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Author

*Unverified author*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Mon, 15 Aug 2016 19:33:14 +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/2016/Aug/15/t1471286047sgkmsq6n7zd8ckb.htm/, Retrieved Sat, 27 Apr 2024 20:36:09 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sat, 27 Apr 2024 20:36:09 +0200

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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	'George Udny Yule' @ yule.wessa.net
R Framework error message	Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

\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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
R Framework error message & Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values. \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	'George Udny Yule' @ yule.wessa.net
R Framework error message	Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	21459.25	642.415912431701	1916
2	21115.5833333333	763.845231626661	2429
3	20360.25	862.160934670974	2429
4	19790.5	1049.19791875855	3463
5	17931.75	889.642842023492	3021
6	15146.25	1394.44365739042	4859
7	10330.5833333333	1101.8160594164	3904
8	6741.66666666667	773.458506066137	2800
9	5252.08333333333	1023.62923493131	3833
10	5533	1042.56222835858	3904

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 21459.25 & 642.415912431701 & 1916 \tabularnewline
2 & 21115.5833333333 & 763.845231626661 & 2429 \tabularnewline
3 & 20360.25 & 862.160934670974 & 2429 \tabularnewline
4 & 19790.5 & 1049.19791875855 & 3463 \tabularnewline
5 & 17931.75 & 889.642842023492 & 3021 \tabularnewline
6 & 15146.25 & 1394.44365739042 & 4859 \tabularnewline
7 & 10330.5833333333 & 1101.8160594164 & 3904 \tabularnewline
8 & 6741.66666666667 & 773.458506066137 & 2800 \tabularnewline
9 & 5252.08333333333 & 1023.62923493131 & 3833 \tabularnewline
10 & 5533 & 1042.56222835858 & 3904 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]21459.25[/C][C]642.415912431701[/C][C]1916[/C][/ROW]
[ROW][C]2[/C][C]21115.5833333333[/C][C]763.845231626661[/C][C]2429[/C][/ROW]
[ROW][C]3[/C][C]20360.25[/C][C]862.160934670974[/C][C]2429[/C][/ROW]
[ROW][C]4[/C][C]19790.5[/C][C]1049.19791875855[/C][C]3463[/C][/ROW]
[ROW][C]5[/C][C]17931.75[/C][C]889.642842023492[/C][C]3021[/C][/ROW]
[ROW][C]6[/C][C]15146.25[/C][C]1394.44365739042[/C][C]4859[/C][/ROW]
[ROW][C]7[/C][C]10330.5833333333[/C][C]1101.8160594164[/C][C]3904[/C][/ROW]
[ROW][C]8[/C][C]6741.66666666667[/C][C]773.458506066137[/C][C]2800[/C][/ROW]
[ROW][C]9[/C][C]5252.08333333333[/C][C]1023.62923493131[/C][C]3833[/C][/ROW]
[ROW][C]10[/C][C]5533[/C][C]1042.56222835858[/C][C]3904[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	21459.25	642.415912431701	1916
2	21115.5833333333	763.845231626661	2429
3	20360.25	862.160934670974	2429
4	19790.5	1049.19791875855	3463
5	17931.75	889.642842023492	3021
6	15146.25	1394.44365739042	4859
7	10330.5833333333	1101.8160594164	3904
8	6741.66666666667	773.458506066137	2800
9	5252.08333333333	1023.62923493131	3833
10	5533	1042.56222835858	3904

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	1096.22241100992
beta	-0.00987778455930086
S.D.	0.0107060577779604
T-STAT	-0.92263508792521
p-value	0.383179968004858

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1096.22241100992 \tabularnewline
beta & -0.00987778455930086 \tabularnewline
S.D. & 0.0107060577779604 \tabularnewline
T-STAT & -0.92263508792521 \tabularnewline
p-value & 0.383179968004858 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1096.22241100992[/C][/ROW]
[ROW][C]beta[/C][C]-0.00987778455930086[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0107060577779604[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.92263508792521[/C][/ROW]
[ROW][C]p-value[/C][C]0.383179968004858[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	1096.22241100992
beta	-0.00987778455930086
S.D.	0.0107060577779604
T-STAT	-0.92263508792521
p-value	0.383179968004858

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	7.83381240370045
beta	-0.105414016004749
S.D.	0.130868795597244
T-STAT	-0.805493895803599
p-value	0.443814994120461
Lambda	1.10541401600475

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 7.83381240370045 \tabularnewline
beta & -0.105414016004749 \tabularnewline
S.D. & 0.130868795597244 \tabularnewline
T-STAT & -0.805493895803599 \tabularnewline
p-value & 0.443814994120461 \tabularnewline
Lambda & 1.10541401600475 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]7.83381240370045[/C][/ROW]
[ROW][C]beta[/C][C]-0.105414016004749[/C][/ROW]
[ROW][C]S.D.[/C][C]0.130868795597244[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.805493895803599[/C][/ROW]
[ROW][C]p-value[/C][C]0.443814994120461[/C][/ROW]
[ROW][C]Lambda[/C][C]1.10541401600475[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	7.83381240370045
beta	-0.105414016004749
S.D.	0.130868795597244
T-STAT	-0.805493895803599
p-value	0.443814994120461
Lambda	1.10541401600475

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