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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, 16 May 2011 18:24:42 +0000

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/May/16/t1305570158qspbz1w938i6iix.htm/, Retrieved Mon, 13 May 2024 17:38:24 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=121663, Retrieved Mon, 13 May 2024 17:38:24 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KdGP281

Estimated Impact

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

-       [Standard Deviation-Mean Plot] [Standard deviatio...] [2011-05-16 18:24:42] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Dataseries X:

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Histogram

Boxplots

5.7
5.6
5.8
5.6
5.6
5.6
5.5
5.4
5.4
5.5
5.4
5.4
5.3
5.4
5.2
5.2
5.1
5
5
4.9
5
5
5
4.9
4.7
4.8
4.7
4.7
4.6
4.6
4.7
4.7
4.5
4.4
4.5
4.4
4.6
4.5
4.4
4.5
4.4
4.6
4.7
4.6
4.7
4.7
4.7
5
5
4.8
5.1
4.9
5.4
5.6
5.8
6.1
6.2
6.6
6.8
7.3
7.8
8.2
8.6
8.9
9.4
9.5
9.5
9.7
9.8
10.1
9.9
9.9
9.7
9.7
9.7
9.8
9.6
9.6
9.5
9.6
9.6
9.7
9.8
9.4
9

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ www.wessa.org

\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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121663&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121663&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121663&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	2 seconds
R Server	'Gwilym Jenkins' @ www.wessa.org

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	5.675	0.095742710775634	0.2
2	5.525	0.0957427107756335	0.199999999999999
3	5.425	0.0499999999999998	0.0999999999999996
4	5.275	0.0957427107756339	0.2
5	5	0.0816496580927723	0.199999999999999
6	4.975	0.0499999999999998	0.0999999999999996
7	4.725	0.0499999999999998	0.0999999999999996
8	4.65	0.0577350269189629	0.100000000000001
9	4.45	0.0577350269189624	0.0999999999999996
10	4.5	0.0816496580927723	0.199999999999999
11	4.575	0.125830573921179	0.3
12	4.775	0.15	0.3
13	4.95	0.12909944487358	0.3
14	5.725	0.298607881119482	0.7
15	6.725	0.457347424467075	1.1
16	8.375	0.478713553878169	1.1
17	9.525	0.125830573921179	0.299999999999999
18	9.925	0.125830573921179	0.299999999999999
19	9.725	0.0500000000000007	0.100000000000001
20	9.575	0.0499999999999998	0.0999999999999996
21	9.625	0.170782512765993	0.4

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 5.675 & 0.095742710775634 & 0.2 \tabularnewline
2 & 5.525 & 0.0957427107756335 & 0.199999999999999 \tabularnewline
3 & 5.425 & 0.0499999999999998 & 0.0999999999999996 \tabularnewline
4 & 5.275 & 0.0957427107756339 & 0.2 \tabularnewline
5 & 5 & 0.0816496580927723 & 0.199999999999999 \tabularnewline
6 & 4.975 & 0.0499999999999998 & 0.0999999999999996 \tabularnewline
7 & 4.725 & 0.0499999999999998 & 0.0999999999999996 \tabularnewline
8 & 4.65 & 0.0577350269189629 & 0.100000000000001 \tabularnewline
9 & 4.45 & 0.0577350269189624 & 0.0999999999999996 \tabularnewline
10 & 4.5 & 0.0816496580927723 & 0.199999999999999 \tabularnewline
11 & 4.575 & 0.125830573921179 & 0.3 \tabularnewline
12 & 4.775 & 0.15 & 0.3 \tabularnewline
13 & 4.95 & 0.12909944487358 & 0.3 \tabularnewline
14 & 5.725 & 0.298607881119482 & 0.7 \tabularnewline
15 & 6.725 & 0.457347424467075 & 1.1 \tabularnewline
16 & 8.375 & 0.478713553878169 & 1.1 \tabularnewline
17 & 9.525 & 0.125830573921179 & 0.299999999999999 \tabularnewline
18 & 9.925 & 0.125830573921179 & 0.299999999999999 \tabularnewline
19 & 9.725 & 0.0500000000000007 & 0.100000000000001 \tabularnewline
20 & 9.575 & 0.0499999999999998 & 0.0999999999999996 \tabularnewline
21 & 9.625 & 0.170782512765993 & 0.4 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121663&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]5.675[/C][C]0.095742710775634[/C][C]0.2[/C][/ROW]
[ROW][C]2[/C][C]5.525[/C][C]0.0957427107756335[/C][C]0.199999999999999[/C][/ROW]
[ROW][C]3[/C][C]5.425[/C][C]0.0499999999999998[/C][C]0.0999999999999996[/C][/ROW]
[ROW][C]4[/C][C]5.275[/C][C]0.0957427107756339[/C][C]0.2[/C][/ROW]
[ROW][C]5[/C][C]5[/C][C]0.0816496580927723[/C][C]0.199999999999999[/C][/ROW]
[ROW][C]6[/C][C]4.975[/C][C]0.0499999999999998[/C][C]0.0999999999999996[/C][/ROW]
[ROW][C]7[/C][C]4.725[/C][C]0.0499999999999998[/C][C]0.0999999999999996[/C][/ROW]
[ROW][C]8[/C][C]4.65[/C][C]0.0577350269189629[/C][C]0.100000000000001[/C][/ROW]
[ROW][C]9[/C][C]4.45[/C][C]0.0577350269189624[/C][C]0.0999999999999996[/C][/ROW]
[ROW][C]10[/C][C]4.5[/C][C]0.0816496580927723[/C][C]0.199999999999999[/C][/ROW]
[ROW][C]11[/C][C]4.575[/C][C]0.125830573921179[/C][C]0.3[/C][/ROW]
[ROW][C]12[/C][C]4.775[/C][C]0.15[/C][C]0.3[/C][/ROW]
[ROW][C]13[/C][C]4.95[/C][C]0.12909944487358[/C][C]0.3[/C][/ROW]
[ROW][C]14[/C][C]5.725[/C][C]0.298607881119482[/C][C]0.7[/C][/ROW]
[ROW][C]15[/C][C]6.725[/C][C]0.457347424467075[/C][C]1.1[/C][/ROW]
[ROW][C]16[/C][C]8.375[/C][C]0.478713553878169[/C][C]1.1[/C][/ROW]
[ROW][C]17[/C][C]9.525[/C][C]0.125830573921179[/C][C]0.299999999999999[/C][/ROW]
[ROW][C]18[/C][C]9.925[/C][C]0.125830573921179[/C][C]0.299999999999999[/C][/ROW]
[ROW][C]19[/C][C]9.725[/C][C]0.0500000000000007[/C][C]0.100000000000001[/C][/ROW]
[ROW][C]20[/C][C]9.575[/C][C]0.0499999999999998[/C][C]0.0999999999999996[/C][/ROW]
[ROW][C]21[/C][C]9.625[/C][C]0.170782512765993[/C][C]0.4[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121663&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121663&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	5.675	0.095742710775634	0.2
2	5.525	0.0957427107756335	0.199999999999999
3	5.425	0.0499999999999998	0.0999999999999996
4	5.275	0.0957427107756339	0.2
5	5	0.0816496580927723	0.199999999999999
6	4.975	0.0499999999999998	0.0999999999999996
7	4.725	0.0499999999999998	0.0999999999999996
8	4.65	0.0577350269189629	0.100000000000001
9	4.45	0.0577350269189624	0.0999999999999996
10	4.5	0.0816496580927723	0.199999999999999
11	4.575	0.125830573921179	0.3
12	4.775	0.15	0.3
13	4.95	0.12909944487358	0.3
14	5.725	0.298607881119482	0.7
15	6.725	0.457347424467075	1.1
16	8.375	0.478713553878169	1.1
17	9.525	0.125830573921179	0.299999999999999
18	9.925	0.125830573921179	0.299999999999999
19	9.725	0.0500000000000007	0.100000000000001
20	9.575	0.0499999999999998	0.0999999999999996
21	9.625	0.170782512765993	0.4

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	0.0571017249804529
beta	0.0125572461976716
S.D.	0.0133615715963026
T-STAT	0.939803084327779
p-value	0.359113952750462

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.0571017249804529 \tabularnewline
beta & 0.0125572461976716 \tabularnewline
S.D. & 0.0133615715963026 \tabularnewline
T-STAT & 0.939803084327779 \tabularnewline
p-value & 0.359113952750462 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121663&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.0571017249804529[/C][/ROW]
[ROW][C]beta[/C][C]0.0125572461976716[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0133615715963026[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.939803084327779[/C][/ROW]
[ROW][C]p-value[/C][C]0.359113952750462[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121663&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121663&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	0.0571017249804529
beta	0.0125572461976716
S.D.	0.0133615715963026
T-STAT	0.939803084327779
p-value	0.359113952750462

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-3.26453704414488
beta	0.558380694717436
S.D.	0.512490930771806
T-STAT	1.08954258737129
p-value	0.289541221619746
Lambda	0.441619305282564

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.26453704414488 \tabularnewline
beta & 0.558380694717436 \tabularnewline
S.D. & 0.512490930771806 \tabularnewline
T-STAT & 1.08954258737129 \tabularnewline
p-value & 0.289541221619746 \tabularnewline
Lambda & 0.441619305282564 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121663&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.26453704414488[/C][/ROW]
[ROW][C]beta[/C][C]0.558380694717436[/C][/ROW]
[ROW][C]S.D.[/C][C]0.512490930771806[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.08954258737129[/C][/ROW]
[ROW][C]p-value[/C][C]0.289541221619746[/C][/ROW]
[ROW][C]Lambda[/C][C]0.441619305282564[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121663&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121663&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	-3.26453704414488
beta	0.558380694717436
S.D.	0.512490930771806
T-STAT	1.08954258737129
p-value	0.289541221619746
Lambda	0.441619305282564

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