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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

Mon, 02 Aug 2010 13:51:46 +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/Aug/02/t1280757786wtzw7fewtj4qnpk.htm/, Retrieved Thu, 02 May 2024 12:43:16 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78220, Retrieved Thu, 02 May 2024 12:43:16 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Van Puyenbroeck Cassandra

Estimated Impact

218

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

-       [Standard Deviation-Mean Plot] [Tijdreeks 2 - Sta...] [2010-08-02 13:51:46] [0e5311d1fc10a1511b42f76588fb6510] [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	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78220&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78220&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78220&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	406.25	1.70782512765993	4
2	402.25	1.25830573921179	3
3	406	1.4142135623731	3
4	402.75	2.21735578260835	5
5	401	7.39369100427294	18
6	394.5	3.3166247903554	7
7	394.5	4.04145188432738	9
8	384.5	9.46924847422786	23
9	365.75	2.06155281280883	4
10	357.5	8.81286937760152	20
11	340	13.735598518691	31
12	318.5	5.06622805119022	11
13	309.75	13.6961065027012	30
14	281.75	19.4315036302735	42
15	250.25	4.03112887414927	9
16	232.25	16.7207455974108	39
17	210.75	12.9711217710728	27
18	185.25	4.5	11
19	169.5	18.1567251085284	41
20	139.75	14.4308696896618	30
21	114	4.16333199893227	10

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 406.25 & 1.70782512765993 & 4 \tabularnewline
2 & 402.25 & 1.25830573921179 & 3 \tabularnewline
3 & 406 & 1.4142135623731 & 3 \tabularnewline
4 & 402.75 & 2.21735578260835 & 5 \tabularnewline
5 & 401 & 7.39369100427294 & 18 \tabularnewline
6 & 394.5 & 3.3166247903554 & 7 \tabularnewline
7 & 394.5 & 4.04145188432738 & 9 \tabularnewline
8 & 384.5 & 9.46924847422786 & 23 \tabularnewline
9 & 365.75 & 2.06155281280883 & 4 \tabularnewline
10 & 357.5 & 8.81286937760152 & 20 \tabularnewline
11 & 340 & 13.735598518691 & 31 \tabularnewline
12 & 318.5 & 5.06622805119022 & 11 \tabularnewline
13 & 309.75 & 13.6961065027012 & 30 \tabularnewline
14 & 281.75 & 19.4315036302735 & 42 \tabularnewline
15 & 250.25 & 4.03112887414927 & 9 \tabularnewline
16 & 232.25 & 16.7207455974108 & 39 \tabularnewline
17 & 210.75 & 12.9711217710728 & 27 \tabularnewline
18 & 185.25 & 4.5 & 11 \tabularnewline
19 & 169.5 & 18.1567251085284 & 41 \tabularnewline
20 & 139.75 & 14.4308696896618 & 30 \tabularnewline
21 & 114 & 4.16333199893227 & 10 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78220&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]406.25[/C][C]1.70782512765993[/C][C]4[/C][/ROW]
[ROW][C]2[/C][C]402.25[/C][C]1.25830573921179[/C][C]3[/C][/ROW]
[ROW][C]3[/C][C]406[/C][C]1.4142135623731[/C][C]3[/C][/ROW]
[ROW][C]4[/C][C]402.75[/C][C]2.21735578260835[/C][C]5[/C][/ROW]
[ROW][C]5[/C][C]401[/C][C]7.39369100427294[/C][C]18[/C][/ROW]
[ROW][C]6[/C][C]394.5[/C][C]3.3166247903554[/C][C]7[/C][/ROW]
[ROW][C]7[/C][C]394.5[/C][C]4.04145188432738[/C][C]9[/C][/ROW]
[ROW][C]8[/C][C]384.5[/C][C]9.46924847422786[/C][C]23[/C][/ROW]
[ROW][C]9[/C][C]365.75[/C][C]2.06155281280883[/C][C]4[/C][/ROW]
[ROW][C]10[/C][C]357.5[/C][C]8.81286937760152[/C][C]20[/C][/ROW]
[ROW][C]11[/C][C]340[/C][C]13.735598518691[/C][C]31[/C][/ROW]
[ROW][C]12[/C][C]318.5[/C][C]5.06622805119022[/C][C]11[/C][/ROW]
[ROW][C]13[/C][C]309.75[/C][C]13.6961065027012[/C][C]30[/C][/ROW]
[ROW][C]14[/C][C]281.75[/C][C]19.4315036302735[/C][C]42[/C][/ROW]
[ROW][C]15[/C][C]250.25[/C][C]4.03112887414927[/C][C]9[/C][/ROW]
[ROW][C]16[/C][C]232.25[/C][C]16.7207455974108[/C][C]39[/C][/ROW]
[ROW][C]17[/C][C]210.75[/C][C]12.9711217710728[/C][C]27[/C][/ROW]
[ROW][C]18[/C][C]185.25[/C][C]4.5[/C][C]11[/C][/ROW]
[ROW][C]19[/C][C]169.5[/C][C]18.1567251085284[/C][C]41[/C][/ROW]
[ROW][C]20[/C][C]139.75[/C][C]14.4308696896618[/C][C]30[/C][/ROW]
[ROW][C]21[/C][C]114[/C][C]4.16333199893227[/C][C]10[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78220&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78220&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	406.25	1.70782512765993	4
2	402.25	1.25830573921179	3
3	406	1.4142135623731	3
4	402.75	2.21735578260835	5
5	401	7.39369100427294	18
6	394.5	3.3166247903554	7
7	394.5	4.04145188432738	9
8	384.5	9.46924847422786	23
9	365.75	2.06155281280883	4
10	357.5	8.81286937760152	20
11	340	13.735598518691	31
12	318.5	5.06622805119022	11
13	309.75	13.6961065027012	30
14	281.75	19.4315036302735	42
15	250.25	4.03112887414927	9
16	232.25	16.7207455974108	39
17	210.75	12.9711217710728	27
18	185.25	4.5	11
19	169.5	18.1567251085284	41
20	139.75	14.4308696896618	30
21	114	4.16333199893227	10

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	17.2993335177467
beta	-0.0301062366064285
S.D.	0.0123123428790058
T-STAT	-2.44520778070302
p-value	0.0243922826927097

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 17.2993335177467 \tabularnewline
beta & -0.0301062366064285 \tabularnewline
S.D. & 0.0123123428790058 \tabularnewline
T-STAT & -2.44520778070302 \tabularnewline
p-value & 0.0243922826927097 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78220&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]17.2993335177467[/C][/ROW]
[ROW][C]beta[/C][C]-0.0301062366064285[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0123123428790058[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.44520778070302[/C][/ROW]
[ROW][C]p-value[/C][C]0.0243922826927097[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78220&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78220&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	17.2993335177467
beta	-0.0301062366064285
S.D.	0.0123123428790058
T-STAT	-2.44520778070302
p-value	0.0243922826927097

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	7.51063777360579
beta	-1.01647685803229
S.D.	0.472032070287234
T-STAT	-2.15340635100017
p-value	0.0443416496189166
Lambda	2.01647685803229

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 7.51063777360579 \tabularnewline
beta & -1.01647685803229 \tabularnewline
S.D. & 0.472032070287234 \tabularnewline
T-STAT & -2.15340635100017 \tabularnewline
p-value & 0.0443416496189166 \tabularnewline
Lambda & 2.01647685803229 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78220&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]7.51063777360579[/C][/ROW]
[ROW][C]beta[/C][C]-1.01647685803229[/C][/ROW]
[ROW][C]S.D.[/C][C]0.472032070287234[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.15340635100017[/C][/ROW]
[ROW][C]p-value[/C][C]0.0443416496189166[/C][/ROW]
[ROW][C]Lambda[/C][C]2.01647685803229[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78220&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78220&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	7.51063777360579
beta	-1.01647685803229
S.D.	0.472032070287234
T-STAT	-2.15340635100017
p-value	0.0443416496189166
Lambda	2.01647685803229

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