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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Mon, 27 Dec 2010 15:56:31 +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/Dec/27/t1293465441yzmi8wwa902cj7g.htm/, Retrieved Tue, 07 May 2024 00:29:22 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116041, Retrieved Tue, 07 May 2024 00:29:22 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

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

-       [Standard Deviation-Mean Plot] [] [2010-12-27 15:56:31] [c984196f1244e05baf3e7c2e52d47a33] [Current]

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Dataseries X:

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Histogram

Boxplots

8.5
8.6
8.5
8.2
8.1
7.9
8.6
8.7
8.7
8.5
8.4
8.5
8.7
8.7
8.6
8.5
8.3
8
8.2
8.1
8.1
8
7.9
7.9
8
8
7.9
8
7.7
7.2
7.5
7.3
7
7
7
7.2
7.3
7.1
6.8
6.4
6.1
6.5
7.7
.9
7.5
6.9
6.6
6.9
7.7
8
8
7.7
7.3
7.4
8.1
8.3
8.1
7.9
7.9
8.3
8.6

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' @ 72.249.76.132

\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' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116041&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' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116041&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116041&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' @ 72.249.76.132

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	8.43333333333333	0.246182981958665	0.799999999999999
2	8.25	0.303015151136344	0.799999999999999
3	7.48333333333333	0.417423554968361	1
4	6.39166666666667	1.79010326433133	6.8
5	7.89166666666667	0.317542648054294	1

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 8.43333333333333 & 0.246182981958665 & 0.799999999999999 \tabularnewline
2 & 8.25 & 0.303015151136344 & 0.799999999999999 \tabularnewline
3 & 7.48333333333333 & 0.417423554968361 & 1 \tabularnewline
4 & 6.39166666666667 & 1.79010326433133 & 6.8 \tabularnewline
5 & 7.89166666666667 & 0.317542648054294 & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116041&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]8.43333333333333[/C][C]0.246182981958665[/C][C]0.799999999999999[/C][/ROW]
[ROW][C]2[/C][C]8.25[/C][C]0.303015151136344[/C][C]0.799999999999999[/C][/ROW]
[ROW][C]3[/C][C]7.48333333333333[/C][C]0.417423554968361[/C][C]1[/C][/ROW]
[ROW][C]4[/C][C]6.39166666666667[/C][C]1.79010326433133[/C][C]6.8[/C][/ROW]
[ROW][C]5[/C][C]7.89166666666667[/C][C]0.317542648054294[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116041&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116041&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	8.43333333333333	0.246182981958665	0.799999999999999
2	8.25	0.303015151136344	0.799999999999999
3	7.48333333333333	0.417423554968361	1
4	6.39166666666667	1.79010326433133	6.8
5	7.89166666666667	0.317542648054294	1

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	6.43283871863642
beta	-0.756565045324659
S.D.	0.171818238103235
T-STAT	-4.40328718113199
p-value	0.0217197719418821

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 6.43283871863642 \tabularnewline
beta & -0.756565045324659 \tabularnewline
S.D. & 0.171818238103235 \tabularnewline
T-STAT & -4.40328718113199 \tabularnewline
p-value & 0.0217197719418821 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116041&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]6.43283871863642[/C][/ROW]
[ROW][C]beta[/C][C]-0.756565045324659[/C][/ROW]
[ROW][C]S.D.[/C][C]0.171818238103235[/C][/ROW]
[ROW][C]T-STAT[/C][C]-4.40328718113199[/C][/ROW]
[ROW][C]p-value[/C][C]0.0217197719418821[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116041&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116041&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	6.43283871863642
beta	-0.756565045324659
S.D.	0.171818238103235
T-STAT	-4.40328718113199
p-value	0.0217197719418821

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	13.5768023659997
beta	-7.06751116176061
S.D.	0.859380582335344
T-STAT	-8.22395956696489
p-value	0.00376340657163947
Lambda	8.06751116176061

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 13.5768023659997 \tabularnewline
beta & -7.06751116176061 \tabularnewline
S.D. & 0.859380582335344 \tabularnewline
T-STAT & -8.22395956696489 \tabularnewline
p-value & 0.00376340657163947 \tabularnewline
Lambda & 8.06751116176061 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116041&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]13.5768023659997[/C][/ROW]
[ROW][C]beta[/C][C]-7.06751116176061[/C][/ROW]
[ROW][C]S.D.[/C][C]0.859380582335344[/C][/ROW]
[ROW][C]T-STAT[/C][C]-8.22395956696489[/C][/ROW]
[ROW][C]p-value[/C][C]0.00376340657163947[/C][/ROW]
[ROW][C]Lambda[/C][C]8.06751116176061[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116041&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116041&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	13.5768023659997
beta	-7.06751116176061
S.D.	0.859380582335344
T-STAT	-8.22395956696489
p-value	0.00376340657163947
Lambda	8.06751116176061

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