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Author

*Unverified author*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Sat, 19 Dec 2009 09:02:41 -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/2009/Dec/19/t1261238651ndzy0m96f6n6ul7.htm/, Retrieved Sat, 04 May 2024 03:14:27 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=69656, Retrieved Sat, 04 May 2024 03:14:27 +0000

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IsPrivate?

No (this computation is public)

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Estimated Impact

120

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

-       [Standard Deviation-Mean Plot] [] [2009-12-19 16:02:41] [e24e91da8d334fb8882bf413603fde71] [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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69656&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69656&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69656&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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	97.425	10.0264234234679	20.9
2	100.925	8.73665649242699	20.6
3	100.8	3.93700393700591	8.4
4	97.9	10.9456231739754	22.4
5	100.575	7.55308987545274	16.6
6	102.5	7.31345791446609	15.7
7	102.425	12.5730863355025	26.7
8	102.6	6.48022633349587	15.7
9	100.375	4.07379839134601	8.8
10	100.925	15.7831925372108	33
11	104	4.26380112106557	9.8
12	106.7	7.29566081082904	14.8
13	103.825	13.9891326869586	29.4
14	109.35	6.5566759871142	14.5
15	109.875	6.19589918144789	13.5
16	106.6	10.8280499937277	24.7
17	111.6	9.2177365262122	22.4
18	112.25	3.72961123979430	8.2
19	107.125	10.7707551576789	20.8
20	100.1	10.9590145542380	24.7
21	95.55	5.12152321092075	11.3

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 97.425 & 10.0264234234679 & 20.9 \tabularnewline
2 & 100.925 & 8.73665649242699 & 20.6 \tabularnewline
3 & 100.8 & 3.93700393700591 & 8.4 \tabularnewline
4 & 97.9 & 10.9456231739754 & 22.4 \tabularnewline
5 & 100.575 & 7.55308987545274 & 16.6 \tabularnewline
6 & 102.5 & 7.31345791446609 & 15.7 \tabularnewline
7 & 102.425 & 12.5730863355025 & 26.7 \tabularnewline
8 & 102.6 & 6.48022633349587 & 15.7 \tabularnewline
9 & 100.375 & 4.07379839134601 & 8.8 \tabularnewline
10 & 100.925 & 15.7831925372108 & 33 \tabularnewline
11 & 104 & 4.26380112106557 & 9.8 \tabularnewline
12 & 106.7 & 7.29566081082904 & 14.8 \tabularnewline
13 & 103.825 & 13.9891326869586 & 29.4 \tabularnewline
14 & 109.35 & 6.5566759871142 & 14.5 \tabularnewline
15 & 109.875 & 6.19589918144789 & 13.5 \tabularnewline
16 & 106.6 & 10.8280499937277 & 24.7 \tabularnewline
17 & 111.6 & 9.2177365262122 & 22.4 \tabularnewline
18 & 112.25 & 3.72961123979430 & 8.2 \tabularnewline
19 & 107.125 & 10.7707551576789 & 20.8 \tabularnewline
20 & 100.1 & 10.9590145542380 & 24.7 \tabularnewline
21 & 95.55 & 5.12152321092075 & 11.3 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69656&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]97.425[/C][C]10.0264234234679[/C][C]20.9[/C][/ROW]
[ROW][C]2[/C][C]100.925[/C][C]8.73665649242699[/C][C]20.6[/C][/ROW]
[ROW][C]3[/C][C]100.8[/C][C]3.93700393700591[/C][C]8.4[/C][/ROW]
[ROW][C]4[/C][C]97.9[/C][C]10.9456231739754[/C][C]22.4[/C][/ROW]
[ROW][C]5[/C][C]100.575[/C][C]7.55308987545274[/C][C]16.6[/C][/ROW]
[ROW][C]6[/C][C]102.5[/C][C]7.31345791446609[/C][C]15.7[/C][/ROW]
[ROW][C]7[/C][C]102.425[/C][C]12.5730863355025[/C][C]26.7[/C][/ROW]
[ROW][C]8[/C][C]102.6[/C][C]6.48022633349587[/C][C]15.7[/C][/ROW]
[ROW][C]9[/C][C]100.375[/C][C]4.07379839134601[/C][C]8.8[/C][/ROW]
[ROW][C]10[/C][C]100.925[/C][C]15.7831925372108[/C][C]33[/C][/ROW]
[ROW][C]11[/C][C]104[/C][C]4.26380112106557[/C][C]9.8[/C][/ROW]
[ROW][C]12[/C][C]106.7[/C][C]7.29566081082904[/C][C]14.8[/C][/ROW]
[ROW][C]13[/C][C]103.825[/C][C]13.9891326869586[/C][C]29.4[/C][/ROW]
[ROW][C]14[/C][C]109.35[/C][C]6.5566759871142[/C][C]14.5[/C][/ROW]
[ROW][C]15[/C][C]109.875[/C][C]6.19589918144789[/C][C]13.5[/C][/ROW]
[ROW][C]16[/C][C]106.6[/C][C]10.8280499937277[/C][C]24.7[/C][/ROW]
[ROW][C]17[/C][C]111.6[/C][C]9.2177365262122[/C][C]22.4[/C][/ROW]
[ROW][C]18[/C][C]112.25[/C][C]3.72961123979430[/C][C]8.2[/C][/ROW]
[ROW][C]19[/C][C]107.125[/C][C]10.7707551576789[/C][C]20.8[/C][/ROW]
[ROW][C]20[/C][C]100.1[/C][C]10.9590145542380[/C][C]24.7[/C][/ROW]
[ROW][C]21[/C][C]95.55[/C][C]5.12152321092075[/C][C]11.3[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69656&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69656&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	97.425	10.0264234234679	20.9
2	100.925	8.73665649242699	20.6
3	100.8	3.93700393700591	8.4
4	97.9	10.9456231739754	22.4
5	100.575	7.55308987545274	16.6
6	102.5	7.31345791446609	15.7
7	102.425	12.5730863355025	26.7
8	102.6	6.48022633349587	15.7
9	100.375	4.07379839134601	8.8
10	100.925	15.7831925372108	33
11	104	4.26380112106557	9.8
12	106.7	7.29566081082904	14.8
13	103.825	13.9891326869586	29.4
14	109.35	6.5566759871142	14.5
15	109.875	6.19589918144789	13.5
16	106.6	10.8280499937277	24.7
17	111.6	9.2177365262122	22.4
18	112.25	3.72961123979430	8.2
19	107.125	10.7707551576789	20.8
20	100.1	10.9590145542380	24.7
21	95.55	5.12152321092075	11.3

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	19.5779253035792
beta	-0.108025817541818
S.D.	0.166559750876079
T-STAT	-0.648570960112627
p-value	0.524377844425968

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 19.5779253035792 \tabularnewline
beta & -0.108025817541818 \tabularnewline
S.D. & 0.166559750876079 \tabularnewline
T-STAT & -0.648570960112627 \tabularnewline
p-value & 0.524377844425968 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69656&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]19.5779253035792[/C][/ROW]
[ROW][C]beta[/C][C]-0.108025817541818[/C][/ROW]
[ROW][C]S.D.[/C][C]0.166559750876079[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.648570960112627[/C][/ROW]
[ROW][C]p-value[/C][C]0.524377844425968[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69656&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69656&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	19.5779253035792
beta	-0.108025817541818
S.D.	0.166559750876079
T-STAT	-0.648570960112627
p-value	0.524377844425968

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	7.75116744384909
beta	-1.23045491927409
S.D.	2.18863488135471
T-STAT	-0.562202005348865
p-value	0.580551257563485
Lambda	2.23045491927409

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 7.75116744384909 \tabularnewline
beta & -1.23045491927409 \tabularnewline
S.D. & 2.18863488135471 \tabularnewline
T-STAT & -0.562202005348865 \tabularnewline
p-value & 0.580551257563485 \tabularnewline
Lambda & 2.23045491927409 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69656&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]7.75116744384909[/C][/ROW]
[ROW][C]beta[/C][C]-1.23045491927409[/C][/ROW]
[ROW][C]S.D.[/C][C]2.18863488135471[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.562202005348865[/C][/ROW]
[ROW][C]p-value[/C][C]0.580551257563485[/C][/ROW]
[ROW][C]Lambda[/C][C]2.23045491927409[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69656&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69656&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	7.75116744384909
beta	-1.23045491927409
S.D.	2.18863488135471
T-STAT	-0.562202005348865
p-value	0.580551257563485
Lambda	2.23045491927409

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

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code