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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

Sun, 18 Dec 2011 03:47:44 -0500

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/2011/Dec/18/t1324198202bccxeyl2h9cam5l.htm/, Retrieved Sun, 05 May 2024 13:59:59 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=156615, Retrieved Sun, 05 May 2024 13:59:59 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

118

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

-       [Standard Deviation-Mean Plot] [Stationariteit in...] [2011-12-18 08:47:44] [51aabe75794be7f34bed5d3096a085df] [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	'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156615&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=156615&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156615&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	251.75	19.5	45
2	301.75	19.6022957839127	39
3	396.25	25.408331966765	55
4	476	14.7196014438797	29
5	481.75	26.4370321077587	62
6	410	42.0872110424691	96
7	343.5	39.7198522991547	93
8	300	21.7102126505784	48
9	377.25	26.849891371599	62
10	426	33.436506994601	77

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 251.75 & 19.5 & 45 \tabularnewline
2 & 301.75 & 19.6022957839127 & 39 \tabularnewline
3 & 396.25 & 25.408331966765 & 55 \tabularnewline
4 & 476 & 14.7196014438797 & 29 \tabularnewline
5 & 481.75 & 26.4370321077587 & 62 \tabularnewline
6 & 410 & 42.0872110424691 & 96 \tabularnewline
7 & 343.5 & 39.7198522991547 & 93 \tabularnewline
8 & 300 & 21.7102126505784 & 48 \tabularnewline
9 & 377.25 & 26.849891371599 & 62 \tabularnewline
10 & 426 & 33.436506994601 & 77 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156615&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]251.75[/C][C]19.5[/C][C]45[/C][/ROW]
[ROW][C]2[/C][C]301.75[/C][C]19.6022957839127[/C][C]39[/C][/ROW]
[ROW][C]3[/C][C]396.25[/C][C]25.408331966765[/C][C]55[/C][/ROW]
[ROW][C]4[/C][C]476[/C][C]14.7196014438797[/C][C]29[/C][/ROW]
[ROW][C]5[/C][C]481.75[/C][C]26.4370321077587[/C][C]62[/C][/ROW]
[ROW][C]6[/C][C]410[/C][C]42.0872110424691[/C][C]96[/C][/ROW]
[ROW][C]7[/C][C]343.5[/C][C]39.7198522991547[/C][C]93[/C][/ROW]
[ROW][C]8[/C][C]300[/C][C]21.7102126505784[/C][C]48[/C][/ROW]
[ROW][C]9[/C][C]377.25[/C][C]26.849891371599[/C][C]62[/C][/ROW]
[ROW][C]10[/C][C]426[/C][C]33.436506994601[/C][C]77[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=156615&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156615&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	251.75	19.5	45
2	301.75	19.6022957839127	39
3	396.25	25.408331966765	55
4	476	14.7196014438797	29
5	481.75	26.4370321077587	62
6	410	42.0872110424691	96
7	343.5	39.7198522991547	93
8	300	21.7102126505784	48
9	377.25	26.849891371599	62
10	426	33.436506994601	77

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	19.9569030917281
beta	0.018569942151408
S.D.	0.0407691802669459
T-STAT	0.455489711341187
p-value	0.660865199085356

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 19.9569030917281 \tabularnewline
beta & 0.018569942151408 \tabularnewline
S.D. & 0.0407691802669459 \tabularnewline
T-STAT & 0.455489711341187 \tabularnewline
p-value & 0.660865199085356 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156615&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]19.9569030917281[/C][/ROW]
[ROW][C]beta[/C][C]0.018569942151408[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0407691802669459[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.455489711341187[/C][/ROW]
[ROW][C]p-value[/C][C]0.660865199085356[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=156615&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156615&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	19.9569030917281
beta	0.018569942151408
S.D.	0.0407691802669459
T-STAT	0.455489711341187
p-value	0.660865199085356

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	1.51461793949285
beta	0.292647078023153
S.D.	0.542005203728509
T-STAT	0.539934074451691
p-value	0.603942893542534
Lambda	0.707352921976847

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.51461793949285 \tabularnewline
beta & 0.292647078023153 \tabularnewline
S.D. & 0.542005203728509 \tabularnewline
T-STAT & 0.539934074451691 \tabularnewline
p-value & 0.603942893542534 \tabularnewline
Lambda & 0.707352921976847 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156615&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.51461793949285[/C][/ROW]
[ROW][C]beta[/C][C]0.292647078023153[/C][/ROW]
[ROW][C]S.D.[/C][C]0.542005203728509[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.539934074451691[/C][/ROW]
[ROW][C]p-value[/C][C]0.603942893542534[/C][/ROW]
[ROW][C]Lambda[/C][C]0.707352921976847[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=156615&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156615&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	1.51461793949285
beta	0.292647078023153
S.D.	0.542005203728509
T-STAT	0.539934074451691
p-value	0.603942893542534
Lambda	0.707352921976847

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 4 ;

Parameters (R input):

par1 = 4 ;

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