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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

Sun, 17 Aug 2014 23:05:13 +0100

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/2014/Aug/17/t1408313122b088rm0m1q2y6bg.htm/, Retrieved Thu, 16 May 2024 06:19:08 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235647, Retrieved Thu, 16 May 2024 06:19:08 +0000

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Estimated Impact

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

-       [Standard Deviation-Mean Plot] [] [2014-08-17 22:05:13] [d41d8cd98f00b204e9800998ecf8427e] [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	'Gertrude Mary Cox' @ cox.wessa.net

\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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235647&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235647&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235647&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	'Gertrude Mary Cox' @ cox.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	40817	641.648870276628	1909
2	40363.25	900.210291088598	2800
3	39822.5	1005.9238630144	3013
4	38234.5	1285.55700697473	3676
5	35750.75	2035.16352369578	5814
6	30691.4166666667	2469.67338504262	7509
7	25053.9166666667	2827.99419628867	8093
8	18827.5833333333	2860.33012901827	8022
9	12065.5833333333	2932.18895764467	9055
10	6888.83333333333	2697.63855767944	7508

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 40817 & 641.648870276628 & 1909 \tabularnewline
2 & 40363.25 & 900.210291088598 & 2800 \tabularnewline
3 & 39822.5 & 1005.9238630144 & 3013 \tabularnewline
4 & 38234.5 & 1285.55700697473 & 3676 \tabularnewline
5 & 35750.75 & 2035.16352369578 & 5814 \tabularnewline
6 & 30691.4166666667 & 2469.67338504262 & 7509 \tabularnewline
7 & 25053.9166666667 & 2827.99419628867 & 8093 \tabularnewline
8 & 18827.5833333333 & 2860.33012901827 & 8022 \tabularnewline
9 & 12065.5833333333 & 2932.18895764467 & 9055 \tabularnewline
10 & 6888.83333333333 & 2697.63855767944 & 7508 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235647&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]40817[/C][C]641.648870276628[/C][C]1909[/C][/ROW]
[ROW][C]2[/C][C]40363.25[/C][C]900.210291088598[/C][C]2800[/C][/ROW]
[ROW][C]3[/C][C]39822.5[/C][C]1005.9238630144[/C][C]3013[/C][/ROW]
[ROW][C]4[/C][C]38234.5[/C][C]1285.55700697473[/C][C]3676[/C][/ROW]
[ROW][C]5[/C][C]35750.75[/C][C]2035.16352369578[/C][C]5814[/C][/ROW]
[ROW][C]6[/C][C]30691.4166666667[/C][C]2469.67338504262[/C][C]7509[/C][/ROW]
[ROW][C]7[/C][C]25053.9166666667[/C][C]2827.99419628867[/C][C]8093[/C][/ROW]
[ROW][C]8[/C][C]18827.5833333333[/C][C]2860.33012901827[/C][C]8022[/C][/ROW]
[ROW][C]9[/C][C]12065.5833333333[/C][C]2932.18895764467[/C][C]9055[/C][/ROW]
[ROW][C]10[/C][C]6888.83333333333[/C][C]2697.63855767944[/C][C]7508[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235647&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235647&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	40817	641.648870276628	1909
2	40363.25	900.210291088598	2800
3	39822.5	1005.9238630144	3013
4	38234.5	1285.55700697473	3676
5	35750.75	2035.16352369578	5814
6	30691.4166666667	2469.67338504262	7509
7	25053.9166666667	2827.99419628867	8093
8	18827.5833333333	2860.33012901827	8022
9	12065.5833333333	2932.18895764467	9055
10	6888.83333333333	2697.63855767944	7508

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	3764.21910722842
beta	-0.062339363678743
S.D.	0.0134588028599478
T-STAT	-4.63186542870462
p-value	0.00168395258971941

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 3764.21910722842 \tabularnewline
beta & -0.062339363678743 \tabularnewline
S.D. & 0.0134588028599478 \tabularnewline
T-STAT & -4.63186542870462 \tabularnewline
p-value & 0.00168395258971941 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235647&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3764.21910722842[/C][/ROW]
[ROW][C]beta[/C][C]-0.062339363678743[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0134588028599478[/C][/ROW]
[ROW][C]T-STAT[/C][C]-4.63186542870462[/C][/ROW]
[ROW][C]p-value[/C][C]0.00168395258971941[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235647&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235647&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	3764.21910722842
beta	-0.062339363678743
S.D.	0.0134588028599478
T-STAT	-4.63186542870462
p-value	0.00168395258971941

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	14.0305316305479
beta	-0.648449284734683
S.D.	0.240032674415033
T-STAT	-2.70150422776804
p-value	0.0270110454397654
Lambda	1.64844928473468

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 14.0305316305479 \tabularnewline
beta & -0.648449284734683 \tabularnewline
S.D. & 0.240032674415033 \tabularnewline
T-STAT & -2.70150422776804 \tabularnewline
p-value & 0.0270110454397654 \tabularnewline
Lambda & 1.64844928473468 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235647&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]14.0305316305479[/C][/ROW]
[ROW][C]beta[/C][C]-0.648449284734683[/C][/ROW]
[ROW][C]S.D.[/C][C]0.240032674415033[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.70150422776804[/C][/ROW]
[ROW][C]p-value[/C][C]0.0270110454397654[/C][/ROW]
[ROW][C]Lambda[/C][C]1.64844928473468[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235647&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235647&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	14.0305316305479
beta	-0.648449284734683
S.D.	0.240032674415033
T-STAT	-2.70150422776804
p-value	0.0270110454397654
Lambda	1.64844928473468

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