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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

Mon, 20 Dec 2010 09:25:49 +0000

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/2010/Dec/20/t1292837021schsair51tfdb7u.htm/, Retrieved Sat, 04 May 2024 04:17:54 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112811, Retrieved Sat, 04 May 2024 04:17:54 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

130

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

-       [Standard Deviation-Mean Plot] [Standard deviatio...] [2010-12-20 09:25:49] [19046f4a6967f3fb6f5f17d42e7d38f2] [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=112811&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=112811&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112811&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	113.2	4.22847490237319	9.2
2	116.5	6.63375208058507	13.9
3	113.375	2.03203510468364	4.59999999999999
4	118.375	5.05791459002621	12
5	116.45	2.70493376382244	5.59999999999999
6	117.55	2.45560583156174	5.9
7	119.425	4.63492179006291	10.9
8	117.85	2.93768616431368	7
9	111.175	3.57246413557925	7.8
10	122.75	2.62995563967658	5.2
11	120.3	6.34297511687798	14.1
12	110.175	7.46921459503385	15
13	102.425	5.36182493808467	10.7000000000000
14	103.65	1.98410349192442	4.60000000000001
15	102.2	3.12729915422238	7.2

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 113.2 & 4.22847490237319 & 9.2 \tabularnewline
2 & 116.5 & 6.63375208058507 & 13.9 \tabularnewline
3 & 113.375 & 2.03203510468364 & 4.59999999999999 \tabularnewline
4 & 118.375 & 5.05791459002621 & 12 \tabularnewline
5 & 116.45 & 2.70493376382244 & 5.59999999999999 \tabularnewline
6 & 117.55 & 2.45560583156174 & 5.9 \tabularnewline
7 & 119.425 & 4.63492179006291 & 10.9 \tabularnewline
8 & 117.85 & 2.93768616431368 & 7 \tabularnewline
9 & 111.175 & 3.57246413557925 & 7.8 \tabularnewline
10 & 122.75 & 2.62995563967658 & 5.2 \tabularnewline
11 & 120.3 & 6.34297511687798 & 14.1 \tabularnewline
12 & 110.175 & 7.46921459503385 & 15 \tabularnewline
13 & 102.425 & 5.36182493808467 & 10.7000000000000 \tabularnewline
14 & 103.65 & 1.98410349192442 & 4.60000000000001 \tabularnewline
15 & 102.2 & 3.12729915422238 & 7.2 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112811&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]113.2[/C][C]4.22847490237319[/C][C]9.2[/C][/ROW]
[ROW][C]2[/C][C]116.5[/C][C]6.63375208058507[/C][C]13.9[/C][/ROW]
[ROW][C]3[/C][C]113.375[/C][C]2.03203510468364[/C][C]4.59999999999999[/C][/ROW]
[ROW][C]4[/C][C]118.375[/C][C]5.05791459002621[/C][C]12[/C][/ROW]
[ROW][C]5[/C][C]116.45[/C][C]2.70493376382244[/C][C]5.59999999999999[/C][/ROW]
[ROW][C]6[/C][C]117.55[/C][C]2.45560583156174[/C][C]5.9[/C][/ROW]
[ROW][C]7[/C][C]119.425[/C][C]4.63492179006291[/C][C]10.9[/C][/ROW]
[ROW][C]8[/C][C]117.85[/C][C]2.93768616431368[/C][C]7[/C][/ROW]
[ROW][C]9[/C][C]111.175[/C][C]3.57246413557925[/C][C]7.8[/C][/ROW]
[ROW][C]10[/C][C]122.75[/C][C]2.62995563967658[/C][C]5.2[/C][/ROW]
[ROW][C]11[/C][C]120.3[/C][C]6.34297511687798[/C][C]14.1[/C][/ROW]
[ROW][C]12[/C][C]110.175[/C][C]7.46921459503385[/C][C]15[/C][/ROW]
[ROW][C]13[/C][C]102.425[/C][C]5.36182493808467[/C][C]10.7000000000000[/C][/ROW]
[ROW][C]14[/C][C]103.65[/C][C]1.98410349192442[/C][C]4.60000000000001[/C][/ROW]
[ROW][C]15[/C][C]102.2[/C][C]3.12729915422238[/C][C]7.2[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112811&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112811&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	113.2	4.22847490237319	9.2
2	116.5	6.63375208058507	13.9
3	113.375	2.03203510468364	4.59999999999999
4	118.375	5.05791459002621	12
5	116.45	2.70493376382244	5.59999999999999
6	117.55	2.45560583156174	5.9
7	119.425	4.63492179006291	10.9
8	117.85	2.93768616431368	7
9	111.175	3.57246413557925	7.8
10	122.75	2.62995563967658	5.2
11	120.3	6.34297511687798	14.1
12	110.175	7.46921459503385	15
13	102.425	5.36182493808467	10.7000000000000
14	103.65	1.98410349192442	4.60000000000001
15	102.2	3.12729915422238	7.2

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	2.31235768192998
beta	0.0155317204584721
S.D.	0.0743288985891416
T-STAT	0.208959378563173
p-value	0.837718611165496

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 2.31235768192998 \tabularnewline
beta & 0.0155317204584721 \tabularnewline
S.D. & 0.0743288985891416 \tabularnewline
T-STAT & 0.208959378563173 \tabularnewline
p-value & 0.837718611165496 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112811&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.31235768192998[/C][/ROW]
[ROW][C]beta[/C][C]0.0155317204584721[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0743288985891416[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.208959378563173[/C][/ROW]
[ROW][C]p-value[/C][C]0.837718611165496[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112811&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112811&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	2.31235768192998
beta	0.0155317204584721
S.D.	0.0743288985891416
T-STAT	0.208959378563173
p-value	0.837718611165496

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-1.54477773795083
beta	0.605019930254538
S.D.	2.02968125827010
T-STAT	0.298086178698914
p-value	0.770348169037986
Lambda	0.394980069745462

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.54477773795083 \tabularnewline
beta & 0.605019930254538 \tabularnewline
S.D. & 2.02968125827010 \tabularnewline
T-STAT & 0.298086178698914 \tabularnewline
p-value & 0.770348169037986 \tabularnewline
Lambda & 0.394980069745462 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112811&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.54477773795083[/C][/ROW]
[ROW][C]beta[/C][C]0.605019930254538[/C][/ROW]
[ROW][C]S.D.[/C][C]2.02968125827010[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.298086178698914[/C][/ROW]
[ROW][C]p-value[/C][C]0.770348169037986[/C][/ROW]
[ROW][C]Lambda[/C][C]0.394980069745462[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112811&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112811&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	-1.54477773795083
beta	0.605019930254538
S.D.	2.02968125827010
T-STAT	0.298086178698914
p-value	0.770348169037986
Lambda	0.394980069745462

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