Free Statistics

of Irreproducible Research!

Author's title

Maarten Verhaegen 2MAR03 - tweede zit - Oefening 8.2 - Standard deviation M...

Author

*Unverified author*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Sun, 17 Aug 2008 12:38:52 -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/Aug/17/t1218998432fbm1zbym7cwlwrz.htm/, Retrieved Tue, 14 May 2024 19:43:45 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=14622, Retrieved Tue, 14 May 2024 19:43:45 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

187

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

-       [Standard Deviation-Mean Plot] [Maarten Verhaegen...] [2008-08-17 18:38:52] [6cae5450d413d5fde7d2ce6324b75128] [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	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=14622&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=14622&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14622&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	0.615	0.00577350269189626	0.01
2	0.5975	0.00957427107756339	0.02
3	0.585	0.01	0.02
4	0.59	0.0216024689946929	0.05
5	0.63	0.0182574185835056	0.04
6	0.6925	0.0330403793359983	0.07
7	0.74	0.00816496580927727	0.02
8	0.7725	0.015	0.03
9	0.8725	0.0221735578260835	0.05
10	0.765	0.00577350269189626	0.01
11	0.7775	0.0125830573921179	0.03
12	0.7525	0.0221735578260835	0.05
13	0.7275	0.0170782512765993	0.04
14	0.7275	0.015	0.03
15	0.75	0.02	0.04
16	0.7725	0.0287228132326902	0.06
17	0.7125	0.0125830573921179	0.03
18	0.7425	0.005	0.01
19	0.7575	0.0309569593683445	0.07
20	0.8375	0.0298607881119482	0.07
21	0.9075	0.0170782512765993	0.04
22	0.9125	0.0537742193496723	0.12
23	1.03	0.0424264068711929	0.09
24	1.0525	0.0411298755975103	0.09

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 0.615 & 0.00577350269189626 & 0.01 \tabularnewline
2 & 0.5975 & 0.00957427107756339 & 0.02 \tabularnewline
3 & 0.585 & 0.01 & 0.02 \tabularnewline
4 & 0.59 & 0.0216024689946929 & 0.05 \tabularnewline
5 & 0.63 & 0.0182574185835056 & 0.04 \tabularnewline
6 & 0.6925 & 0.0330403793359983 & 0.07 \tabularnewline
7 & 0.74 & 0.00816496580927727 & 0.02 \tabularnewline
8 & 0.7725 & 0.015 & 0.03 \tabularnewline
9 & 0.8725 & 0.0221735578260835 & 0.05 \tabularnewline
10 & 0.765 & 0.00577350269189626 & 0.01 \tabularnewline
11 & 0.7775 & 0.0125830573921179 & 0.03 \tabularnewline
12 & 0.7525 & 0.0221735578260835 & 0.05 \tabularnewline
13 & 0.7275 & 0.0170782512765993 & 0.04 \tabularnewline
14 & 0.7275 & 0.015 & 0.03 \tabularnewline
15 & 0.75 & 0.02 & 0.04 \tabularnewline
16 & 0.7725 & 0.0287228132326902 & 0.06 \tabularnewline
17 & 0.7125 & 0.0125830573921179 & 0.03 \tabularnewline
18 & 0.7425 & 0.005 & 0.01 \tabularnewline
19 & 0.7575 & 0.0309569593683445 & 0.07 \tabularnewline
20 & 0.8375 & 0.0298607881119482 & 0.07 \tabularnewline
21 & 0.9075 & 0.0170782512765993 & 0.04 \tabularnewline
22 & 0.9125 & 0.0537742193496723 & 0.12 \tabularnewline
23 & 1.03 & 0.0424264068711929 & 0.09 \tabularnewline
24 & 1.0525 & 0.0411298755975103 & 0.09 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14622&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]0.615[/C][C]0.00577350269189626[/C][C]0.01[/C][/ROW]
[ROW][C]2[/C][C]0.5975[/C][C]0.00957427107756339[/C][C]0.02[/C][/ROW]
[ROW][C]3[/C][C]0.585[/C][C]0.01[/C][C]0.02[/C][/ROW]
[ROW][C]4[/C][C]0.59[/C][C]0.0216024689946929[/C][C]0.05[/C][/ROW]
[ROW][C]5[/C][C]0.63[/C][C]0.0182574185835056[/C][C]0.04[/C][/ROW]
[ROW][C]6[/C][C]0.6925[/C][C]0.0330403793359983[/C][C]0.07[/C][/ROW]
[ROW][C]7[/C][C]0.74[/C][C]0.00816496580927727[/C][C]0.02[/C][/ROW]
[ROW][C]8[/C][C]0.7725[/C][C]0.015[/C][C]0.03[/C][/ROW]
[ROW][C]9[/C][C]0.8725[/C][C]0.0221735578260835[/C][C]0.05[/C][/ROW]
[ROW][C]10[/C][C]0.765[/C][C]0.00577350269189626[/C][C]0.01[/C][/ROW]
[ROW][C]11[/C][C]0.7775[/C][C]0.0125830573921179[/C][C]0.03[/C][/ROW]
[ROW][C]12[/C][C]0.7525[/C][C]0.0221735578260835[/C][C]0.05[/C][/ROW]
[ROW][C]13[/C][C]0.7275[/C][C]0.0170782512765993[/C][C]0.04[/C][/ROW]
[ROW][C]14[/C][C]0.7275[/C][C]0.015[/C][C]0.03[/C][/ROW]
[ROW][C]15[/C][C]0.75[/C][C]0.02[/C][C]0.04[/C][/ROW]
[ROW][C]16[/C][C]0.7725[/C][C]0.0287228132326902[/C][C]0.06[/C][/ROW]
[ROW][C]17[/C][C]0.7125[/C][C]0.0125830573921179[/C][C]0.03[/C][/ROW]
[ROW][C]18[/C][C]0.7425[/C][C]0.005[/C][C]0.01[/C][/ROW]
[ROW][C]19[/C][C]0.7575[/C][C]0.0309569593683445[/C][C]0.07[/C][/ROW]
[ROW][C]20[/C][C]0.8375[/C][C]0.0298607881119482[/C][C]0.07[/C][/ROW]
[ROW][C]21[/C][C]0.9075[/C][C]0.0170782512765993[/C][C]0.04[/C][/ROW]
[ROW][C]22[/C][C]0.9125[/C][C]0.0537742193496723[/C][C]0.12[/C][/ROW]
[ROW][C]23[/C][C]1.03[/C][C]0.0424264068711929[/C][C]0.09[/C][/ROW]
[ROW][C]24[/C][C]1.0525[/C][C]0.0411298755975103[/C][C]0.09[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14622&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14622&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	0.615	0.00577350269189626	0.01
2	0.5975	0.00957427107756339	0.02
3	0.585	0.01	0.02
4	0.59	0.0216024689946929	0.05
5	0.63	0.0182574185835056	0.04
6	0.6925	0.0330403793359983	0.07
7	0.74	0.00816496580927727	0.02
8	0.7725	0.015	0.03
9	0.8725	0.0221735578260835	0.05
10	0.765	0.00577350269189626	0.01
11	0.7775	0.0125830573921179	0.03
12	0.7525	0.0221735578260835	0.05
13	0.7275	0.0170782512765993	0.04
14	0.7275	0.015	0.03
15	0.75	0.02	0.04
16	0.7725	0.0287228132326902	0.06
17	0.7125	0.0125830573921179	0.03
18	0.7425	0.005	0.01
19	0.7575	0.0309569593683445	0.07
20	0.8375	0.0298607881119482	0.07
21	0.9075	0.0170782512765993	0.04
22	0.9125	0.0537742193496723	0.12
23	1.03	0.0424264068711929	0.09
24	1.0525	0.0411298755975103	0.09

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-0.0294060601060306
beta	0.0656917438455527
S.D.	0.0166576912784645
T-STAT	3.94362836646402
p-value	0.000691934428151954

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.0294060601060306 \tabularnewline
beta & 0.0656917438455527 \tabularnewline
S.D. & 0.0166576912784645 \tabularnewline
T-STAT & 3.94362836646402 \tabularnewline
p-value & 0.000691934428151954 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14622&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.0294060601060306[/C][/ROW]
[ROW][C]beta[/C][C]0.0656917438455527[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0166576912784645[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.94362836646402[/C][/ROW]
[ROW][C]p-value[/C][C]0.000691934428151954[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14622&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14622&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	-0.0294060601060306
beta	0.0656917438455527
S.D.	0.0166576912784645
T-STAT	3.94362836646402
p-value	0.000691934428151954

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-3.43240175196246
beta	2.23885628969463
S.D.	0.7325369930036
T-STAT	3.05630474785269
p-value	0.00578597986009984
Lambda	-1.23885628969463

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.43240175196246 \tabularnewline
beta & 2.23885628969463 \tabularnewline
S.D. & 0.7325369930036 \tabularnewline
T-STAT & 3.05630474785269 \tabularnewline
p-value & 0.00578597986009984 \tabularnewline
Lambda & -1.23885628969463 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14622&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.43240175196246[/C][/ROW]
[ROW][C]beta[/C][C]2.23885628969463[/C][/ROW]
[ROW][C]S.D.[/C][C]0.7325369930036[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.05630474785269[/C][/ROW]
[ROW][C]p-value[/C][C]0.00578597986009984[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.23885628969463[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14622&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14622&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	-3.43240175196246
beta	2.23885628969463
S.D.	0.7325369930036
T-STAT	3.05630474785269
p-value	0.00578597986009984
Lambda	-1.23885628969463

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ;

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

Maarten Verhaegen 2MAR03 - tweede zit - Oefening 8.2 - Standard deviation M...

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code