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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

Tue, 24 Nov 2009 04:32:14 -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/2009/Nov/24/t1259062493em4wxm4sh211kt3.htm/, Retrieved Sat, 20 Apr 2024 15:22:29 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58997, Retrieved Sat, 20 Apr 2024 15:22:29 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

133

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

-       [Standard Deviation-Mean Plot] [ws4] [2009-11-24 11:32:14] [94ba0ef70f5b330d175ff4daa1c9cd40] [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' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58997&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58997&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58997&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' @ 72.249.127.135

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	406.733333333333	6.70296180577637	20.8000000000000
2	413.341666666667	5.9562737487205	19.3
3	416.266666666667	3.46812323712391	11.6000000000000
4	433.733333333333	7.12885727593181	21.4000000000000
5	480.866666666667	14.6069929288763	46.9
6	508.558333333333	15.2666277953720	44.7
7	603.783333333333	44.504950354546	116.6
8	669.891666666667	6.49019656983912	18.6000000000000
9	702.616666666667	32.6632357505647	102

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 406.733333333333 & 6.70296180577637 & 20.8000000000000 \tabularnewline
2 & 413.341666666667 & 5.9562737487205 & 19.3 \tabularnewline
3 & 416.266666666667 & 3.46812323712391 & 11.6000000000000 \tabularnewline
4 & 433.733333333333 & 7.12885727593181 & 21.4000000000000 \tabularnewline
5 & 480.866666666667 & 14.6069929288763 & 46.9 \tabularnewline
6 & 508.558333333333 & 15.2666277953720 & 44.7 \tabularnewline
7 & 603.783333333333 & 44.504950354546 & 116.6 \tabularnewline
8 & 669.891666666667 & 6.49019656983912 & 18.6000000000000 \tabularnewline
9 & 702.616666666667 & 32.6632357505647 & 102 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58997&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]406.733333333333[/C][C]6.70296180577637[/C][C]20.8000000000000[/C][/ROW]
[ROW][C]2[/C][C]413.341666666667[/C][C]5.9562737487205[/C][C]19.3[/C][/ROW]
[ROW][C]3[/C][C]416.266666666667[/C][C]3.46812323712391[/C][C]11.6000000000000[/C][/ROW]
[ROW][C]4[/C][C]433.733333333333[/C][C]7.12885727593181[/C][C]21.4000000000000[/C][/ROW]
[ROW][C]5[/C][C]480.866666666667[/C][C]14.6069929288763[/C][C]46.9[/C][/ROW]
[ROW][C]6[/C][C]508.558333333333[/C][C]15.2666277953720[/C][C]44.7[/C][/ROW]
[ROW][C]7[/C][C]603.783333333333[/C][C]44.504950354546[/C][C]116.6[/C][/ROW]
[ROW][C]8[/C][C]669.891666666667[/C][C]6.49019656983912[/C][C]18.6000000000000[/C][/ROW]
[ROW][C]9[/C][C]702.616666666667[/C][C]32.6632357505647[/C][C]102[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58997&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58997&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	406.733333333333	6.70296180577637	20.8000000000000
2	413.341666666667	5.9562737487205	19.3
3	416.266666666667	3.46812323712391	11.6000000000000
4	433.733333333333	7.12885727593181	21.4000000000000
5	480.866666666667	14.6069929288763	46.9
6	508.558333333333	15.2666277953720	44.7
7	603.783333333333	44.504950354546	116.6
8	669.891666666667	6.49019656983912	18.6000000000000
9	702.616666666667	32.6632357505647	102

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-24.5005208831673
beta	0.0770726842589467
S.D.	0.0359767549724671
T-STAT	2.14229116322276
p-value	0.0693991211009065

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -24.5005208831673 \tabularnewline
beta & 0.0770726842589467 \tabularnewline
S.D. & 0.0359767549724671 \tabularnewline
T-STAT & 2.14229116322276 \tabularnewline
p-value & 0.0693991211009065 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58997&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-24.5005208831673[/C][/ROW]
[ROW][C]beta[/C][C]0.0770726842589467[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0359767549724671[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.14229116322276[/C][/ROW]
[ROW][C]p-value[/C][C]0.0693991211009065[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58997&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58997&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	-24.5005208831673
beta	0.0770726842589467
S.D.	0.0359767549724671
T-STAT	2.14229116322276
p-value	0.0693991211009065

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-13.8572822753218
beta	2.60977547491682
S.D.	1.11399731780098
T-STAT	2.34271253010599
p-value	0.051638371908914
Lambda	-1.60977547491682

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -13.8572822753218 \tabularnewline
beta & 2.60977547491682 \tabularnewline
S.D. & 1.11399731780098 \tabularnewline
T-STAT & 2.34271253010599 \tabularnewline
p-value & 0.051638371908914 \tabularnewline
Lambda & -1.60977547491682 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58997&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-13.8572822753218[/C][/ROW]
[ROW][C]beta[/C][C]2.60977547491682[/C][/ROW]
[ROW][C]S.D.[/C][C]1.11399731780098[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.34271253010599[/C][/ROW]
[ROW][C]p-value[/C][C]0.051638371908914[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.60977547491682[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58997&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58997&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	-13.8572822753218
beta	2.60977547491682
S.D.	1.11399731780098
T-STAT	2.34271253010599
p-value	0.051638371908914
Lambda	-1.60977547491682

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