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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, 07 Dec 2011 15:52:58 -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/Dec/07/t1323291315nq2qb6u2q10lvep.htm/, Retrieved Thu, 02 May 2024 15:54:48 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=152724, Retrieved Thu, 02 May 2024 15:54:48 +0000

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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)

-     [Bootstrap Plot - Central Tendency] [Bootstrap Plot Ma...] [2011-12-07 19:27:53] [cd4d40f02277e4fcf26b7d594bde661c]
- RMPD    [Standard Deviation-Mean Plot] [standard deviatio...] [2011-12-07 20:52:58] [aa823a344a22650d2ad0f207182fbcde] [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=152724&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=152724&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152724&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	30.485	0.147986485869487	0.329999999999998
2	30.985	0.131782649338472	0.309999999999999
3	31.1775	0.0386221007541878	0.0799999999999983
4	31.46	0.19356308187944	0.460000000000001
5	31.965	0.169803808359332	0.389999999999997
6	32.5175	0.262090951134652	0.609999999999999
7	34.815	0.910695704759094	2.16999999999999
8	37.9175	0.759797122044211	1.79
9	39.6375	0.377215676591877	0.840000000000003
10	41.05	0.669576980886689	1.5
11	42.2025	0.32221886971436	0.689999999999998
12	43.2425	0.359200501113236	0.75
13	45.64	1.93819503662557	4.36
14	50.21	0.508396170979549	1.13
15	52.095	0.632376470150494	1.41
16	53.8075	0.872711292467331	2.07
17	56.3725	0.59583974355526	1.33
18	58.06	0.60404194114868	1.41
19	60.5775	1.54549614471642	3.23999999999999
20	65.15	1.50299700598504	3.32999999999999
21	71.4475	1.93797789805079	4.55000000000001

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 30.485 & 0.147986485869487 & 0.329999999999998 \tabularnewline
2 & 30.985 & 0.131782649338472 & 0.309999999999999 \tabularnewline
3 & 31.1775 & 0.0386221007541878 & 0.0799999999999983 \tabularnewline
4 & 31.46 & 0.19356308187944 & 0.460000000000001 \tabularnewline
5 & 31.965 & 0.169803808359332 & 0.389999999999997 \tabularnewline
6 & 32.5175 & 0.262090951134652 & 0.609999999999999 \tabularnewline
7 & 34.815 & 0.910695704759094 & 2.16999999999999 \tabularnewline
8 & 37.9175 & 0.759797122044211 & 1.79 \tabularnewline
9 & 39.6375 & 0.377215676591877 & 0.840000000000003 \tabularnewline
10 & 41.05 & 0.669576980886689 & 1.5 \tabularnewline
11 & 42.2025 & 0.32221886971436 & 0.689999999999998 \tabularnewline
12 & 43.2425 & 0.359200501113236 & 0.75 \tabularnewline
13 & 45.64 & 1.93819503662557 & 4.36 \tabularnewline
14 & 50.21 & 0.508396170979549 & 1.13 \tabularnewline
15 & 52.095 & 0.632376470150494 & 1.41 \tabularnewline
16 & 53.8075 & 0.872711292467331 & 2.07 \tabularnewline
17 & 56.3725 & 0.59583974355526 & 1.33 \tabularnewline
18 & 58.06 & 0.60404194114868 & 1.41 \tabularnewline
19 & 60.5775 & 1.54549614471642 & 3.23999999999999 \tabularnewline
20 & 65.15 & 1.50299700598504 & 3.32999999999999 \tabularnewline
21 & 71.4475 & 1.93797789805079 & 4.55000000000001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152724&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]30.485[/C][C]0.147986485869487[/C][C]0.329999999999998[/C][/ROW]
[ROW][C]2[/C][C]30.985[/C][C]0.131782649338472[/C][C]0.309999999999999[/C][/ROW]
[ROW][C]3[/C][C]31.1775[/C][C]0.0386221007541878[/C][C]0.0799999999999983[/C][/ROW]
[ROW][C]4[/C][C]31.46[/C][C]0.19356308187944[/C][C]0.460000000000001[/C][/ROW]
[ROW][C]5[/C][C]31.965[/C][C]0.169803808359332[/C][C]0.389999999999997[/C][/ROW]
[ROW][C]6[/C][C]32.5175[/C][C]0.262090951134652[/C][C]0.609999999999999[/C][/ROW]
[ROW][C]7[/C][C]34.815[/C][C]0.910695704759094[/C][C]2.16999999999999[/C][/ROW]
[ROW][C]8[/C][C]37.9175[/C][C]0.759797122044211[/C][C]1.79[/C][/ROW]
[ROW][C]9[/C][C]39.6375[/C][C]0.377215676591877[/C][C]0.840000000000003[/C][/ROW]
[ROW][C]10[/C][C]41.05[/C][C]0.669576980886689[/C][C]1.5[/C][/ROW]
[ROW][C]11[/C][C]42.2025[/C][C]0.32221886971436[/C][C]0.689999999999998[/C][/ROW]
[ROW][C]12[/C][C]43.2425[/C][C]0.359200501113236[/C][C]0.75[/C][/ROW]
[ROW][C]13[/C][C]45.64[/C][C]1.93819503662557[/C][C]4.36[/C][/ROW]
[ROW][C]14[/C][C]50.21[/C][C]0.508396170979549[/C][C]1.13[/C][/ROW]
[ROW][C]15[/C][C]52.095[/C][C]0.632376470150494[/C][C]1.41[/C][/ROW]
[ROW][C]16[/C][C]53.8075[/C][C]0.872711292467331[/C][C]2.07[/C][/ROW]
[ROW][C]17[/C][C]56.3725[/C][C]0.59583974355526[/C][C]1.33[/C][/ROW]
[ROW][C]18[/C][C]58.06[/C][C]0.60404194114868[/C][C]1.41[/C][/ROW]
[ROW][C]19[/C][C]60.5775[/C][C]1.54549614471642[/C][C]3.23999999999999[/C][/ROW]
[ROW][C]20[/C][C]65.15[/C][C]1.50299700598504[/C][C]3.32999999999999[/C][/ROW]
[ROW][C]21[/C][C]71.4475[/C][C]1.93797789805079[/C][C]4.55000000000001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152724&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152724&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	30.485	0.147986485869487	0.329999999999998
2	30.985	0.131782649338472	0.309999999999999
3	31.1775	0.0386221007541878	0.0799999999999983
4	31.46	0.19356308187944	0.460000000000001
5	31.965	0.169803808359332	0.389999999999997
6	32.5175	0.262090951134652	0.609999999999999
7	34.815	0.910695704759094	2.16999999999999
8	37.9175	0.759797122044211	1.79
9	39.6375	0.377215676591877	0.840000000000003
10	41.05	0.669576980886689	1.5
11	42.2025	0.32221886971436	0.689999999999998
12	43.2425	0.359200501113236	0.75
13	45.64	1.93819503662557	4.36
14	50.21	0.508396170979549	1.13
15	52.095	0.632376470150494	1.41
16	53.8075	0.872711292467331	2.07
17	56.3725	0.59583974355526	1.33
18	58.06	0.60404194114868	1.41
19	60.5775	1.54549614471642	3.23999999999999
20	65.15	1.50299700598504	3.32999999999999
21	71.4475	1.93797789805079	4.55000000000001

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-0.829191089643735
beta	0.0338999681325687
S.D.	0.00727454962032084
T-STAT	4.66007792948061
p-value	0.000170631813808691

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.829191089643735 \tabularnewline
beta & 0.0338999681325687 \tabularnewline
S.D. & 0.00727454962032084 \tabularnewline
T-STAT & 4.66007792948061 \tabularnewline
p-value & 0.000170631813808691 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152724&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.829191089643735[/C][/ROW]
[ROW][C]beta[/C][C]0.0338999681325687[/C][/ROW]
[ROW][C]S.D.[/C][C]0.00727454962032084[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.66007792948061[/C][/ROW]
[ROW][C]p-value[/C][C]0.000170631813808691[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152724&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152724&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	-0.829191089643735
beta	0.0338999681325687
S.D.	0.00727454962032084
T-STAT	4.66007792948061
p-value	0.000170631813808691

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-11.4171668501138
beta	2.82940998108097
S.D.	0.528164772186914
T-STAT	5.3570592551365
p-value	3.60366486580385e-05
Lambda	-1.82940998108097

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -11.4171668501138 \tabularnewline
beta & 2.82940998108097 \tabularnewline
S.D. & 0.528164772186914 \tabularnewline
T-STAT & 5.3570592551365 \tabularnewline
p-value & 3.60366486580385e-05 \tabularnewline
Lambda & -1.82940998108097 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152724&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-11.4171668501138[/C][/ROW]
[ROW][C]beta[/C][C]2.82940998108097[/C][/ROW]
[ROW][C]S.D.[/C][C]0.528164772186914[/C][/ROW]
[ROW][C]T-STAT[/C][C]5.3570592551365[/C][/ROW]
[ROW][C]p-value[/C][C]3.60366486580385e-05[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.82940998108097[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152724&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152724&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	-11.4171668501138
beta	2.82940998108097
S.D.	0.528164772186914
T-STAT	5.3570592551365
p-value	3.60366486580385e-05
Lambda	-1.82940998108097

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')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code