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Free Statistics

of Irreproducible Research!

Author's title

Author

*Unverified author*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Sat, 05 Jan 2013 07:20:12 -0500

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/2013/Jan/05/t13573884225xb3ys0k473x3dk.htm/, Retrieved Fri, 03 May 2024 06:51:41 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=205030, Retrieved Fri, 03 May 2024 06:51:41 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

182

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

-       [Standard Deviation-Mean Plot] [Prijs per 150 cl ...] [2013-01-05 12:20:12] [778963f9ed1fb67b9d5ff0854a52552f] [Current]

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Dataseries X:

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Histogram

Boxplots

1.26
1.27
1.24
1.25
1.27
1.25
1.26
1.27
1.26
1.26
1.28
1.27
1.28
1.27
1.26
1.27
1.27
1.28
1.27
1.26
1.3
1.31
1.28
1.29
1.31
1.29
1.29
1.32
1.3
1.29
1.31
1.29
1.33
1.35
1.32
1.33
1.34
1.34
1.33
1.33
1.35
1.32
1.35
1.32
1.36
1.37
1.34
1.32
1.34
1.32
1.33
1.35
1.33
1.33
1.35
1.33
1.36
1.39
1.37
1.37
1.39
1.37
1.39
1.39
1.39
1.37
1.38
1.37
1.41
1.41
1.42
1.42

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	'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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205030&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205030&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205030&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	'Gertrude Mary Cox' @ cox.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	1.26166666666667	0.0111464085804543	0.04
2	1.27833333333333	0.0152752523165195	0.05
3	1.31083333333333	0.0197522534195852	0.0600000000000001
4	1.33916666666667	0.0162135371797393	0.05
5	1.3475	0.0213733053554704	0.0699999999999998
6	1.3925	0.0186474468152418	0.0499999999999998

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 1.26166666666667 & 0.0111464085804543 & 0.04 \tabularnewline
2 & 1.27833333333333 & 0.0152752523165195 & 0.05 \tabularnewline
3 & 1.31083333333333 & 0.0197522534195852 & 0.0600000000000001 \tabularnewline
4 & 1.33916666666667 & 0.0162135371797393 & 0.05 \tabularnewline
5 & 1.3475 & 0.0213733053554704 & 0.0699999999999998 \tabularnewline
6 & 1.3925 & 0.0186474468152418 & 0.0499999999999998 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205030&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]1.26166666666667[/C][C]0.0111464085804543[/C][C]0.04[/C][/ROW]
[ROW][C]2[/C][C]1.27833333333333[/C][C]0.0152752523165195[/C][C]0.05[/C][/ROW]
[ROW][C]3[/C][C]1.31083333333333[/C][C]0.0197522534195852[/C][C]0.0600000000000001[/C][/ROW]
[ROW][C]4[/C][C]1.33916666666667[/C][C]0.0162135371797393[/C][C]0.05[/C][/ROW]
[ROW][C]5[/C][C]1.3475[/C][C]0.0213733053554704[/C][C]0.0699999999999998[/C][/ROW]
[ROW][C]6[/C][C]1.3925[/C][C]0.0186474468152418[/C][C]0.0499999999999998[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205030&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205030&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	1.26166666666667	0.0111464085804543	0.04
2	1.27833333333333	0.0152752523165195	0.05
3	1.31083333333333	0.0197522534195852	0.0600000000000001
4	1.33916666666667	0.0162135371797393	0.05
5	1.3475	0.0213733053554704	0.0699999999999998
6	1.3925	0.0186474468152418	0.0499999999999998

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-0.052750177929507
beta	0.0528258854027809
S.D.	0.0274469583925416
T-STAT	1.9246535316327
p-value	0.12659163688779

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.052750177929507 \tabularnewline
beta & 0.0528258854027809 \tabularnewline
S.D. & 0.0274469583925416 \tabularnewline
T-STAT & 1.9246535316327 \tabularnewline
p-value & 0.12659163688779 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205030&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.052750177929507[/C][/ROW]
[ROW][C]beta[/C][C]0.0528258854027809[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0274469583925416[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.9246535316327[/C][/ROW]
[ROW][C]p-value[/C][C]0.12659163688779[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205030&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205030&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	-0.052750177929507
beta	0.0528258854027809
S.D.	0.0274469583925416
T-STAT	1.9246535316327
p-value	0.12659163688779

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-5.3774451361875
beta	4.61809075136819
S.D.	2.23915649164025
T-STAT	2.06242429620687
p-value	0.108154795420192
Lambda	-3.61809075136819

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -5.3774451361875 \tabularnewline
beta & 4.61809075136819 \tabularnewline
S.D. & 2.23915649164025 \tabularnewline
T-STAT & 2.06242429620687 \tabularnewline
p-value & 0.108154795420192 \tabularnewline
Lambda & -3.61809075136819 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205030&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-5.3774451361875[/C][/ROW]
[ROW][C]beta[/C][C]4.61809075136819[/C][/ROW]
[ROW][C]S.D.[/C][C]2.23915649164025[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.06242429620687[/C][/ROW]
[ROW][C]p-value[/C][C]0.108154795420192[/C][/ROW]
[ROW][C]Lambda[/C][C]-3.61809075136819[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205030&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205030&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	-5.3774451361875
beta	4.61809075136819
S.D.	2.23915649164025
T-STAT	2.06242429620687
p-value	0.108154795420192
Lambda	-3.61809075136819

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