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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

Wed, 08 Dec 2010 13:10:54 +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/2010/Dec/08/t1291813777gxfi3ywb8t7g5oc.htm/, Retrieved Fri, 03 May 2024 11:02:10 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=106886, Retrieved Fri, 03 May 2024 11:02:10 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W83

Estimated Impact

133

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

-       [Standard Deviation-Mean Plot] [] [2010-12-08 13:10:54] [97983bf7277c2e38098275bb77d0f83a] [Current]

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Dataseries X:

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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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106886&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106886&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106886&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	100.15	2.12994522621279	4.5
2	101.825	0.287228132326903	0.700000000000003
3	98.025	0.499165971062399	1
4	98.5	1.32916013582512	2.89999999999999
5	97.525	1.33759734848222	3.10000000000001
6	94.375	2.67254560297855	6.3
7	91.325	1.49749791318719	3.2
8	93.025	0.939414711402801	2.10000000000001
9	89.25	2.17944947177033	4.69999999999999
10	88.225	1.86793111935817	4.10000000000001
11	87.1	2.03141986469235	4.5
12	86.325	2.16544837543329	5.09999999999999
13	86.85	0.82663978450915	1.80000000000000
14	87.125	0.903234926989282	2
15	86.65	0.645497224367904	1.40000000000001
16	88.95	2.40069434400411	5.7
17	95.55	1.16761865920913	2.70000000000000
18	95.3	1.44913767461894	2.69999999999999
19	94.4	0.848528137423856	1.80000000000000
20	96.625	0.377491721763541	0.700000000000003
21	96.125	0.946484724300047	2.20000000000000
22	95.25	0.939858145324784	1.90000000000001
23	95.225	2.5863423336184	6.2
24	96.275	1.17862914721581	2.80000000000000
25	96.725	2.07585323822920	4.90000000000001
26	101.25	0.238047614284761	0.5
27	102.15	0.834665601703262	2
28	102.175	1.18708326020826	2.70000000000000
29	102.225	1.13541475535007	2.20000000000000
30	102.65	0.341565025531985	0.799999999999997

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 100.15 & 2.12994522621279 & 4.5 \tabularnewline
2 & 101.825 & 0.287228132326903 & 0.700000000000003 \tabularnewline
3 & 98.025 & 0.499165971062399 & 1 \tabularnewline
4 & 98.5 & 1.32916013582512 & 2.89999999999999 \tabularnewline
5 & 97.525 & 1.33759734848222 & 3.10000000000001 \tabularnewline
6 & 94.375 & 2.67254560297855 & 6.3 \tabularnewline
7 & 91.325 & 1.49749791318719 & 3.2 \tabularnewline
8 & 93.025 & 0.939414711402801 & 2.10000000000001 \tabularnewline
9 & 89.25 & 2.17944947177033 & 4.69999999999999 \tabularnewline
10 & 88.225 & 1.86793111935817 & 4.10000000000001 \tabularnewline
11 & 87.1 & 2.03141986469235 & 4.5 \tabularnewline
12 & 86.325 & 2.16544837543329 & 5.09999999999999 \tabularnewline
13 & 86.85 & 0.82663978450915 & 1.80000000000000 \tabularnewline
14 & 87.125 & 0.903234926989282 & 2 \tabularnewline
15 & 86.65 & 0.645497224367904 & 1.40000000000001 \tabularnewline
16 & 88.95 & 2.40069434400411 & 5.7 \tabularnewline
17 & 95.55 & 1.16761865920913 & 2.70000000000000 \tabularnewline
18 & 95.3 & 1.44913767461894 & 2.69999999999999 \tabularnewline
19 & 94.4 & 0.848528137423856 & 1.80000000000000 \tabularnewline
20 & 96.625 & 0.377491721763541 & 0.700000000000003 \tabularnewline
21 & 96.125 & 0.946484724300047 & 2.20000000000000 \tabularnewline
22 & 95.25 & 0.939858145324784 & 1.90000000000001 \tabularnewline
23 & 95.225 & 2.5863423336184 & 6.2 \tabularnewline
24 & 96.275 & 1.17862914721581 & 2.80000000000000 \tabularnewline
25 & 96.725 & 2.07585323822920 & 4.90000000000001 \tabularnewline
26 & 101.25 & 0.238047614284761 & 0.5 \tabularnewline
27 & 102.15 & 0.834665601703262 & 2 \tabularnewline
28 & 102.175 & 1.18708326020826 & 2.70000000000000 \tabularnewline
29 & 102.225 & 1.13541475535007 & 2.20000000000000 \tabularnewline
30 & 102.65 & 0.341565025531985 & 0.799999999999997 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106886&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]100.15[/C][C]2.12994522621279[/C][C]4.5[/C][/ROW]
[ROW][C]2[/C][C]101.825[/C][C]0.287228132326903[/C][C]0.700000000000003[/C][/ROW]
[ROW][C]3[/C][C]98.025[/C][C]0.499165971062399[/C][C]1[/C][/ROW]
[ROW][C]4[/C][C]98.5[/C][C]1.32916013582512[/C][C]2.89999999999999[/C][/ROW]
[ROW][C]5[/C][C]97.525[/C][C]1.33759734848222[/C][C]3.10000000000001[/C][/ROW]
[ROW][C]6[/C][C]94.375[/C][C]2.67254560297855[/C][C]6.3[/C][/ROW]
[ROW][C]7[/C][C]91.325[/C][C]1.49749791318719[/C][C]3.2[/C][/ROW]
[ROW][C]8[/C][C]93.025[/C][C]0.939414711402801[/C][C]2.10000000000001[/C][/ROW]
[ROW][C]9[/C][C]89.25[/C][C]2.17944947177033[/C][C]4.69999999999999[/C][/ROW]
[ROW][C]10[/C][C]88.225[/C][C]1.86793111935817[/C][C]4.10000000000001[/C][/ROW]
[ROW][C]11[/C][C]87.1[/C][C]2.03141986469235[/C][C]4.5[/C][/ROW]
[ROW][C]12[/C][C]86.325[/C][C]2.16544837543329[/C][C]5.09999999999999[/C][/ROW]
[ROW][C]13[/C][C]86.85[/C][C]0.82663978450915[/C][C]1.80000000000000[/C][/ROW]
[ROW][C]14[/C][C]87.125[/C][C]0.903234926989282[/C][C]2[/C][/ROW]
[ROW][C]15[/C][C]86.65[/C][C]0.645497224367904[/C][C]1.40000000000001[/C][/ROW]
[ROW][C]16[/C][C]88.95[/C][C]2.40069434400411[/C][C]5.7[/C][/ROW]
[ROW][C]17[/C][C]95.55[/C][C]1.16761865920913[/C][C]2.70000000000000[/C][/ROW]
[ROW][C]18[/C][C]95.3[/C][C]1.44913767461894[/C][C]2.69999999999999[/C][/ROW]
[ROW][C]19[/C][C]94.4[/C][C]0.848528137423856[/C][C]1.80000000000000[/C][/ROW]
[ROW][C]20[/C][C]96.625[/C][C]0.377491721763541[/C][C]0.700000000000003[/C][/ROW]
[ROW][C]21[/C][C]96.125[/C][C]0.946484724300047[/C][C]2.20000000000000[/C][/ROW]
[ROW][C]22[/C][C]95.25[/C][C]0.939858145324784[/C][C]1.90000000000001[/C][/ROW]
[ROW][C]23[/C][C]95.225[/C][C]2.5863423336184[/C][C]6.2[/C][/ROW]
[ROW][C]24[/C][C]96.275[/C][C]1.17862914721581[/C][C]2.80000000000000[/C][/ROW]
[ROW][C]25[/C][C]96.725[/C][C]2.07585323822920[/C][C]4.90000000000001[/C][/ROW]
[ROW][C]26[/C][C]101.25[/C][C]0.238047614284761[/C][C]0.5[/C][/ROW]
[ROW][C]27[/C][C]102.15[/C][C]0.834665601703262[/C][C]2[/C][/ROW]
[ROW][C]28[/C][C]102.175[/C][C]1.18708326020826[/C][C]2.70000000000000[/C][/ROW]
[ROW][C]29[/C][C]102.225[/C][C]1.13541475535007[/C][C]2.20000000000000[/C][/ROW]
[ROW][C]30[/C][C]102.65[/C][C]0.341565025531985[/C][C]0.799999999999997[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106886&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106886&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	100.15	2.12994522621279	4.5
2	101.825	0.287228132326903	0.700000000000003
3	98.025	0.499165971062399	1
4	98.5	1.32916013582512	2.89999999999999
5	97.525	1.33759734848222	3.10000000000001
6	94.375	2.67254560297855	6.3
7	91.325	1.49749791318719	3.2
8	93.025	0.939414711402801	2.10000000000001
9	89.25	2.17944947177033	4.69999999999999
10	88.225	1.86793111935817	4.10000000000001
11	87.1	2.03141986469235	4.5
12	86.325	2.16544837543329	5.09999999999999
13	86.85	0.82663978450915	1.80000000000000
14	87.125	0.903234926989282	2
15	86.65	0.645497224367904	1.40000000000001
16	88.95	2.40069434400411	5.7
17	95.55	1.16761865920913	2.70000000000000
18	95.3	1.44913767461894	2.69999999999999
19	94.4	0.848528137423856	1.80000000000000
20	96.625	0.377491721763541	0.700000000000003
21	96.125	0.946484724300047	2.20000000000000
22	95.25	0.939858145324784	1.90000000000001
23	95.225	2.5863423336184	6.2
24	96.275	1.17862914721581	2.80000000000000
25	96.725	2.07585323822920	4.90000000000001
26	101.25	0.238047614284761	0.5
27	102.15	0.834665601703262	2
28	102.175	1.18708326020826	2.70000000000000
29	102.225	1.13541475535007	2.20000000000000
30	102.65	0.341565025531985	0.799999999999997

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	6.06005946671867
beta	-0.0501491645365279
S.D.	0.0233036247251385
T-STAT	-2.15198987831409
p-value	0.0401668445585302

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 6.06005946671867 \tabularnewline
beta & -0.0501491645365279 \tabularnewline
S.D. & 0.0233036247251385 \tabularnewline
T-STAT & -2.15198987831409 \tabularnewline
p-value & 0.0401668445585302 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106886&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]6.06005946671867[/C][/ROW]
[ROW][C]beta[/C][C]-0.0501491645365279[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0233036247251385[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.15198987831409[/C][/ROW]
[ROW][C]p-value[/C][C]0.0401668445585302[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106886&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106886&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	6.06005946671867
beta	-0.0501491645365279
S.D.	0.0233036247251385
T-STAT	-2.15198987831409
p-value	0.0401668445585302

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	21.8927373782133
beta	-4.79211614615054
S.D.	2.00394760110827
T-STAT	-2.39133804870960
p-value	0.0237480685447771
Lambda	5.79211614615054

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 21.8927373782133 \tabularnewline
beta & -4.79211614615054 \tabularnewline
S.D. & 2.00394760110827 \tabularnewline
T-STAT & -2.39133804870960 \tabularnewline
p-value & 0.0237480685447771 \tabularnewline
Lambda & 5.79211614615054 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106886&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]21.8927373782133[/C][/ROW]
[ROW][C]beta[/C][C]-4.79211614615054[/C][/ROW]
[ROW][C]S.D.[/C][C]2.00394760110827[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.39133804870960[/C][/ROW]
[ROW][C]p-value[/C][C]0.0237480685447771[/C][/ROW]
[ROW][C]Lambda[/C][C]5.79211614615054[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106886&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106886&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	21.8927373782133
beta	-4.79211614615054
S.D.	2.00394760110827
T-STAT	-2.39133804870960
p-value	0.0237480685447771
Lambda	5.79211614615054

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