1989[/C][/ROW]
[ROW][C]13[/C][C]1866.75[/C][C]778.860866907563[/C][C]1746[/C][/ROW]
[ROW][C]14[/C][C]1088.5[/C][C]292.427198917383[/C][C]609[/C][/ROW]
[ROW][C]15[/C][C]1177[/C][C]735.978713460292[/C][C]1642[/C][/ROW]
[ROW][C]16[/C][C]1409.25[/C][C]600.012985970582[/C][C]1325[/C][/ROW]
[ROW][C]17[/C][C]1140[/C][C]438.545322629258[/C][C]1038[/C][/ROW]
[ROW][C]18[/C][C]912[/C][C]570.668029593388[/C][C]1295[/C][/ROW]
[ROW][C]19[/C][C]1337[/C][C]495.450636626227[/C][C]1147[/C][/ROW]
[ROW][C]20[/C][C]1203.75[/C][C]420.221667694563[/C][C]942[/C][/ROW]
[ROW][C]21[/C][C]938.75[/C][C]536.802493163609[/C][C]1250[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121366&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121366&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	1836.5	485.626399611883	1056
2	1448.5	386.689798158679	810
3	1535.75	987.901943514638	2301
4	2225.25	662.795783028227	1492
5	1349	363.166628422822	794
6	997.25	716.737690279133	1733
7	1745.75	406.746747579703	896
8	1236.25	412.697932310465	1002
9	1096.75	668.331940979431	1509
10	2111.25	574.583544839217	1278
11	1519.25	395.230207178888	940
12	1235.75	828.370840867784	1989
13	1866.75	778.860866907563	1746
14	1088.5	292.427198917383	609
15	1177	735.978713460292	1642
16	1409.25	600.012985970582	1325
17	1140	438.545322629258	1038
18	912	570.668029593388	1295
19	1337	495.450636626227	1147
20	1203.75	420.221667694563	942
21	938.75	536.802493163609	1250

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	484.471324873897
beta	0.0538570583174877
S.D.	0.109617118661329
T-STAT	0.491319777195416
p-value	0.628827700403929

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 484.471324873897 \tabularnewline
beta & 0.0538570583174877 \tabularnewline
S.D. & 0.109617118661329 \tabularnewline
T-STAT & 0.491319777195416 \tabularnewline
p-value & 0.628827700403929 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121366&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]484.471324873897[/C][/ROW]
[ROW][C]beta[/C][C]0.0538570583174877[/C][/ROW]
[ROW][C]S.D.[/C][C]0.109617118661329[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.491319777195416[/C][/ROW]
[ROW][C]p-value[/C][C]0.628827700403929[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121366&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121366&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	484.471324873897
beta	0.0538570583174877
S.D.	0.109617118661329
T-STAT	0.491319777195416
p-value	0.628827700403929

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	5.40369851258795
beta	0.121551285801388
S.D.	0.282297001155001
T-STAT	0.430579444004251
p-value	0.671619035008393
Lambda	0.878448714198612

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 5.40369851258795 \tabularnewline
beta & 0.121551285801388 \tabularnewline
S.D. & 0.282297001155001 \tabularnewline
T-STAT & 0.430579444004251 \tabularnewline
p-value & 0.671619035008393 \tabularnewline
Lambda & 0.878448714198612 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121366&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]5.40369851258795[/C][/ROW]
[ROW][C]beta[/C][C]0.121551285801388[/C][/ROW]
[ROW][C]S.D.[/C][C]0.282297001155001[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.430579444004251[/C][/ROW]
[ROW][C]p-value[/C][C]0.671619035008393[/C][/ROW]
[ROW][C]Lambda[/C][C]0.878448714198612[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121366&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121366&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	5.40369851258795
beta	0.121551285801388
S.D.	0.282297001155001
T-STAT	0.430579444004251
p-value	0.671619035008393
Lambda	0.878448714198612

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')

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code