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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

Wed, 30 Nov 2011 07:43:27 -0500

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/2011/Nov/30/t1322657053x9gsw1bxpkf6r3s.htm/, Retrieved Mon, 29 Apr 2024 16:50:25 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=148911, Retrieved Mon, 29 Apr 2024 16:50:25 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W83

Estimated Impact

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

-       [Standard Deviation-Mean Plot] [Standard deviatio...] [2011-11-30 12:43:27] [18e7d68ff235439d3990cca8ff3322f3] [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' @ jenkins.wessa.net

\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' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148911&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148911&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148911&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' @ jenkins.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	34.5	9.67815409397198	20
2	23.5	8.34665601703261	17
3	25	1.82574185835055	4
4	38.25	9.21502396451939	20
5	34.5	7.68114574786861	16
6	32.25	11.8145390656315	26
7	48.25	3.77491721763537	9
8	47.5	2.88675134594813	7
9	39.25	6.13052471924984	14
10	27.25	12.8419884233972	29
11	24	4.89897948556636	12
12	23.25	3.77491721763537	9
13	19.25	5.37742193496723	12
14	21	6.32455532033676	14
15	18	7.11805216802087	16
16	26.75	5.1234753829798	12
17	29.25	8.61684396980704	18
18	21.75	7.71902411793961	17
19	27	5.71547606649408	13
20	32.25	5.56027577253743	11
21	27	2.16024689946929	5

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 34.5 & 9.67815409397198 & 20 \tabularnewline
2 & 23.5 & 8.34665601703261 & 17 \tabularnewline
3 & 25 & 1.82574185835055 & 4 \tabularnewline
4 & 38.25 & 9.21502396451939 & 20 \tabularnewline
5 & 34.5 & 7.68114574786861 & 16 \tabularnewline
6 & 32.25 & 11.8145390656315 & 26 \tabularnewline
7 & 48.25 & 3.77491721763537 & 9 \tabularnewline
8 & 47.5 & 2.88675134594813 & 7 \tabularnewline
9 & 39.25 & 6.13052471924984 & 14 \tabularnewline
10 & 27.25 & 12.8419884233972 & 29 \tabularnewline
11 & 24 & 4.89897948556636 & 12 \tabularnewline
12 & 23.25 & 3.77491721763537 & 9 \tabularnewline
13 & 19.25 & 5.37742193496723 & 12 \tabularnewline
14 & 21 & 6.32455532033676 & 14 \tabularnewline
15 & 18 & 7.11805216802087 & 16 \tabularnewline
16 & 26.75 & 5.1234753829798 & 12 \tabularnewline
17 & 29.25 & 8.61684396980704 & 18 \tabularnewline
18 & 21.75 & 7.71902411793961 & 17 \tabularnewline
19 & 27 & 5.71547606649408 & 13 \tabularnewline
20 & 32.25 & 5.56027577253743 & 11 \tabularnewline
21 & 27 & 2.16024689946929 & 5 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148911&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]34.5[/C][C]9.67815409397198[/C][C]20[/C][/ROW]
[ROW][C]2[/C][C]23.5[/C][C]8.34665601703261[/C][C]17[/C][/ROW]
[ROW][C]3[/C][C]25[/C][C]1.82574185835055[/C][C]4[/C][/ROW]
[ROW][C]4[/C][C]38.25[/C][C]9.21502396451939[/C][C]20[/C][/ROW]
[ROW][C]5[/C][C]34.5[/C][C]7.68114574786861[/C][C]16[/C][/ROW]
[ROW][C]6[/C][C]32.25[/C][C]11.8145390656315[/C][C]26[/C][/ROW]
[ROW][C]7[/C][C]48.25[/C][C]3.77491721763537[/C][C]9[/C][/ROW]
[ROW][C]8[/C][C]47.5[/C][C]2.88675134594813[/C][C]7[/C][/ROW]
[ROW][C]9[/C][C]39.25[/C][C]6.13052471924984[/C][C]14[/C][/ROW]
[ROW][C]10[/C][C]27.25[/C][C]12.8419884233972[/C][C]29[/C][/ROW]
[ROW][C]11[/C][C]24[/C][C]4.89897948556636[/C][C]12[/C][/ROW]
[ROW][C]12[/C][C]23.25[/C][C]3.77491721763537[/C][C]9[/C][/ROW]
[ROW][C]13[/C][C]19.25[/C][C]5.37742193496723[/C][C]12[/C][/ROW]
[ROW][C]14[/C][C]21[/C][C]6.32455532033676[/C][C]14[/C][/ROW]
[ROW][C]15[/C][C]18[/C][C]7.11805216802087[/C][C]16[/C][/ROW]
[ROW][C]16[/C][C]26.75[/C][C]5.1234753829798[/C][C]12[/C][/ROW]
[ROW][C]17[/C][C]29.25[/C][C]8.61684396980704[/C][C]18[/C][/ROW]
[ROW][C]18[/C][C]21.75[/C][C]7.71902411793961[/C][C]17[/C][/ROW]
[ROW][C]19[/C][C]27[/C][C]5.71547606649408[/C][C]13[/C][/ROW]
[ROW][C]20[/C][C]32.25[/C][C]5.56027577253743[/C][C]11[/C][/ROW]
[ROW][C]21[/C][C]27[/C][C]2.16024689946929[/C][C]5[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148911&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148911&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	34.5	9.67815409397198	20
2	23.5	8.34665601703261	17
3	25	1.82574185835055	4
4	38.25	9.21502396451939	20
5	34.5	7.68114574786861	16
6	32.25	11.8145390656315	26
7	48.25	3.77491721763537	9
8	47.5	2.88675134594813	7
9	39.25	6.13052471924984	14
10	27.25	12.8419884233972	29
11	24	4.89897948556636	12
12	23.25	3.77491721763537	9
13	19.25	5.37742193496723	12
14	21	6.32455532033676	14
15	18	7.11805216802087	16
16	26.75	5.1234753829798	12
17	29.25	8.61684396980704	18
18	21.75	7.71902411793961	17
19	27	5.71547606649408	13
20	32.25	5.56027577253743	11
21	27	2.16024689946929	5

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	7.08331441490287
beta	-0.0196287082268678
S.D.	0.0796084087758674
T-STAT	-0.246565765208688
p-value	0.807888614318818

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 7.08331441490287 \tabularnewline
beta & -0.0196287082268678 \tabularnewline
S.D. & 0.0796084087758674 \tabularnewline
T-STAT & -0.246565765208688 \tabularnewline
p-value & 0.807888614318818 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148911&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]7.08331441490287[/C][/ROW]
[ROW][C]beta[/C][C]-0.0196287082268678[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0796084087758674[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.246565765208688[/C][/ROW]
[ROW][C]p-value[/C][C]0.807888614318818[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148911&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148911&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	7.08331441490287
beta	-0.0196287082268678
S.D.	0.0796084087758674
T-STAT	-0.246565765208688
p-value	0.807888614318818

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	2.04503595615056
beta	-0.0853574309764783
S.D.	0.432235679296362
T-STAT	-0.197478910383872
p-value	0.845550105236564
Lambda	1.08535743097648

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 2.04503595615056 \tabularnewline
beta & -0.0853574309764783 \tabularnewline
S.D. & 0.432235679296362 \tabularnewline
T-STAT & -0.197478910383872 \tabularnewline
p-value & 0.845550105236564 \tabularnewline
Lambda & 1.08535743097648 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148911&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.04503595615056[/C][/ROW]
[ROW][C]beta[/C][C]-0.0853574309764783[/C][/ROW]
[ROW][C]S.D.[/C][C]0.432235679296362[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.197478910383872[/C][/ROW]
[ROW][C]p-value[/C][C]0.845550105236564[/C][/ROW]
[ROW][C]Lambda[/C][C]1.08535743097648[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148911&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148911&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	2.04503595615056
beta	-0.0853574309764783
S.D.	0.432235679296362
T-STAT	-0.197478910383872
p-value	0.845550105236564
Lambda	1.08535743097648

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