Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Mon, 08 Dec 2008 13:47:21 -0700

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/Dec/08/t1228769313occemitqtxf6b6j.htm/, Retrieved Thu, 16 May 2024 05:18:13 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30998, Retrieved Thu, 16 May 2024 05:18:13 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

191

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

F     [Law of Averages] [Random Walk Simul...] [2008-11-25 17:50:19] [b98453cac15ba1066b407e146608df68]
F       [Law of Averages] [Non Stationary Ti...] [2008-11-30 21:33:42] [82d201ca7b4e7cd2c6f885d29b5b6937]
F RMPD      [Standard Deviation-Mean Plot] [SMP] [2008-12-08 20:47:21] [00a0a665d7a07edd2e460056b0c0c354] [Current]

Feedback Forum

2008-12-15 21:46:10 [Inge Meelberghs] [reply] 
Uit de eerste tabel van de SMP kunnen we de beta waarde en de p-waarde aflezen. De p-waarde heeft betrekking op de beta waarde van de regressie rechte. Hier wordt de beta dus eigenlijk getoetst. Aan de hand van deze waarde kunnen we ook nagaan of de helling positief of negatief is en of deze te wijten is aan toeval ?  
In dit geval bedraagt beta -0.0747181178000781 wat wil zeggen de rechte dus een dalend verloop aanneemt. De P-waarde is vrij groot,0.197451813170098. Deze is dus > dan 5% wat ervoor zorgt dat de beta waarde niet significant is van 0. (aan de eerste voorwaarde is in dit geval dus niet voldaan)  
 
In de scaterplot zien we aan de linkerkant van de grafiek duidelijk een outlier die we niet mogen negeren.  
Als outliers in de scatterplot meer naar links of rechts wijken moeten we opletten doordat deze dan een invloed hebben op het verloop van de regressierechte. In deze berekening is dit het geval waardoor er niet aan de tweede voorwaarde is voldaan.  
 
Uit de tweede tabel kunnen we dan de lambda waarde aflezen die 1.99737253529032 bedraagt. Maar doordat er niet aan de twee voorwaarden ( beta significant van 0 en geen invloedrijke outliers) is voldaan mogen we deze niet als optimale lambda waarde aannemen en moeten we 1 nemen.

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

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=30998&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=30998&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30998&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	14920.675	2270.81646752147	5022.8
2	15663.5	1522.95543160877	3320.6
3	16395.75	1058.28450648522	2450.2
4	16745.525	1929.98882099526	4005.5
5	17100.675	1384.09491335192	3132.3
6	17473.175	986.422084691268	2328.4
7	17795.075	1888.57073007605	4060.5
8	18595	1665.48384761506	3556.9
9	18494.95	1314.70267994960	2625.4
10	18880.825	1824.52874714724	3795.8
11	19048.075	1678.04802747120	4007.2
12	19725.575	921.533838680564	2249.80000000000
13	20093.325	1847.08909616365	4424.6
14	20550.1	1792.47663490118	3811.3
15	22711	825.47258383708	1753

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 14920.675 & 2270.81646752147 & 5022.8 \tabularnewline
2 & 15663.5 & 1522.95543160877 & 3320.6 \tabularnewline
3 & 16395.75 & 1058.28450648522 & 2450.2 \tabularnewline
4 & 16745.525 & 1929.98882099526 & 4005.5 \tabularnewline
5 & 17100.675 & 1384.09491335192 & 3132.3 \tabularnewline
6 & 17473.175 & 986.422084691268 & 2328.4 \tabularnewline
7 & 17795.075 & 1888.57073007605 & 4060.5 \tabularnewline
8 & 18595 & 1665.48384761506 & 3556.9 \tabularnewline
9 & 18494.95 & 1314.70267994960 & 2625.4 \tabularnewline
10 & 18880.825 & 1824.52874714724 & 3795.8 \tabularnewline
11 & 19048.075 & 1678.04802747120 & 4007.2 \tabularnewline
12 & 19725.575 & 921.533838680564 & 2249.80000000000 \tabularnewline
13 & 20093.325 & 1847.08909616365 & 4424.6 \tabularnewline
14 & 20550.1 & 1792.47663490118 & 3811.3 \tabularnewline
15 & 22711 & 825.47258383708 & 1753 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30998&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]14920.675[/C][C]2270.81646752147[/C][C]5022.8[/C][/ROW]
[ROW][C]2[/C][C]15663.5[/C][C]1522.95543160877[/C][C]3320.6[/C][/ROW]
[ROW][C]3[/C][C]16395.75[/C][C]1058.28450648522[/C][C]2450.2[/C][/ROW]
[ROW][C]4[/C][C]16745.525[/C][C]1929.98882099526[/C][C]4005.5[/C][/ROW]
[ROW][C]5[/C][C]17100.675[/C][C]1384.09491335192[/C][C]3132.3[/C][/ROW]
[ROW][C]6[/C][C]17473.175[/C][C]986.422084691268[/C][C]2328.4[/C][/ROW]
[ROW][C]7[/C][C]17795.075[/C][C]1888.57073007605[/C][C]4060.5[/C][/ROW]
[ROW][C]8[/C][C]18595[/C][C]1665.48384761506[/C][C]3556.9[/C][/ROW]
[ROW][C]9[/C][C]18494.95[/C][C]1314.70267994960[/C][C]2625.4[/C][/ROW]
[ROW][C]10[/C][C]18880.825[/C][C]1824.52874714724[/C][C]3795.8[/C][/ROW]
[ROW][C]11[/C][C]19048.075[/C][C]1678.04802747120[/C][C]4007.2[/C][/ROW]
[ROW][C]12[/C][C]19725.575[/C][C]921.533838680564[/C][C]2249.80000000000[/C][/ROW]
[ROW][C]13[/C][C]20093.325[/C][C]1847.08909616365[/C][C]4424.6[/C][/ROW]
[ROW][C]14[/C][C]20550.1[/C][C]1792.47663490118[/C][C]3811.3[/C][/ROW]
[ROW][C]15[/C][C]22711[/C][C]825.47258383708[/C][C]1753[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30998&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30998&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	14920.675	2270.81646752147	5022.8
2	15663.5	1522.95543160877	3320.6
3	16395.75	1058.28450648522	2450.2
4	16745.525	1929.98882099526	4005.5
5	17100.675	1384.09491335192	3132.3
6	17473.175	986.422084691268	2328.4
7	17795.075	1888.57073007605	4060.5
8	18595	1665.48384761506	3556.9
9	18494.95	1314.70267994960	2625.4
10	18880.825	1824.52874714724	3795.8
11	19048.075	1678.04802747120	4007.2
12	19725.575	921.533838680564	2249.80000000000
13	20093.325	1847.08909616365	4424.6
14	20550.1	1792.47663490118	3811.3
15	22711	825.47258383708	1753

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	2893.17800640192
beta	-0.0747181178000781
S.D.	0.055005639597577
T-STAT	-1.35837194779877
p-value	0.197451813170098

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 2893.17800640192 \tabularnewline
beta & -0.0747181178000781 \tabularnewline
S.D. & 0.055005639597577 \tabularnewline
T-STAT & -1.35837194779877 \tabularnewline
p-value & 0.197451813170098 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30998&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2893.17800640192[/C][/ROW]
[ROW][C]beta[/C][C]-0.0747181178000781[/C][/ROW]
[ROW][C]S.D.[/C][C]0.055005639597577[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.35837194779877[/C][/ROW]
[ROW][C]p-value[/C][C]0.197451813170098[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30998&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30998&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	2893.17800640192
beta	-0.0747181178000781
S.D.	0.055005639597577
T-STAT	-1.35837194779877
p-value	0.197451813170098

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	17.0717399589404
beta	-0.997372535290324
S.D.	0.725474501147471
T-STAT	-1.37478647934944
p-value	0.192431168732869
Lambda	1.99737253529032

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 17.0717399589404 \tabularnewline
beta & -0.997372535290324 \tabularnewline
S.D. & 0.725474501147471 \tabularnewline
T-STAT & -1.37478647934944 \tabularnewline
p-value & 0.192431168732869 \tabularnewline
Lambda & 1.99737253529032 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30998&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]17.0717399589404[/C][/ROW]
[ROW][C]beta[/C][C]-0.997372535290324[/C][/ROW]
[ROW][C]S.D.[/C][C]0.725474501147471[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.37478647934944[/C][/ROW]
[ROW][C]p-value[/C][C]0.192431168732869[/C][/ROW]
[ROW][C]Lambda[/C][C]1.99737253529032[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30998&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30998&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	17.0717399589404
beta	-0.997372535290324
S.D.	0.725474501147471
T-STAT	-1.37478647934944
p-value	0.192431168732869
Lambda	1.99737253529032

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