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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

Tue, 09 Aug 2011 11:28:44 -0400

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/Aug/09/t1312903759iwvvag77a11ky17.htm/, Retrieved Tue, 14 May 2024 15:03:46 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123495, Retrieved Tue, 14 May 2024 15:03:46 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Nick Verbeke

Estimated Impact

139

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

-       [Standard Deviation-Mean Plot] [TIJDREEKS B - STA...] [2011-08-09 15:28:44] [af5734c86e7bdbdfefb37d9aed9dbb03] [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	0 seconds
R Server	'Gwilym Jenkins' @ jenkins.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 & 0 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123495&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]0 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123495&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123495&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	0 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	249.166666666667	51.9542339395205	170
2	258.333333333333	38.0987552488943	140
3	255.833333333333	47.9504163093755	160
4	284.166666666667	59.0005136084476	200
5	307.5	80.3543289550612	260
6	326.666666666667	76.1975104977886	240
7	357.5	104.544466398492	380
8	355.833333333333	99.5862653302364	340
9	360	109.875963125368	390

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 249.166666666667 & 51.9542339395205 & 170 \tabularnewline
2 & 258.333333333333 & 38.0987552488943 & 140 \tabularnewline
3 & 255.833333333333 & 47.9504163093755 & 160 \tabularnewline
4 & 284.166666666667 & 59.0005136084476 & 200 \tabularnewline
5 & 307.5 & 80.3543289550612 & 260 \tabularnewline
6 & 326.666666666667 & 76.1975104977886 & 240 \tabularnewline
7 & 357.5 & 104.544466398492 & 380 \tabularnewline
8 & 355.833333333333 & 99.5862653302364 & 340 \tabularnewline
9 & 360 & 109.875963125368 & 390 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123495&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]249.166666666667[/C][C]51.9542339395205[/C][C]170[/C][/ROW]
[ROW][C]2[/C][C]258.333333333333[/C][C]38.0987552488943[/C][C]140[/C][/ROW]
[ROW][C]3[/C][C]255.833333333333[/C][C]47.9504163093755[/C][C]160[/C][/ROW]
[ROW][C]4[/C][C]284.166666666667[/C][C]59.0005136084476[/C][C]200[/C][/ROW]
[ROW][C]5[/C][C]307.5[/C][C]80.3543289550612[/C][C]260[/C][/ROW]
[ROW][C]6[/C][C]326.666666666667[/C][C]76.1975104977886[/C][C]240[/C][/ROW]
[ROW][C]7[/C][C]357.5[/C][C]104.544466398492[/C][C]380[/C][/ROW]
[ROW][C]8[/C][C]355.833333333333[/C][C]99.5862653302364[/C][C]340[/C][/ROW]
[ROW][C]9[/C][C]360[/C][C]109.875963125368[/C][C]390[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123495&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123495&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	249.166666666667	51.9542339395205	170
2	258.333333333333	38.0987552488943	140
3	255.833333333333	47.9504163093755	160
4	284.166666666667	59.0005136084476	200
5	307.5	80.3543289550612	260
6	326.666666666667	76.1975104977886	240
7	357.5	104.544466398492	380
8	355.833333333333	99.5862653302364	340
9	360	109.875963125368	390

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-96.0210777154978
beta	0.555989892142528
S.D.	0.0542935584198431
T-STAT	10.2404393508922
p-value	1.82885733186438e-05

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -96.0210777154978 \tabularnewline
beta & 0.555989892142528 \tabularnewline
S.D. & 0.0542935584198431 \tabularnewline
T-STAT & 10.2404393508922 \tabularnewline
p-value & 1.82885733186438e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123495&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-96.0210777154978[/C][/ROW]
[ROW][C]beta[/C][C]0.555989892142528[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0542935584198431[/C][/ROW]
[ROW][C]T-STAT[/C][C]10.2404393508922[/C][/ROW]
[ROW][C]p-value[/C][C]1.82885733186438e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123495&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123495&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	-96.0210777154978
beta	0.555989892142528
S.D.	0.0542935584198431
T-STAT	10.2404393508922
p-value	1.82885733186438e-05

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-9.31079879572673
beta	2.37255395598742
S.D.	0.282172007815765
T-STAT	8.40818327215682
p-value	6.62479516114281e-05
Lambda	-1.37255395598742

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -9.31079879572673 \tabularnewline
beta & 2.37255395598742 \tabularnewline
S.D. & 0.282172007815765 \tabularnewline
T-STAT & 8.40818327215682 \tabularnewline
p-value & 6.62479516114281e-05 \tabularnewline
Lambda & -1.37255395598742 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123495&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-9.31079879572673[/C][/ROW]
[ROW][C]beta[/C][C]2.37255395598742[/C][/ROW]
[ROW][C]S.D.[/C][C]0.282172007815765[/C][/ROW]
[ROW][C]T-STAT[/C][C]8.40818327215682[/C][/ROW]
[ROW][C]p-value[/C][C]6.62479516114281e-05[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.37255395598742[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123495&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123495&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	-9.31079879572673
beta	2.37255395598742
S.D.	0.282172007815765
T-STAT	8.40818327215682
p-value	6.62479516114281e-05
Lambda	-1.37255395598742

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