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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 Jul 2016 09:45:34 +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/Jul/18/t146883158204bl3zgedtde8mh.htm/, Retrieved Fri, 03 May 2024 07:21:39 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=295887, Retrieved Fri, 03 May 2024 07:21:39 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

152

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

-     [Univariate Data Series] [] [2016-07-18 07:02:10] [53ea9856f51a263258ed46ae39fddedd]
- RMPD    [Standard Deviation-Mean Plot] [] [2016-07-18 08:45:34] [b94c13d84d922b33c8d74b1e5b1d38c1] [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	'Gertrude Mary Cox' @ cox.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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295887&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295887&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295887&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	'Gertrude Mary Cox' @ cox.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	1927.25	90.1747041732174	269
2	1732.58333333333	103.123454993018	331
3	1507.08333333333	99.0752315927221	310
4	1388.16666666667	123.587167128258	444
5	1285.58333333333	145.233015488486	516
6	1351.83333333333	157.899757230128	485
7	1498.25	157.81008436495	517
8	1389	201.219012295287	651
9	1019.41666666667	226.394449953388	754
10	498.583333333333	209.222134381503	640

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 1927.25 & 90.1747041732174 & 269 \tabularnewline
2 & 1732.58333333333 & 103.123454993018 & 331 \tabularnewline
3 & 1507.08333333333 & 99.0752315927221 & 310 \tabularnewline
4 & 1388.16666666667 & 123.587167128258 & 444 \tabularnewline
5 & 1285.58333333333 & 145.233015488486 & 516 \tabularnewline
6 & 1351.83333333333 & 157.899757230128 & 485 \tabularnewline
7 & 1498.25 & 157.81008436495 & 517 \tabularnewline
8 & 1389 & 201.219012295287 & 651 \tabularnewline
9 & 1019.41666666667 & 226.394449953388 & 754 \tabularnewline
10 & 498.583333333333 & 209.222134381503 & 640 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295887&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]1927.25[/C][C]90.1747041732174[/C][C]269[/C][/ROW]
[ROW][C]2[/C][C]1732.58333333333[/C][C]103.123454993018[/C][C]331[/C][/ROW]
[ROW][C]3[/C][C]1507.08333333333[/C][C]99.0752315927221[/C][C]310[/C][/ROW]
[ROW][C]4[/C][C]1388.16666666667[/C][C]123.587167128258[/C][C]444[/C][/ROW]
[ROW][C]5[/C][C]1285.58333333333[/C][C]145.233015488486[/C][C]516[/C][/ROW]
[ROW][C]6[/C][C]1351.83333333333[/C][C]157.899757230128[/C][C]485[/C][/ROW]
[ROW][C]7[/C][C]1498.25[/C][C]157.81008436495[/C][C]517[/C][/ROW]
[ROW][C]8[/C][C]1389[/C][C]201.219012295287[/C][C]651[/C][/ROW]
[ROW][C]9[/C][C]1019.41666666667[/C][C]226.394449953388[/C][C]754[/C][/ROW]
[ROW][C]10[/C][C]498.583333333333[/C][C]209.222134381503[/C][C]640[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295887&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295887&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	1927.25	90.1747041732174	269
2	1732.58333333333	103.123454993018	331
3	1507.08333333333	99.0752315927221	310
4	1388.16666666667	123.587167128258	444
5	1285.58333333333	145.233015488486	516
6	1351.83333333333	157.899757230128	485
7	1498.25	157.81008436495	517
8	1389	201.219012295287	651
9	1019.41666666667	226.394449953388	754
10	498.583333333333	209.222134381503	640

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	284.515166058026
beta	-0.0979141879339823
S.D.	0.0271510365572308
T-STAT	-3.60627807809813
p-value	0.00691894502810646

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 284.515166058026 \tabularnewline
beta & -0.0979141879339823 \tabularnewline
S.D. & 0.0271510365572308 \tabularnewline
T-STAT & -3.60627807809813 \tabularnewline
p-value & 0.00691894502810646 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295887&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]284.515166058026[/C][/ROW]
[ROW][C]beta[/C][C]-0.0979141879339823[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0271510365572308[/C][/ROW]
[ROW][C]T-STAT[/C][C]-3.60627807809813[/C][/ROW]
[ROW][C]p-value[/C][C]0.00691894502810646[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295887&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295887&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	284.515166058026
beta	-0.0979141879339823
S.D.	0.0271510365572308
T-STAT	-3.60627807809813
p-value	0.00691894502810646

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	9.35232077060154
beta	-0.611486919832253
S.D.	0.22058561550257
T-STAT	-2.77210695919167
p-value	0.0242177863492112
Lambda	1.61148691983225

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 9.35232077060154 \tabularnewline
beta & -0.611486919832253 \tabularnewline
S.D. & 0.22058561550257 \tabularnewline
T-STAT & -2.77210695919167 \tabularnewline
p-value & 0.0242177863492112 \tabularnewline
Lambda & 1.61148691983225 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295887&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]9.35232077060154[/C][/ROW]
[ROW][C]beta[/C][C]-0.611486919832253[/C][/ROW]
[ROW][C]S.D.[/C][C]0.22058561550257[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.77210695919167[/C][/ROW]
[ROW][C]p-value[/C][C]0.0242177863492112[/C][/ROW]
[ROW][C]Lambda[/C][C]1.61148691983225[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295887&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295887&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	9.35232077060154
beta	-0.611486919832253
S.D.	0.22058561550257
T-STAT	-2.77210695919167
p-value	0.0242177863492112
Lambda	1.61148691983225

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