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Free Statistics

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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

Fri, 14 Dec 2007 03:12:40 -0700

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/2007/Dec/14/t1197626238o9g2u7jkyysgkg1.htm/, Retrieved Thu, 02 May 2024 16:27:21 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3791, Retrieved Thu, 02 May 2024 16:27:21 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

221

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

-       [Standard Deviation-Mean Plot] [SMP - Serie 3 - p...] [2007-12-14 10:12:40] [921757a21ec3444367392306fe4aab7f] [Current]

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Dataseries X:

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Histogram

Boxplots

2,9
2,6
2,5
3,2
3,1
3,1
2,9
2,5
2,8
3,1
2,6
2,3
2,3
2,6
2,9
2
2,2
2,4
2,3
2,6
1,9
1,1
1,3
1,6
1,7
1,9
1,6
1,8
1,8
1,5
1,6
1
1,5
1,8
1,7
1,2
1,4
1,1
1,3
1,3
1,3
1,3
0,9
1,3
1,8
2,7
2,6
2,9
2,2
2,1
2,3
2,3
2,7
2,6
2,9
3,1
2,8
2,1
2,3
2,2

Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3791&T=0

[TABLE]
[ROW][C]Summary of compuational 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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3791&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3791&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 compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	2.8	0.295419578350399	1.8
2	2.1	0.544392906239268	1.8
3	1.59166666666667	0.264431923988467	0.6
4	1.65833333333333	0.682852750443226	1.6
5	2.46666666666667	0.339339822525319	1.8

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 2.8 & 0.295419578350399 & 1.8 \tabularnewline
2 & 2.1 & 0.544392906239268 & 1.8 \tabularnewline
3 & 1.59166666666667 & 0.264431923988467 & 0.6 \tabularnewline
4 & 1.65833333333333 & 0.682852750443226 & 1.6 \tabularnewline
5 & 2.46666666666667 & 0.339339822525319 & 1.8 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3791&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]2.8[/C][C]0.295419578350399[/C][C]1.8[/C][/ROW]
[ROW][C]2[/C][C]2.1[/C][C]0.544392906239268[/C][C]1.8[/C][/ROW]
[ROW][C]3[/C][C]1.59166666666667[/C][C]0.264431923988467[/C][C]0.6[/C][/ROW]
[ROW][C]4[/C][C]1.65833333333333[/C][C]0.682852750443226[/C][C]1.6[/C][/ROW]
[ROW][C]5[/C][C]2.46666666666667[/C][C]0.339339822525319[/C][C]1.8[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3791&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3791&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	2.8	0.295419578350399	1.8
2	2.1	0.544392906239268	1.8
3	1.59166666666667	0.264431923988467	0.6
4	1.65833333333333	0.682852750443226	1.6
5	2.46666666666667	0.339339822525319	1.8

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	0.730224710859869
beta	-0.143612550023799
S.D.	0.183385997587989
T-STAT	-0.783116224317475
p-value	0.490692145503611

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.730224710859869 \tabularnewline
beta & -0.143612550023799 \tabularnewline
S.D. & 0.183385997587989 \tabularnewline
T-STAT & -0.783116224317475 \tabularnewline
p-value & 0.490692145503611 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3791&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.730224710859869[/C][/ROW]
[ROW][C]beta[/C][C]-0.143612550023799[/C][/ROW]
[ROW][C]S.D.[/C][C]0.183385997587989[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.783116224317475[/C][/ROW]
[ROW][C]p-value[/C][C]0.490692145503611[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3791&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3791&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	0.730224710859869
beta	-0.143612550023799
S.D.	0.183385997587989
T-STAT	-0.783116224317475
p-value	0.490692145503611

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-0.542704277714738
beta	-0.522993673644196
S.D.	0.916042344325416
T-STAT	-0.570927399681872
p-value	0.608014202582531
Lambda	1.52299367364420

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -0.542704277714738 \tabularnewline
beta & -0.522993673644196 \tabularnewline
S.D. & 0.916042344325416 \tabularnewline
T-STAT & -0.570927399681872 \tabularnewline
p-value & 0.608014202582531 \tabularnewline
Lambda & 1.52299367364420 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3791&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.542704277714738[/C][/ROW]
[ROW][C]beta[/C][C]-0.522993673644196[/C][/ROW]
[ROW][C]S.D.[/C][C]0.916042344325416[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.570927399681872[/C][/ROW]
[ROW][C]p-value[/C][C]0.608014202582531[/C][/ROW]
[ROW][C]Lambda[/C][C]1.52299367364420[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3791&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3791&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	-0.542704277714738
beta	-0.522993673644196
S.D.	0.916042344325416
T-STAT	-0.570927399681872
p-value	0.608014202582531
Lambda	1.52299367364420

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