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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

Wed, 17 Dec 2008 08:40:08 -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/17/t12295284728cj3vodsppeugtz.htm/, Retrieved Sun, 26 May 2024 17:44:32 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=34412, Retrieved Sun, 26 May 2024 17:44:32 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

154

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

-       [Standard Deviation-Mean Plot] [Paper 3de Hypohes...] [2008-12-17 15:40:08] [0da3c04827d8ef68db874351a2e09488] [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	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34412&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34412&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34412&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	'George Udny Yule' @ 72.249.76.132

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	101.075	4.51100506169819	10.6
2	114.05	4.66368952654441	9
3	134.325	8.98679586949653	21.1
4	149.425	11.1804516903388	26.7
5	167.225	15.1271004051228	28.7
6	194.925	19.7921491169268	47.8
7	203.95	10.0884422319140	23.5
8	221.45	12.9405048845347	29.1
9	247.825	7.45134216098014	14.7000000000000
10	210.775	7.19368936406533	14.5
11	208.925	17.6647247360382	41.8
12	244.6	12.4010752222002	29.6
13	299.425	23.9940791307633	52.4
14	348.125	28.5390229919199	62
15	442.8	30.3547909453077	65.8

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 101.075 & 4.51100506169819 & 10.6 \tabularnewline
2 & 114.05 & 4.66368952654441 & 9 \tabularnewline
3 & 134.325 & 8.98679586949653 & 21.1 \tabularnewline
4 & 149.425 & 11.1804516903388 & 26.7 \tabularnewline
5 & 167.225 & 15.1271004051228 & 28.7 \tabularnewline
6 & 194.925 & 19.7921491169268 & 47.8 \tabularnewline
7 & 203.95 & 10.0884422319140 & 23.5 \tabularnewline
8 & 221.45 & 12.9405048845347 & 29.1 \tabularnewline
9 & 247.825 & 7.45134216098014 & 14.7000000000000 \tabularnewline
10 & 210.775 & 7.19368936406533 & 14.5 \tabularnewline
11 & 208.925 & 17.6647247360382 & 41.8 \tabularnewline
12 & 244.6 & 12.4010752222002 & 29.6 \tabularnewline
13 & 299.425 & 23.9940791307633 & 52.4 \tabularnewline
14 & 348.125 & 28.5390229919199 & 62 \tabularnewline
15 & 442.8 & 30.3547909453077 & 65.8 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34412&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]101.075[/C][C]4.51100506169819[/C][C]10.6[/C][/ROW]
[ROW][C]2[/C][C]114.05[/C][C]4.66368952654441[/C][C]9[/C][/ROW]
[ROW][C]3[/C][C]134.325[/C][C]8.98679586949653[/C][C]21.1[/C][/ROW]
[ROW][C]4[/C][C]149.425[/C][C]11.1804516903388[/C][C]26.7[/C][/ROW]
[ROW][C]5[/C][C]167.225[/C][C]15.1271004051228[/C][C]28.7[/C][/ROW]
[ROW][C]6[/C][C]194.925[/C][C]19.7921491169268[/C][C]47.8[/C][/ROW]
[ROW][C]7[/C][C]203.95[/C][C]10.0884422319140[/C][C]23.5[/C][/ROW]
[ROW][C]8[/C][C]221.45[/C][C]12.9405048845347[/C][C]29.1[/C][/ROW]
[ROW][C]9[/C][C]247.825[/C][C]7.45134216098014[/C][C]14.7000000000000[/C][/ROW]
[ROW][C]10[/C][C]210.775[/C][C]7.19368936406533[/C][C]14.5[/C][/ROW]
[ROW][C]11[/C][C]208.925[/C][C]17.6647247360382[/C][C]41.8[/C][/ROW]
[ROW][C]12[/C][C]244.6[/C][C]12.4010752222002[/C][C]29.6[/C][/ROW]
[ROW][C]13[/C][C]299.425[/C][C]23.9940791307633[/C][C]52.4[/C][/ROW]
[ROW][C]14[/C][C]348.125[/C][C]28.5390229919199[/C][C]62[/C][/ROW]
[ROW][C]15[/C][C]442.8[/C][C]30.3547909453077[/C][C]65.8[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34412&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34412&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	101.075	4.51100506169819	10.6
2	114.05	4.66368952654441	9
3	134.325	8.98679586949653	21.1
4	149.425	11.1804516903388	26.7
5	167.225	15.1271004051228	28.7
6	194.925	19.7921491169268	47.8
7	203.95	10.0884422319140	23.5
8	221.45	12.9405048845347	29.1
9	247.825	7.45134216098014	14.7000000000000
10	210.775	7.19368936406533	14.5
11	208.925	17.6647247360382	41.8
12	244.6	12.4010752222002	29.6
13	299.425	23.9940791307633	52.4
14	348.125	28.5390229919199	62
15	442.8	30.3547909453077	65.8

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-2.23154765085898
beta	0.0755152416007589
S.D.	0.0138210907357166
T-STAT	5.46376860153386
p-value	0.000108640816119861

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -2.23154765085898 \tabularnewline
beta & 0.0755152416007589 \tabularnewline
S.D. & 0.0138210907357166 \tabularnewline
T-STAT & 5.46376860153386 \tabularnewline
p-value & 0.000108640816119861 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34412&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.23154765085898[/C][/ROW]
[ROW][C]beta[/C][C]0.0755152416007589[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0138210907357166[/C][/ROW]
[ROW][C]T-STAT[/C][C]5.46376860153386[/C][/ROW]
[ROW][C]p-value[/C][C]0.000108640816119861[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34412&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34412&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	-2.23154765085898
beta	0.0755152416007589
S.D.	0.0138210907357166
T-STAT	5.46376860153386
p-value	0.000108640816119861

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-3.78869966690267
beta	1.18377575934465
S.D.	0.250616592331992
T-STAT	4.72345325714309
p-value	0.000398014318118424
Lambda	-0.183775759344647

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.78869966690267 \tabularnewline
beta & 1.18377575934465 \tabularnewline
S.D. & 0.250616592331992 \tabularnewline
T-STAT & 4.72345325714309 \tabularnewline
p-value & 0.000398014318118424 \tabularnewline
Lambda & -0.183775759344647 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34412&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.78869966690267[/C][/ROW]
[ROW][C]beta[/C][C]1.18377575934465[/C][/ROW]
[ROW][C]S.D.[/C][C]0.250616592331992[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.72345325714309[/C][/ROW]
[ROW][C]p-value[/C][C]0.000398014318118424[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.183775759344647[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34412&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34412&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	-3.78869966690267
beta	1.18377575934465
S.D.	0.250616592331992
T-STAT	4.72345325714309
p-value	0.000398014318118424
Lambda	-0.183775759344647

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