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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, 18 Aug 2014 10:16:35 +0100

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/2014/Aug/18/t1408353417dbddiz3qkzusiyx.htm/, Retrieved Thu, 16 May 2024 06:06:23 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235694, Retrieved Thu, 16 May 2024 06:06:23 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Van Reusel Raphael

Estimated Impact

131

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

-       [Standard Deviation-Mean Plot] [Tijdreeks 1] [2014-08-18 09:16:35] [bf566d88435d8cc6ce5d208f6f8dd684] [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	'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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235694&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235694&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235694&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	'Gwilym Jenkins' @ jenkins.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	1079.75	90.1747041732174	269
2	1314.16666666667	158.562768376285	403
3	1727.5	141.944611476705	372
4	2122.75	150.359039997903	393
5	2556.66666666667	214.648691135214	569
6	3218.91666666667	252.127477977937	724
7	4036.08333333333	291.792721677979	806
8	4896.33333333333	320.067133109555	848
9	5829.5	368.429221030432	1023
10	6764.58333333333	406.980557572993	1096

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 1079.75 & 90.1747041732174 & 269 \tabularnewline
2 & 1314.16666666667 & 158.562768376285 & 403 \tabularnewline
3 & 1727.5 & 141.944611476705 & 372 \tabularnewline
4 & 2122.75 & 150.359039997903 & 393 \tabularnewline
5 & 2556.66666666667 & 214.648691135214 & 569 \tabularnewline
6 & 3218.91666666667 & 252.127477977937 & 724 \tabularnewline
7 & 4036.08333333333 & 291.792721677979 & 806 \tabularnewline
8 & 4896.33333333333 & 320.067133109555 & 848 \tabularnewline
9 & 5829.5 & 368.429221030432 & 1023 \tabularnewline
10 & 6764.58333333333 & 406.980557572993 & 1096 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235694&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]1079.75[/C][C]90.1747041732174[/C][C]269[/C][/ROW]
[ROW][C]2[/C][C]1314.16666666667[/C][C]158.562768376285[/C][C]403[/C][/ROW]
[ROW][C]3[/C][C]1727.5[/C][C]141.944611476705[/C][C]372[/C][/ROW]
[ROW][C]4[/C][C]2122.75[/C][C]150.359039997903[/C][C]393[/C][/ROW]
[ROW][C]5[/C][C]2556.66666666667[/C][C]214.648691135214[/C][C]569[/C][/ROW]
[ROW][C]6[/C][C]3218.91666666667[/C][C]252.127477977937[/C][C]724[/C][/ROW]
[ROW][C]7[/C][C]4036.08333333333[/C][C]291.792721677979[/C][C]806[/C][/ROW]
[ROW][C]8[/C][C]4896.33333333333[/C][C]320.067133109555[/C][C]848[/C][/ROW]
[ROW][C]9[/C][C]5829.5[/C][C]368.429221030432[/C][C]1023[/C][/ROW]
[ROW][C]10[/C][C]6764.58333333333[/C][C]406.980557572993[/C][C]1096[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235694&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235694&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	1079.75	90.1747041732174	269
2	1314.16666666667	158.562768376285	403
3	1727.5	141.944611476705	372
4	2122.75	150.359039997903	393
5	2556.66666666667	214.648691135214	569
6	3218.91666666667	252.127477977937	724
7	4036.08333333333	291.792721677979	806
8	4896.33333333333	320.067133109555	848
9	5829.5	368.429221030432	1023
10	6764.58333333333	406.980557572993	1096

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	61.7482665118851
beta	0.0529896564119498
S.D.	0.00349941095359969
T-STAT	15.1424502907958
p-value	3.58108558402338e-07

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 61.7482665118851 \tabularnewline
beta & 0.0529896564119498 \tabularnewline
S.D. & 0.00349941095359969 \tabularnewline
T-STAT & 15.1424502907958 \tabularnewline
p-value & 3.58108558402338e-07 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235694&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]61.7482665118851[/C][/ROW]
[ROW][C]beta[/C][C]0.0529896564119498[/C][/ROW]
[ROW][C]S.D.[/C][C]0.00349941095359969[/C][/ROW]
[ROW][C]T-STAT[/C][C]15.1424502907958[/C][/ROW]
[ROW][C]p-value[/C][C]3.58108558402338e-07[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235694&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235694&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	61.7482665118851
beta	0.0529896564119498
S.D.	0.00349941095359969
T-STAT	15.1424502907958
p-value	3.58108558402338e-07

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-0.554019716370179
beta	0.746456596625949
S.D.	0.0667724889780572
T-STAT	11.1791039700684
p-value	3.67198492345331e-06
Lambda	0.253543403374051

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -0.554019716370179 \tabularnewline
beta & 0.746456596625949 \tabularnewline
S.D. & 0.0667724889780572 \tabularnewline
T-STAT & 11.1791039700684 \tabularnewline
p-value & 3.67198492345331e-06 \tabularnewline
Lambda & 0.253543403374051 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235694&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.554019716370179[/C][/ROW]
[ROW][C]beta[/C][C]0.746456596625949[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0667724889780572[/C][/ROW]
[ROW][C]T-STAT[/C][C]11.1791039700684[/C][/ROW]
[ROW][C]p-value[/C][C]3.67198492345331e-06[/C][/ROW]
[ROW][C]Lambda[/C][C]0.253543403374051[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235694&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235694&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	-0.554019716370179
beta	0.746456596625949
S.D.	0.0667724889780572
T-STAT	11.1791039700684
p-value	3.67198492345331e-06
Lambda	0.253543403374051

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = 12 ;

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