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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

Fri, 26 Dec 2008 13:22:18 -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/26/t123032298226mvrtfuisiguue.htm/, Retrieved Mon, 20 May 2024 09:13:48 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36646, Retrieved Mon, 20 May 2024 09:13:48 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

210

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

-       [Standard Deviation-Mean Plot] [opgave 8 oefening...] [2008-12-26 20:22:18] [c434db3e06036413789480a9f3c4e100] [Current]
-   P     [Standard Deviation-Mean Plot] [Opgave 8 oefening...] [2009-01-15 23:24:42] [74be16979710d4c4e7c6647856088456] 

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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=36646&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=36646&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36646&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	0.8775	0.00957427107756339	0.02
2	0.8725	0.005	0.01
3	0.855	0.01	0.02
4	0.8475	0.0221735578260835	0.05
5	0.91	0.0216024689946928	0.0499999999999999
6	0.955	0.0173205080756888	0.04
7	1.01	0.0391578004149025	0.09
8	1.0875	0.0275378527364305	0.06
9	1.07	0.0374165738677395	0.09
10	1.0325	0.0298607881119482	0.07
11	1.0575	0.0518812747209113	0.11
12	0.9775	0.045	0.1
13	0.975	0.0387298334620742	0.09
14	1	0.00816496580927727	0.02
15	1	0.0182574185835056	0.04
16	1.0175	0.015	0.03
17	0.9825	0.0262995563967659	0.06
18	1.015	0.0173205080756888	0.04
19	1.03	0.0216024689946929	0.05
20	1.125	0.00577350269189613	0.00999999999999979
21	1.13	0.0374165738677393	0.0899999999999999
22	1.135	0.058022983951764	0.14
23	1.2575	0.051234753829798	0.11
24	1.31	0.058309518948453	0.11

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 0.8775 & 0.00957427107756339 & 0.02 \tabularnewline
2 & 0.8725 & 0.005 & 0.01 \tabularnewline
3 & 0.855 & 0.01 & 0.02 \tabularnewline
4 & 0.8475 & 0.0221735578260835 & 0.05 \tabularnewline
5 & 0.91 & 0.0216024689946928 & 0.0499999999999999 \tabularnewline
6 & 0.955 & 0.0173205080756888 & 0.04 \tabularnewline
7 & 1.01 & 0.0391578004149025 & 0.09 \tabularnewline
8 & 1.0875 & 0.0275378527364305 & 0.06 \tabularnewline
9 & 1.07 & 0.0374165738677395 & 0.09 \tabularnewline
10 & 1.0325 & 0.0298607881119482 & 0.07 \tabularnewline
11 & 1.0575 & 0.0518812747209113 & 0.11 \tabularnewline
12 & 0.9775 & 0.045 & 0.1 \tabularnewline
13 & 0.975 & 0.0387298334620742 & 0.09 \tabularnewline
14 & 1 & 0.00816496580927727 & 0.02 \tabularnewline
15 & 1 & 0.0182574185835056 & 0.04 \tabularnewline
16 & 1.0175 & 0.015 & 0.03 \tabularnewline
17 & 0.9825 & 0.0262995563967659 & 0.06 \tabularnewline
18 & 1.015 & 0.0173205080756888 & 0.04 \tabularnewline
19 & 1.03 & 0.0216024689946929 & 0.05 \tabularnewline
20 & 1.125 & 0.00577350269189613 & 0.00999999999999979 \tabularnewline
21 & 1.13 & 0.0374165738677393 & 0.0899999999999999 \tabularnewline
22 & 1.135 & 0.058022983951764 & 0.14 \tabularnewline
23 & 1.2575 & 0.051234753829798 & 0.11 \tabularnewline
24 & 1.31 & 0.058309518948453 & 0.11 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36646&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]0.8775[/C][C]0.00957427107756339[/C][C]0.02[/C][/ROW]
[ROW][C]2[/C][C]0.8725[/C][C]0.005[/C][C]0.01[/C][/ROW]
[ROW][C]3[/C][C]0.855[/C][C]0.01[/C][C]0.02[/C][/ROW]
[ROW][C]4[/C][C]0.8475[/C][C]0.0221735578260835[/C][C]0.05[/C][/ROW]
[ROW][C]5[/C][C]0.91[/C][C]0.0216024689946928[/C][C]0.0499999999999999[/C][/ROW]
[ROW][C]6[/C][C]0.955[/C][C]0.0173205080756888[/C][C]0.04[/C][/ROW]
[ROW][C]7[/C][C]1.01[/C][C]0.0391578004149025[/C][C]0.09[/C][/ROW]
[ROW][C]8[/C][C]1.0875[/C][C]0.0275378527364305[/C][C]0.06[/C][/ROW]
[ROW][C]9[/C][C]1.07[/C][C]0.0374165738677395[/C][C]0.09[/C][/ROW]
[ROW][C]10[/C][C]1.0325[/C][C]0.0298607881119482[/C][C]0.07[/C][/ROW]
[ROW][C]11[/C][C]1.0575[/C][C]0.0518812747209113[/C][C]0.11[/C][/ROW]
[ROW][C]12[/C][C]0.9775[/C][C]0.045[/C][C]0.1[/C][/ROW]
[ROW][C]13[/C][C]0.975[/C][C]0.0387298334620742[/C][C]0.09[/C][/ROW]
[ROW][C]14[/C][C]1[/C][C]0.00816496580927727[/C][C]0.02[/C][/ROW]
[ROW][C]15[/C][C]1[/C][C]0.0182574185835056[/C][C]0.04[/C][/ROW]
[ROW][C]16[/C][C]1.0175[/C][C]0.015[/C][C]0.03[/C][/ROW]
[ROW][C]17[/C][C]0.9825[/C][C]0.0262995563967659[/C][C]0.06[/C][/ROW]
[ROW][C]18[/C][C]1.015[/C][C]0.0173205080756888[/C][C]0.04[/C][/ROW]
[ROW][C]19[/C][C]1.03[/C][C]0.0216024689946929[/C][C]0.05[/C][/ROW]
[ROW][C]20[/C][C]1.125[/C][C]0.00577350269189613[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]21[/C][C]1.13[/C][C]0.0374165738677393[/C][C]0.0899999999999999[/C][/ROW]
[ROW][C]22[/C][C]1.135[/C][C]0.058022983951764[/C][C]0.14[/C][/ROW]
[ROW][C]23[/C][C]1.2575[/C][C]0.051234753829798[/C][C]0.11[/C][/ROW]
[ROW][C]24[/C][C]1.31[/C][C]0.058309518948453[/C][C]0.11[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36646&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36646&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	0.8775	0.00957427107756339	0.02
2	0.8725	0.005	0.01
3	0.855	0.01	0.02
4	0.8475	0.0221735578260835	0.05
5	0.91	0.0216024689946928	0.0499999999999999
6	0.955	0.0173205080756888	0.04
7	1.01	0.0391578004149025	0.09
8	1.0875	0.0275378527364305	0.06
9	1.07	0.0374165738677395	0.09
10	1.0325	0.0298607881119482	0.07
11	1.0575	0.0518812747209113	0.11
12	0.9775	0.045	0.1
13	0.975	0.0387298334620742	0.09
14	1	0.00816496580927727	0.02
15	1	0.0182574185835056	0.04
16	1.0175	0.015	0.03
17	0.9825	0.0262995563967659	0.06
18	1.015	0.0173205080756888	0.04
19	1.03	0.0216024689946929	0.05
20	1.125	0.00577350269189613	0.00999999999999979
21	1.13	0.0374165738677393	0.0899999999999999
22	1.135	0.058022983951764	0.14
23	1.2575	0.051234753829798	0.11
24	1.31	0.058309518948453	0.11

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-0.0670910848800358
beta	0.0930633191014461
S.D.	0.0233152536869742
T-STAT	3.99152075936617
p-value	0.00061573837063213

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.0670910848800358 \tabularnewline
beta & 0.0930633191014461 \tabularnewline
S.D. & 0.0233152536869742 \tabularnewline
T-STAT & 3.99152075936617 \tabularnewline
p-value & 0.00061573837063213 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36646&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.0670910848800358[/C][/ROW]
[ROW][C]beta[/C][C]0.0930633191014461[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0233152536869742[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.99152075936617[/C][/ROW]
[ROW][C]p-value[/C][C]0.00061573837063213[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36646&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36646&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	-0.0670910848800358
beta	0.0930633191014461
S.D.	0.0233152536869742
T-STAT	3.99152075936617
p-value	0.00061573837063213

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-3.84084476171975
beta	3.53177326954623
S.D.	1.15668878179351
T-STAT	3.05334790579539
p-value	0.00582595948343067
Lambda	-2.53177326954623

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.84084476171975 \tabularnewline
beta & 3.53177326954623 \tabularnewline
S.D. & 1.15668878179351 \tabularnewline
T-STAT & 3.05334790579539 \tabularnewline
p-value & 0.00582595948343067 \tabularnewline
Lambda & -2.53177326954623 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36646&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.84084476171975[/C][/ROW]
[ROW][C]beta[/C][C]3.53177326954623[/C][/ROW]
[ROW][C]S.D.[/C][C]1.15668878179351[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.05334790579539[/C][/ROW]
[ROW][C]p-value[/C][C]0.00582595948343067[/C][/ROW]
[ROW][C]Lambda[/C][C]-2.53177326954623[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36646&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36646&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	-3.84084476171975
beta	3.53177326954623
S.D.	1.15668878179351
T-STAT	3.05334790579539
p-value	0.00582595948343067
Lambda	-2.53177326954623

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