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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

Fri, 14 May 2010 16:28:35 +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/2010/May/14/t12738545843y4kjnn7jthsu6e.htm/, Retrieved Thu, 02 May 2024 19:14:41 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=75998, Retrieved Thu, 02 May 2024 19:14:41 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W83

Estimated Impact

175

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

-       [Standard Deviation-Mean Plot] [] [2010-05-14 16:28:35] [1c63715a73aab28ce271608ca6a82d4c] [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=75998&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=75998&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=75998&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	10424.75	3474.64793180547	7845
2	11531.75	3127.20443580738	6336
3	8603.5	1140.61518488928	2496
4	10558	2856.2104264217	6547
5	12216.25	3438.87262291971	7951
6	9800	2203.50190983958	5149
7	13458.5	3145.91528811569	6333
8	14561.25	5153.97829351269	11903
9	9970.25	3013.36936280083	6688
10	14152.75	4465.44528388081	9517
11	14713.5	5221.29929551384	11486
12	12614.5	3386.94095017908	7974
13	16235	4564.33660751118	8992
14	16519.25	4995.51681510532	11709
15	12759	1814.16684274995	3960
16	17065.25	5352.34156701532	10944
17	18686	4386.24045548501	8774
18	15583.25	3156.8091880885	6802
19	16954.5	4953.3766597477	9461
20	17777.75	2936.12844575982	5564
21	15454.5	1794.527700167	4161
22	16127.5	4897.49435936378	9377
23	18462.25	5421.73443189539	10647
24	15154.25	1785.30396571564	3589
25	17331.25	4229.30808958944	8515
26	20482.25	4167.03158735328	9377
27	16871	3241.80782897444	6957

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 10424.75 & 3474.64793180547 & 7845 \tabularnewline
2 & 11531.75 & 3127.20443580738 & 6336 \tabularnewline
3 & 8603.5 & 1140.61518488928 & 2496 \tabularnewline
4 & 10558 & 2856.2104264217 & 6547 \tabularnewline
5 & 12216.25 & 3438.87262291971 & 7951 \tabularnewline
6 & 9800 & 2203.50190983958 & 5149 \tabularnewline
7 & 13458.5 & 3145.91528811569 & 6333 \tabularnewline
8 & 14561.25 & 5153.97829351269 & 11903 \tabularnewline
9 & 9970.25 & 3013.36936280083 & 6688 \tabularnewline
10 & 14152.75 & 4465.44528388081 & 9517 \tabularnewline
11 & 14713.5 & 5221.29929551384 & 11486 \tabularnewline
12 & 12614.5 & 3386.94095017908 & 7974 \tabularnewline
13 & 16235 & 4564.33660751118 & 8992 \tabularnewline
14 & 16519.25 & 4995.51681510532 & 11709 \tabularnewline
15 & 12759 & 1814.16684274995 & 3960 \tabularnewline
16 & 17065.25 & 5352.34156701532 & 10944 \tabularnewline
17 & 18686 & 4386.24045548501 & 8774 \tabularnewline
18 & 15583.25 & 3156.8091880885 & 6802 \tabularnewline
19 & 16954.5 & 4953.3766597477 & 9461 \tabularnewline
20 & 17777.75 & 2936.12844575982 & 5564 \tabularnewline
21 & 15454.5 & 1794.527700167 & 4161 \tabularnewline
22 & 16127.5 & 4897.49435936378 & 9377 \tabularnewline
23 & 18462.25 & 5421.73443189539 & 10647 \tabularnewline
24 & 15154.25 & 1785.30396571564 & 3589 \tabularnewline
25 & 17331.25 & 4229.30808958944 & 8515 \tabularnewline
26 & 20482.25 & 4167.03158735328 & 9377 \tabularnewline
27 & 16871 & 3241.80782897444 & 6957 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=75998&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]10424.75[/C][C]3474.64793180547[/C][C]7845[/C][/ROW]
[ROW][C]2[/C][C]11531.75[/C][C]3127.20443580738[/C][C]6336[/C][/ROW]
[ROW][C]3[/C][C]8603.5[/C][C]1140.61518488928[/C][C]2496[/C][/ROW]
[ROW][C]4[/C][C]10558[/C][C]2856.2104264217[/C][C]6547[/C][/ROW]
[ROW][C]5[/C][C]12216.25[/C][C]3438.87262291971[/C][C]7951[/C][/ROW]
[ROW][C]6[/C][C]9800[/C][C]2203.50190983958[/C][C]5149[/C][/ROW]
[ROW][C]7[/C][C]13458.5[/C][C]3145.91528811569[/C][C]6333[/C][/ROW]
[ROW][C]8[/C][C]14561.25[/C][C]5153.97829351269[/C][C]11903[/C][/ROW]
[ROW][C]9[/C][C]9970.25[/C][C]3013.36936280083[/C][C]6688[/C][/ROW]
[ROW][C]10[/C][C]14152.75[/C][C]4465.44528388081[/C][C]9517[/C][/ROW]
[ROW][C]11[/C][C]14713.5[/C][C]5221.29929551384[/C][C]11486[/C][/ROW]
[ROW][C]12[/C][C]12614.5[/C][C]3386.94095017908[/C][C]7974[/C][/ROW]
[ROW][C]13[/C][C]16235[/C][C]4564.33660751118[/C][C]8992[/C][/ROW]
[ROW][C]14[/C][C]16519.25[/C][C]4995.51681510532[/C][C]11709[/C][/ROW]
[ROW][C]15[/C][C]12759[/C][C]1814.16684274995[/C][C]3960[/C][/ROW]
[ROW][C]16[/C][C]17065.25[/C][C]5352.34156701532[/C][C]10944[/C][/ROW]
[ROW][C]17[/C][C]18686[/C][C]4386.24045548501[/C][C]8774[/C][/ROW]
[ROW][C]18[/C][C]15583.25[/C][C]3156.8091880885[/C][C]6802[/C][/ROW]
[ROW][C]19[/C][C]16954.5[/C][C]4953.3766597477[/C][C]9461[/C][/ROW]
[ROW][C]20[/C][C]17777.75[/C][C]2936.12844575982[/C][C]5564[/C][/ROW]
[ROW][C]21[/C][C]15454.5[/C][C]1794.527700167[/C][C]4161[/C][/ROW]
[ROW][C]22[/C][C]16127.5[/C][C]4897.49435936378[/C][C]9377[/C][/ROW]
[ROW][C]23[/C][C]18462.25[/C][C]5421.73443189539[/C][C]10647[/C][/ROW]
[ROW][C]24[/C][C]15154.25[/C][C]1785.30396571564[/C][C]3589[/C][/ROW]
[ROW][C]25[/C][C]17331.25[/C][C]4229.30808958944[/C][C]8515[/C][/ROW]
[ROW][C]26[/C][C]20482.25[/C][C]4167.03158735328[/C][C]9377[/C][/ROW]
[ROW][C]27[/C][C]16871[/C][C]3241.80782897444[/C][C]6957[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=75998&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=75998&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	10424.75	3474.64793180547	7845
2	11531.75	3127.20443580738	6336
3	8603.5	1140.61518488928	2496
4	10558	2856.2104264217	6547
5	12216.25	3438.87262291971	7951
6	9800	2203.50190983958	5149
7	13458.5	3145.91528811569	6333
8	14561.25	5153.97829351269	11903
9	9970.25	3013.36936280083	6688
10	14152.75	4465.44528388081	9517
11	14713.5	5221.29929551384	11486
12	12614.5	3386.94095017908	7974
13	16235	4564.33660751118	8992
14	16519.25	4995.51681510532	11709
15	12759	1814.16684274995	3960
16	17065.25	5352.34156701532	10944
17	18686	4386.24045548501	8774
18	15583.25	3156.8091880885	6802
19	16954.5	4953.3766597477	9461
20	17777.75	2936.12844575982	5564
21	15454.5	1794.527700167	4161
22	16127.5	4897.49435936378	9377
23	18462.25	5421.73443189539	10647
24	15154.25	1785.30396571564	3589
25	17331.25	4229.30808958944	8515
26	20482.25	4167.03158735328	9377
27	16871	3241.80782897444	6957

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	326.810919523699
beta	0.227118747787356
S.D.	0.0657085621655016
T-STAT	3.45645590623802
p-value	0.00196890708343522

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 326.810919523699 \tabularnewline
beta & 0.227118747787356 \tabularnewline
S.D. & 0.0657085621655016 \tabularnewline
T-STAT & 3.45645590623802 \tabularnewline
p-value & 0.00196890708343522 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=75998&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]326.810919523699[/C][/ROW]
[ROW][C]beta[/C][C]0.227118747787356[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0657085621655016[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.45645590623802[/C][/ROW]
[ROW][C]p-value[/C][C]0.00196890708343522[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=75998&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=75998&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	326.810919523699
beta	0.227118747787356
S.D.	0.0657085621655016
T-STAT	3.45645590623802
p-value	0.00196890708343522

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-1.68555016283801
beta	1.02637587351065
S.D.	0.2898432859338
T-STAT	3.54114075888954
p-value	0.00159220303366251
Lambda	-0.0263758735106545

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.68555016283801 \tabularnewline
beta & 1.02637587351065 \tabularnewline
S.D. & 0.2898432859338 \tabularnewline
T-STAT & 3.54114075888954 \tabularnewline
p-value & 0.00159220303366251 \tabularnewline
Lambda & -0.0263758735106545 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=75998&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.68555016283801[/C][/ROW]
[ROW][C]beta[/C][C]1.02637587351065[/C][/ROW]
[ROW][C]S.D.[/C][C]0.2898432859338[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.54114075888954[/C][/ROW]
[ROW][C]p-value[/C][C]0.00159220303366251[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.0263758735106545[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=75998&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=75998&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	-1.68555016283801
beta	1.02637587351065
S.D.	0.2898432859338
T-STAT	3.54114075888954
p-value	0.00159220303366251
Lambda	-0.0263758735106545

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