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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

Thu, 30 Oct 2014 15:06:38 +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/2014/Oct/30/t14146816153kw5gzn0nn08p1q.htm/, Retrieved Mon, 13 May 2024 07:34:14 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=249957, Retrieved Mon, 13 May 2024 07:34:14 +0000

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Estimated Impact

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

-       [Standard Deviation-Mean Plot] [] [2014-10-30 15:06:38] [138e2467cf1c89ca2583ec64b039d8e8] [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=249957&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=249957&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=249957&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	347.216666666667	45.2320850188394	138.5
2	310.333333333333	25.9172576177388	67.7
3	291.55	30.8076289253165	75.3
4	310.616666666667	14.8591467596307	49.3
5	250.35	9.01075115423993	33.6
6	256.816666666667	3.94019688786633	13.3
7	253.033333333333	2.42986469257909	7.30000000000001
8	263.933333333333	4.39820900188275	13
9	266.85	4.43160139329915	15
10	344.858333333333	29.6914881691196	104.3
11	293.25	16.6569395857593	51.5
12	284.433333333333	3.98596020901849	15.7
13	307.266666666667	10.1860272685258	32.2
14	296.625	5.68892464674683	16.9
15	280.866666666667	11.9555489842646	34.6
16	257.775	10.8560938061198	32.4
17	247.158333333333	5.41403199327844	19.6
18	340.133333333333	95.3387389863908	196.7
19	403.791666666667	17.5879327605003	64.6
20	343.025	10.8259053788922	30.7
21	411.075	49.9922016645869	136.9
22	376.5	21.5070812862774	58.7
23	342.733333333333	4.98877527935252	15.8
24	344.975	15.0015226499906	46.5
25	309.258333333333	9.84640758978838	31.1
26	292.375	5.22478794698016	17.3
27	291.625	6.46108983207801	22.9
28	284.941666666667	5.6527480578972	18.2
29	326.841666666667	18.2154009929327	54.2
30	320.316666666667	7.40071659102049	23.6

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 347.216666666667 & 45.2320850188394 & 138.5 \tabularnewline
2 & 310.333333333333 & 25.9172576177388 & 67.7 \tabularnewline
3 & 291.55 & 30.8076289253165 & 75.3 \tabularnewline
4 & 310.616666666667 & 14.8591467596307 & 49.3 \tabularnewline
5 & 250.35 & 9.01075115423993 & 33.6 \tabularnewline
6 & 256.816666666667 & 3.94019688786633 & 13.3 \tabularnewline
7 & 253.033333333333 & 2.42986469257909 & 7.30000000000001 \tabularnewline
8 & 263.933333333333 & 4.39820900188275 & 13 \tabularnewline
9 & 266.85 & 4.43160139329915 & 15 \tabularnewline
10 & 344.858333333333 & 29.6914881691196 & 104.3 \tabularnewline
11 & 293.25 & 16.6569395857593 & 51.5 \tabularnewline
12 & 284.433333333333 & 3.98596020901849 & 15.7 \tabularnewline
13 & 307.266666666667 & 10.1860272685258 & 32.2 \tabularnewline
14 & 296.625 & 5.68892464674683 & 16.9 \tabularnewline
15 & 280.866666666667 & 11.9555489842646 & 34.6 \tabularnewline
16 & 257.775 & 10.8560938061198 & 32.4 \tabularnewline
17 & 247.158333333333 & 5.41403199327844 & 19.6 \tabularnewline
18 & 340.133333333333 & 95.3387389863908 & 196.7 \tabularnewline
19 & 403.791666666667 & 17.5879327605003 & 64.6 \tabularnewline
20 & 343.025 & 10.8259053788922 & 30.7 \tabularnewline
21 & 411.075 & 49.9922016645869 & 136.9 \tabularnewline
22 & 376.5 & 21.5070812862774 & 58.7 \tabularnewline
23 & 342.733333333333 & 4.98877527935252 & 15.8 \tabularnewline
24 & 344.975 & 15.0015226499906 & 46.5 \tabularnewline
25 & 309.258333333333 & 9.84640758978838 & 31.1 \tabularnewline
26 & 292.375 & 5.22478794698016 & 17.3 \tabularnewline
27 & 291.625 & 6.46108983207801 & 22.9 \tabularnewline
28 & 284.941666666667 & 5.6527480578972 & 18.2 \tabularnewline
29 & 326.841666666667 & 18.2154009929327 & 54.2 \tabularnewline
30 & 320.316666666667 & 7.40071659102049 & 23.6 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=249957&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]347.216666666667[/C][C]45.2320850188394[/C][C]138.5[/C][/ROW]
[ROW][C]2[/C][C]310.333333333333[/C][C]25.9172576177388[/C][C]67.7[/C][/ROW]
[ROW][C]3[/C][C]291.55[/C][C]30.8076289253165[/C][C]75.3[/C][/ROW]
[ROW][C]4[/C][C]310.616666666667[/C][C]14.8591467596307[/C][C]49.3[/C][/ROW]
[ROW][C]5[/C][C]250.35[/C][C]9.01075115423993[/C][C]33.6[/C][/ROW]
[ROW][C]6[/C][C]256.816666666667[/C][C]3.94019688786633[/C][C]13.3[/C][/ROW]
[ROW][C]7[/C][C]253.033333333333[/C][C]2.42986469257909[/C][C]7.30000000000001[/C][/ROW]
[ROW][C]8[/C][C]263.933333333333[/C][C]4.39820900188275[/C][C]13[/C][/ROW]
[ROW][C]9[/C][C]266.85[/C][C]4.43160139329915[/C][C]15[/C][/ROW]
[ROW][C]10[/C][C]344.858333333333[/C][C]29.6914881691196[/C][C]104.3[/C][/ROW]
[ROW][C]11[/C][C]293.25[/C][C]16.6569395857593[/C][C]51.5[/C][/ROW]
[ROW][C]12[/C][C]284.433333333333[/C][C]3.98596020901849[/C][C]15.7[/C][/ROW]
[ROW][C]13[/C][C]307.266666666667[/C][C]10.1860272685258[/C][C]32.2[/C][/ROW]
[ROW][C]14[/C][C]296.625[/C][C]5.68892464674683[/C][C]16.9[/C][/ROW]
[ROW][C]15[/C][C]280.866666666667[/C][C]11.9555489842646[/C][C]34.6[/C][/ROW]
[ROW][C]16[/C][C]257.775[/C][C]10.8560938061198[/C][C]32.4[/C][/ROW]
[ROW][C]17[/C][C]247.158333333333[/C][C]5.41403199327844[/C][C]19.6[/C][/ROW]
[ROW][C]18[/C][C]340.133333333333[/C][C]95.3387389863908[/C][C]196.7[/C][/ROW]
[ROW][C]19[/C][C]403.791666666667[/C][C]17.5879327605003[/C][C]64.6[/C][/ROW]
[ROW][C]20[/C][C]343.025[/C][C]10.8259053788922[/C][C]30.7[/C][/ROW]
[ROW][C]21[/C][C]411.075[/C][C]49.9922016645869[/C][C]136.9[/C][/ROW]
[ROW][C]22[/C][C]376.5[/C][C]21.5070812862774[/C][C]58.7[/C][/ROW]
[ROW][C]23[/C][C]342.733333333333[/C][C]4.98877527935252[/C][C]15.8[/C][/ROW]
[ROW][C]24[/C][C]344.975[/C][C]15.0015226499906[/C][C]46.5[/C][/ROW]
[ROW][C]25[/C][C]309.258333333333[/C][C]9.84640758978838[/C][C]31.1[/C][/ROW]
[ROW][C]26[/C][C]292.375[/C][C]5.22478794698016[/C][C]17.3[/C][/ROW]
[ROW][C]27[/C][C]291.625[/C][C]6.46108983207801[/C][C]22.9[/C][/ROW]
[ROW][C]28[/C][C]284.941666666667[/C][C]5.6527480578972[/C][C]18.2[/C][/ROW]
[ROW][C]29[/C][C]326.841666666667[/C][C]18.2154009929327[/C][C]54.2[/C][/ROW]
[ROW][C]30[/C][C]320.316666666667[/C][C]7.40071659102049[/C][C]23.6[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=249957&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=249957&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	347.216666666667	45.2320850188394	138.5
2	310.333333333333	25.9172576177388	67.7
3	291.55	30.8076289253165	75.3
4	310.616666666667	14.8591467596307	49.3
5	250.35	9.01075115423993	33.6
6	256.816666666667	3.94019688786633	13.3
7	253.033333333333	2.42986469257909	7.30000000000001
8	263.933333333333	4.39820900188275	13
9	266.85	4.43160139329915	15
10	344.858333333333	29.6914881691196	104.3
11	293.25	16.6569395857593	51.5
12	284.433333333333	3.98596020901849	15.7
13	307.266666666667	10.1860272685258	32.2
14	296.625	5.68892464674683	16.9
15	280.866666666667	11.9555489842646	34.6
16	257.775	10.8560938061198	32.4
17	247.158333333333	5.41403199327844	19.6
18	340.133333333333	95.3387389863908	196.7
19	403.791666666667	17.5879327605003	64.6
20	343.025	10.8259053788922	30.7
21	411.075	49.9922016645869	136.9
22	376.5	21.5070812862774	58.7
23	342.733333333333	4.98877527935252	15.8
24	344.975	15.0015226499906	46.5
25	309.258333333333	9.84640758978838	31.1
26	292.375	5.22478794698016	17.3
27	291.625	6.46108983207801	22.9
28	284.941666666667	5.6527480578972	18.2
29	326.841666666667	18.2154009929327	54.2
30	320.316666666667	7.40071659102049	23.6

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-51.3894931938325
beta	0.221089058290842
S.D.	0.0716075118835778
T-STAT	3.08751208463012
p-value	0.00451871666804964

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -51.3894931938325 \tabularnewline
beta & 0.221089058290842 \tabularnewline
S.D. & 0.0716075118835778 \tabularnewline
T-STAT & 3.08751208463012 \tabularnewline
p-value & 0.00451871666804964 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=249957&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-51.3894931938325[/C][/ROW]
[ROW][C]beta[/C][C]0.221089058290842[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0716075118835778[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.08751208463012[/C][/ROW]
[ROW][C]p-value[/C][C]0.00451871666804964[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=249957&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=249957&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	-51.3894931938325
beta	0.221089058290842
S.D.	0.0716075118835778
T-STAT	3.08751208463012
p-value	0.00451871666804964

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-21.3502374337831
beta	4.15281399501749
S.D.	0.911682675353873
T-STAT	4.55510903879529
p-value	9.35065553689939e-05
Lambda	-3.15281399501749

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -21.3502374337831 \tabularnewline
beta & 4.15281399501749 \tabularnewline
S.D. & 0.911682675353873 \tabularnewline
T-STAT & 4.55510903879529 \tabularnewline
p-value & 9.35065553689939e-05 \tabularnewline
Lambda & -3.15281399501749 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=249957&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-21.3502374337831[/C][/ROW]
[ROW][C]beta[/C][C]4.15281399501749[/C][/ROW]
[ROW][C]S.D.[/C][C]0.911682675353873[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.55510903879529[/C][/ROW]
[ROW][C]p-value[/C][C]9.35065553689939e-05[/C][/ROW]
[ROW][C]Lambda[/C][C]-3.15281399501749[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=249957&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=249957&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	-21.3502374337831
beta	4.15281399501749
S.D.	0.911682675353873
T-STAT	4.55510903879529
p-value	9.35065553689939e-05
Lambda	-3.15281399501749

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