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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, 18 May 2008 15:10:48 -0600

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/2008/May/18/t1211145144nu4j4pd9j8ziech.htm/, Retrieved Tue, 14 May 2024 00:17:02 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=12846, Retrieved Tue, 14 May 2024 00:17:02 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

153

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

-       [Standard Deviation-Mean Plot] [standars deviatio...] [2008-05-18 21:10:48] [cd7facba9466f9e80bdffad33137a939] [Current]

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Dataseries X:

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Histogram

Boxplots

1.08
1.08
1.09
1.1
1.1
1.11
1.1
1.1
1.11
1.11
1.11
1.11
1.11
1.12
1.11
1.11
1.12
1.12
1.11
1.12
1.11
1.11
1.1
1.1
1.1
1.11
1.1
1.1
1.09
1.1
1.1
1.11
1.13
1.13
1.13
1.13
1.14
1.14
1.14
1.15
1.15
1.15
1.15
1.15
1.15
1.14
1.14
1.14
1.13
1.12
1.13
1.13
1.13
1.12
1.13
1.12
1.12
1.11
1.11
1.11
1.11
1.14
1.15
1.15
1.16
1.15
1.16
1.13
1.13
1.12
1.12
1.11
1.11

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12846&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12846&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12846&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	1.1	0.0112815214963553	0.03
2	1.11166666666667	0.00717740562565274	0.02
3	1.11083333333333	0.0150504203102488	0.0399999999999998
4	1.145	0.00522232967867094	0.01
5	1.12166666666667	0.00834847109936713	0.0199999999999998
6	1.13583333333333	0.0183195540504145	0.0499999999999998

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 1.1 & 0.0112815214963553 & 0.03 \tabularnewline
2 & 1.11166666666667 & 0.00717740562565274 & 0.02 \tabularnewline
3 & 1.11083333333333 & 0.0150504203102488 & 0.0399999999999998 \tabularnewline
4 & 1.145 & 0.00522232967867094 & 0.01 \tabularnewline
5 & 1.12166666666667 & 0.00834847109936713 & 0.0199999999999998 \tabularnewline
6 & 1.13583333333333 & 0.0183195540504145 & 0.0499999999999998 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12846&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]1.1[/C][C]0.0112815214963553[/C][C]0.03[/C][/ROW]
[ROW][C]2[/C][C]1.11166666666667[/C][C]0.00717740562565274[/C][C]0.02[/C][/ROW]
[ROW][C]3[/C][C]1.11083333333333[/C][C]0.0150504203102488[/C][C]0.0399999999999998[/C][/ROW]
[ROW][C]4[/C][C]1.145[/C][C]0.00522232967867094[/C][C]0.01[/C][/ROW]
[ROW][C]5[/C][C]1.12166666666667[/C][C]0.00834847109936713[/C][C]0.0199999999999998[/C][/ROW]
[ROW][C]6[/C][C]1.13583333333333[/C][C]0.0183195540504145[/C][C]0.0499999999999998[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12846&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12846&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	1.1	0.0112815214963553	0.03
2	1.11166666666667	0.00717740562565274	0.02
3	1.11083333333333	0.0150504203102488	0.0399999999999998
4	1.145	0.00522232967867094	0.01
5	1.12166666666667	0.00834847109936713	0.0199999999999998
6	1.13583333333333	0.0183195540504145	0.0499999999999998

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	0.0449479046803624
beta	-0.0303773569994743
S.D.	0.147176390053251
T-STAT	-0.206401019813594
p-value	0.84655794566222

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.0449479046803624 \tabularnewline
beta & -0.0303773569994743 \tabularnewline
S.D. & 0.147176390053251 \tabularnewline
T-STAT & -0.206401019813594 \tabularnewline
p-value & 0.84655794566222 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12846&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.0449479046803624[/C][/ROW]
[ROW][C]beta[/C][C]-0.0303773569994743[/C][/ROW]
[ROW][C]S.D.[/C][C]0.147176390053251[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.206401019813594[/C][/ROW]
[ROW][C]p-value[/C][C]0.84655794566222[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12846&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12846&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	0.0449479046803624
beta	-0.0303773569994743
S.D.	0.147176390053251
T-STAT	-0.206401019813594
p-value	0.84655794566222

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-3.68848018935144
beta	-8.08218805504474
S.D.	15.1452989993911
T-STAT	-0.533643347375955
p-value	0.62186334041275
Lambda	9.08218805504474

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.68848018935144 \tabularnewline
beta & -8.08218805504474 \tabularnewline
S.D. & 15.1452989993911 \tabularnewline
T-STAT & -0.533643347375955 \tabularnewline
p-value & 0.62186334041275 \tabularnewline
Lambda & 9.08218805504474 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12846&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.68848018935144[/C][/ROW]
[ROW][C]beta[/C][C]-8.08218805504474[/C][/ROW]
[ROW][C]S.D.[/C][C]15.1452989993911[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.533643347375955[/C][/ROW]
[ROW][C]p-value[/C][C]0.62186334041275[/C][/ROW]
[ROW][C]Lambda[/C][C]9.08218805504474[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12846&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12846&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	-3.68848018935144
beta	-8.08218805504474
S.D.	15.1452989993911
T-STAT	-0.533643347375955
p-value	0.62186334041275
Lambda	9.08218805504474

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