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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, 20 Dec 2009 01:38:06 -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/Dec/20/t1261298379us1xzlqrqirp6sr.htm/, Retrieved Sat, 27 Apr 2024 06:14:32 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=69795, Retrieved Sat, 27 Apr 2024 06:14:32 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

173

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

-     [Standard Deviation-Mean Plot] [Paper: Differenti...] [2009-12-20 07:53:34] [1d635fe1113b56bab3f378c464a289bc]
-    D    [Standard Deviation-Mean Plot] [Paper Differentia...] [2009-12-20 08:38:06] [762da55b2e2304daaed24a7cc507d14d] [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	11 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 & 11 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69795&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]11 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=69795&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69795&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	11 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	85	4.602765966835	13.4
2	80.4166666666667	4.70083809419967	12.6
3	84.7	5.0448894032386	14
4	92.8	5.56155635509604	15.2
5	107.266666666667	7.43276937662273	18.6
6	117.466666666667	4.54099174857278	13.6
7	118.833333333333	5.35559746829653	15.2
8	118.766666666667	5.01041339853733	15.2
9	114.516666666667	4.33795790526819	14
10	109.566666666667	4.7801356643611	15.8
11	102.6	4.56787199311173	15.4
12	95.8833333333333	4.914881545476	16.4
13	93.65	5.6672103126029	16.4
14	96.9833333333333	5.50666263115268	14
15	106.266666666667	6.26524806638439	15.8
16	113.883333333333	5.84680695039194	15.2
17	119.2	4.39669297209949	12.4
18	118.816666666667	3.77403409276246	10.6
19	108.166666666667	4.38330164754074	13.4
20	101.083333333333	3.90380544721391	13
21	109.016666666667	6.00451850061622	19

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 85 & 4.602765966835 & 13.4 \tabularnewline
2 & 80.4166666666667 & 4.70083809419967 & 12.6 \tabularnewline
3 & 84.7 & 5.0448894032386 & 14 \tabularnewline
4 & 92.8 & 5.56155635509604 & 15.2 \tabularnewline
5 & 107.266666666667 & 7.43276937662273 & 18.6 \tabularnewline
6 & 117.466666666667 & 4.54099174857278 & 13.6 \tabularnewline
7 & 118.833333333333 & 5.35559746829653 & 15.2 \tabularnewline
8 & 118.766666666667 & 5.01041339853733 & 15.2 \tabularnewline
9 & 114.516666666667 & 4.33795790526819 & 14 \tabularnewline
10 & 109.566666666667 & 4.7801356643611 & 15.8 \tabularnewline
11 & 102.6 & 4.56787199311173 & 15.4 \tabularnewline
12 & 95.8833333333333 & 4.914881545476 & 16.4 \tabularnewline
13 & 93.65 & 5.6672103126029 & 16.4 \tabularnewline
14 & 96.9833333333333 & 5.50666263115268 & 14 \tabularnewline
15 & 106.266666666667 & 6.26524806638439 & 15.8 \tabularnewline
16 & 113.883333333333 & 5.84680695039194 & 15.2 \tabularnewline
17 & 119.2 & 4.39669297209949 & 12.4 \tabularnewline
18 & 118.816666666667 & 3.77403409276246 & 10.6 \tabularnewline
19 & 108.166666666667 & 4.38330164754074 & 13.4 \tabularnewline
20 & 101.083333333333 & 3.90380544721391 & 13 \tabularnewline
21 & 109.016666666667 & 6.00451850061622 & 19 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69795&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]85[/C][C]4.602765966835[/C][C]13.4[/C][/ROW]
[ROW][C]2[/C][C]80.4166666666667[/C][C]4.70083809419967[/C][C]12.6[/C][/ROW]
[ROW][C]3[/C][C]84.7[/C][C]5.0448894032386[/C][C]14[/C][/ROW]
[ROW][C]4[/C][C]92.8[/C][C]5.56155635509604[/C][C]15.2[/C][/ROW]
[ROW][C]5[/C][C]107.266666666667[/C][C]7.43276937662273[/C][C]18.6[/C][/ROW]
[ROW][C]6[/C][C]117.466666666667[/C][C]4.54099174857278[/C][C]13.6[/C][/ROW]
[ROW][C]7[/C][C]118.833333333333[/C][C]5.35559746829653[/C][C]15.2[/C][/ROW]
[ROW][C]8[/C][C]118.766666666667[/C][C]5.01041339853733[/C][C]15.2[/C][/ROW]
[ROW][C]9[/C][C]114.516666666667[/C][C]4.33795790526819[/C][C]14[/C][/ROW]
[ROW][C]10[/C][C]109.566666666667[/C][C]4.7801356643611[/C][C]15.8[/C][/ROW]
[ROW][C]11[/C][C]102.6[/C][C]4.56787199311173[/C][C]15.4[/C][/ROW]
[ROW][C]12[/C][C]95.8833333333333[/C][C]4.914881545476[/C][C]16.4[/C][/ROW]
[ROW][C]13[/C][C]93.65[/C][C]5.6672103126029[/C][C]16.4[/C][/ROW]
[ROW][C]14[/C][C]96.9833333333333[/C][C]5.50666263115268[/C][C]14[/C][/ROW]
[ROW][C]15[/C][C]106.266666666667[/C][C]6.26524806638439[/C][C]15.8[/C][/ROW]
[ROW][C]16[/C][C]113.883333333333[/C][C]5.84680695039194[/C][C]15.2[/C][/ROW]
[ROW][C]17[/C][C]119.2[/C][C]4.39669297209949[/C][C]12.4[/C][/ROW]
[ROW][C]18[/C][C]118.816666666667[/C][C]3.77403409276246[/C][C]10.6[/C][/ROW]
[ROW][C]19[/C][C]108.166666666667[/C][C]4.38330164754074[/C][C]13.4[/C][/ROW]
[ROW][C]20[/C][C]101.083333333333[/C][C]3.90380544721391[/C][C]13[/C][/ROW]
[ROW][C]21[/C][C]109.016666666667[/C][C]6.00451850061622[/C][C]19[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69795&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69795&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	85	4.602765966835	13.4
2	80.4166666666667	4.70083809419967	12.6
3	84.7	5.0448894032386	14
4	92.8	5.56155635509604	15.2
5	107.266666666667	7.43276937662273	18.6
6	117.466666666667	4.54099174857278	13.6
7	118.833333333333	5.35559746829653	15.2
8	118.766666666667	5.01041339853733	15.2
9	114.516666666667	4.33795790526819	14
10	109.566666666667	4.7801356643611	15.8
11	102.6	4.56787199311173	15.4
12	95.8833333333333	4.914881545476	16.4
13	93.65	5.6672103126029	16.4
14	96.9833333333333	5.50666263115268	14
15	106.266666666667	6.26524806638439	15.8
16	113.883333333333	5.84680695039194	15.2
17	119.2	4.39669297209949	12.4
18	118.816666666667	3.77403409276246	10.6
19	108.166666666667	4.38330164754074	13.4
20	101.083333333333	3.90380544721391	13
21	109.016666666667	6.00451850061622	19

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	5.56125351592452
beta	-0.00464141949566085
S.D.	0.0160831407986403
T-STAT	-0.288589122844292
p-value	0.776020707566455

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 5.56125351592452 \tabularnewline
beta & -0.00464141949566085 \tabularnewline
S.D. & 0.0160831407986403 \tabularnewline
T-STAT & -0.288589122844292 \tabularnewline
p-value & 0.776020707566455 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69795&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]5.56125351592452[/C][/ROW]
[ROW][C]beta[/C][C]-0.00464141949566085[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0160831407986403[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.288589122844292[/C][/ROW]
[ROW][C]p-value[/C][C]0.776020707566455[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69795&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69795&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	5.56125351592452
beta	-0.00464141949566085
S.D.	0.0160831407986403
T-STAT	-0.288589122844292
p-value	0.776020707566455

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	2.08092562714484
beta	-0.101096359426534
S.D.	0.305969602501163
T-STAT	-0.330413082215086
p-value	0.744703470598958
Lambda	1.10109635942653

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 2.08092562714484 \tabularnewline
beta & -0.101096359426534 \tabularnewline
S.D. & 0.305969602501163 \tabularnewline
T-STAT & -0.330413082215086 \tabularnewline
p-value & 0.744703470598958 \tabularnewline
Lambda & 1.10109635942653 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69795&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.08092562714484[/C][/ROW]
[ROW][C]beta[/C][C]-0.101096359426534[/C][/ROW]
[ROW][C]S.D.[/C][C]0.305969602501163[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.330413082215086[/C][/ROW]
[ROW][C]p-value[/C][C]0.744703470598958[/C][/ROW]
[ROW][C]Lambda[/C][C]1.10109635942653[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69795&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69795&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	2.08092562714484
beta	-0.101096359426534
S.D.	0.305969602501163
T-STAT	-0.330413082215086
p-value	0.744703470598958
Lambda	1.10109635942653

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