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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

Wed, 02 Jun 2010 19:11:14 +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/Jun/02/t12755058989cy8j4wglwry587.htm/, Retrieved Fri, 26 Apr 2024 20:25:07 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77324, Retrieved Fri, 26 Apr 2024 20:25:07 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W83

Estimated Impact

141

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

-       [Standard Deviation-Mean Plot] [] [2010-06-02 19:11:14] [701fd7cac8325e39d69fe7641072905f] [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	'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 & 1 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77324&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77324&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77324&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	963.5	250.321792898661	854
2	1087.08333333333	293.490733424517	1047
3	987.416666666667	240.938867513707	860
4	1127.83333333333	328.884846753757	1093
5	1327.5	440.785352833698	1559
6	1373.5	320.874798579814	1274
7	1512	423.059204969105	1547
8	1717.83333333333	431.579726824674	1372
9	1862.83333333333	471.852217491362	1941
10	1970.91666666667	384.980863357538	1365
11	1912.75	456.262309921108	1469
12	1949.5	476.827870600931	1815
13	2072.5	476.838165800134	1623
14	2184.16666666667	668.68607029462	2439
15	2396.58333333333	627.603009775119	2629

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 963.5 & 250.321792898661 & 854 \tabularnewline
2 & 1087.08333333333 & 293.490733424517 & 1047 \tabularnewline
3 & 987.416666666667 & 240.938867513707 & 860 \tabularnewline
4 & 1127.83333333333 & 328.884846753757 & 1093 \tabularnewline
5 & 1327.5 & 440.785352833698 & 1559 \tabularnewline
6 & 1373.5 & 320.874798579814 & 1274 \tabularnewline
7 & 1512 & 423.059204969105 & 1547 \tabularnewline
8 & 1717.83333333333 & 431.579726824674 & 1372 \tabularnewline
9 & 1862.83333333333 & 471.852217491362 & 1941 \tabularnewline
10 & 1970.91666666667 & 384.980863357538 & 1365 \tabularnewline
11 & 1912.75 & 456.262309921108 & 1469 \tabularnewline
12 & 1949.5 & 476.827870600931 & 1815 \tabularnewline
13 & 2072.5 & 476.838165800134 & 1623 \tabularnewline
14 & 2184.16666666667 & 668.68607029462 & 2439 \tabularnewline
15 & 2396.58333333333 & 627.603009775119 & 2629 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77324&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]963.5[/C][C]250.321792898661[/C][C]854[/C][/ROW]
[ROW][C]2[/C][C]1087.08333333333[/C][C]293.490733424517[/C][C]1047[/C][/ROW]
[ROW][C]3[/C][C]987.416666666667[/C][C]240.938867513707[/C][C]860[/C][/ROW]
[ROW][C]4[/C][C]1127.83333333333[/C][C]328.884846753757[/C][C]1093[/C][/ROW]
[ROW][C]5[/C][C]1327.5[/C][C]440.785352833698[/C][C]1559[/C][/ROW]
[ROW][C]6[/C][C]1373.5[/C][C]320.874798579814[/C][C]1274[/C][/ROW]
[ROW][C]7[/C][C]1512[/C][C]423.059204969105[/C][C]1547[/C][/ROW]
[ROW][C]8[/C][C]1717.83333333333[/C][C]431.579726824674[/C][C]1372[/C][/ROW]
[ROW][C]9[/C][C]1862.83333333333[/C][C]471.852217491362[/C][C]1941[/C][/ROW]
[ROW][C]10[/C][C]1970.91666666667[/C][C]384.980863357538[/C][C]1365[/C][/ROW]
[ROW][C]11[/C][C]1912.75[/C][C]456.262309921108[/C][C]1469[/C][/ROW]
[ROW][C]12[/C][C]1949.5[/C][C]476.827870600931[/C][C]1815[/C][/ROW]
[ROW][C]13[/C][C]2072.5[/C][C]476.838165800134[/C][C]1623[/C][/ROW]
[ROW][C]14[/C][C]2184.16666666667[/C][C]668.68607029462[/C][C]2439[/C][/ROW]
[ROW][C]15[/C][C]2396.58333333333[/C][C]627.603009775119[/C][C]2629[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77324&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77324&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	963.5	250.321792898661	854
2	1087.08333333333	293.490733424517	1047
3	987.416666666667	240.938867513707	860
4	1127.83333333333	328.884846753757	1093
5	1327.5	440.785352833698	1559
6	1373.5	320.874798579814	1274
7	1512	423.059204969105	1547
8	1717.83333333333	431.579726824674	1372
9	1862.83333333333	471.852217491362	1941
10	1970.91666666667	384.980863357538	1365
11	1912.75	456.262309921108	1469
12	1949.5	476.827870600931	1815
13	2072.5	476.838165800134	1623
14	2184.16666666667	668.68607029462	2439
15	2396.58333333333	627.603009775119	2629

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	35.5113750519347
beta	0.23563506673956
S.D.	0.0335106142653839
T-STAT	7.03165465346211
p-value	8.91054594589722e-06

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 35.5113750519347 \tabularnewline
beta & 0.23563506673956 \tabularnewline
S.D. & 0.0335106142653839 \tabularnewline
T-STAT & 7.03165465346211 \tabularnewline
p-value & 8.91054594589722e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77324&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]35.5113750519347[/C][/ROW]
[ROW][C]beta[/C][C]0.23563506673956[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0335106142653839[/C][/ROW]
[ROW][C]T-STAT[/C][C]7.03165465346211[/C][/ROW]
[ROW][C]p-value[/C][C]8.91054594589722e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77324&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77324&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	35.5113750519347
beta	0.23563506673956
S.D.	0.0335106142653839
T-STAT	7.03165465346211
p-value	8.91054594589722e-06

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-0.602352801540589
beta	0.897422439154783
S.D.	0.113919397780967
T-STAT	7.87769648221157
p-value	2.64593753421172e-06
Lambda	0.102577560845217

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -0.602352801540589 \tabularnewline
beta & 0.897422439154783 \tabularnewline
S.D. & 0.113919397780967 \tabularnewline
T-STAT & 7.87769648221157 \tabularnewline
p-value & 2.64593753421172e-06 \tabularnewline
Lambda & 0.102577560845217 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77324&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.602352801540589[/C][/ROW]
[ROW][C]beta[/C][C]0.897422439154783[/C][/ROW]
[ROW][C]S.D.[/C][C]0.113919397780967[/C][/ROW]
[ROW][C]T-STAT[/C][C]7.87769648221157[/C][/ROW]
[ROW][C]p-value[/C][C]2.64593753421172e-06[/C][/ROW]
[ROW][C]Lambda[/C][C]0.102577560845217[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77324&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77324&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	-0.602352801540589
beta	0.897422439154783
S.D.	0.113919397780967
T-STAT	7.87769648221157
p-value	2.64593753421172e-06
Lambda	0.102577560845217

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = 12 ;

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