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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, 10 Aug 2010 14:07:12 +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/Aug/10/t1281449221egpxntf6arrt6ir.htm/, Retrieved Sun, 05 May 2024 00:10:33 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78581, Retrieved Sun, 05 May 2024 00:10:33 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

184

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

-       [Standard Deviation-Mean Plot] [Tijdreeks 1 - Sta...] [2010-08-10 14:07:12] [f91e4cd4d3d1892f3fcf702e4827e40c] [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	'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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78581&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78581&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78581&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	'Gwilym Jenkins' @ 72.249.127.135

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	354.25	1.70782512765993	4
2	361.25	12.5266382827424	26
3	348	1.41421356237310	3
4	348	4.39696865275764	10
5	358.75	11.4418821295566	24
6	352.5	4.50924975282289	10
7	345.25	3.77491721763537	7
8	369.5	8.85061203156784	18
9	365.75	5.61990510002912	13
10	357	8.60232526704263	21
11	372.5	14.8884742894182	32
12	362	6.58280588604383	16
13	358.25	7.36545993132812	15
14	371.5	19.1224126790180	41
15	344.75	6.07590871118606	14
16	336.5	15.0222057856583	34
17	333	19.6129209111409	43
18	309.5	5.91607978309962	13
19	283.25	13.7446959466795	27
20	276.5	16.3401346383682	36
21	261	3.91578004149024	9
22	233.75	13.6717470232106	26
23	225.75	17.1731379388470	37
24	213.25	2.98607881119482	7
25	187	16.9901932498329	37
26	170.5	22.4870333006972	51
27	141	3.74165738677394	9
28	119.75	13.3260396717604	31
29	108	26.9196334794266	61
30	61.75	3.30403793359983	7

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 354.25 & 1.70782512765993 & 4 \tabularnewline
2 & 361.25 & 12.5266382827424 & 26 \tabularnewline
3 & 348 & 1.41421356237310 & 3 \tabularnewline
4 & 348 & 4.39696865275764 & 10 \tabularnewline
5 & 358.75 & 11.4418821295566 & 24 \tabularnewline
6 & 352.5 & 4.50924975282289 & 10 \tabularnewline
7 & 345.25 & 3.77491721763537 & 7 \tabularnewline
8 & 369.5 & 8.85061203156784 & 18 \tabularnewline
9 & 365.75 & 5.61990510002912 & 13 \tabularnewline
10 & 357 & 8.60232526704263 & 21 \tabularnewline
11 & 372.5 & 14.8884742894182 & 32 \tabularnewline
12 & 362 & 6.58280588604383 & 16 \tabularnewline
13 & 358.25 & 7.36545993132812 & 15 \tabularnewline
14 & 371.5 & 19.1224126790180 & 41 \tabularnewline
15 & 344.75 & 6.07590871118606 & 14 \tabularnewline
16 & 336.5 & 15.0222057856583 & 34 \tabularnewline
17 & 333 & 19.6129209111409 & 43 \tabularnewline
18 & 309.5 & 5.91607978309962 & 13 \tabularnewline
19 & 283.25 & 13.7446959466795 & 27 \tabularnewline
20 & 276.5 & 16.3401346383682 & 36 \tabularnewline
21 & 261 & 3.91578004149024 & 9 \tabularnewline
22 & 233.75 & 13.6717470232106 & 26 \tabularnewline
23 & 225.75 & 17.1731379388470 & 37 \tabularnewline
24 & 213.25 & 2.98607881119482 & 7 \tabularnewline
25 & 187 & 16.9901932498329 & 37 \tabularnewline
26 & 170.5 & 22.4870333006972 & 51 \tabularnewline
27 & 141 & 3.74165738677394 & 9 \tabularnewline
28 & 119.75 & 13.3260396717604 & 31 \tabularnewline
29 & 108 & 26.9196334794266 & 61 \tabularnewline
30 & 61.75 & 3.30403793359983 & 7 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78581&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]354.25[/C][C]1.70782512765993[/C][C]4[/C][/ROW]
[ROW][C]2[/C][C]361.25[/C][C]12.5266382827424[/C][C]26[/C][/ROW]
[ROW][C]3[/C][C]348[/C][C]1.41421356237310[/C][C]3[/C][/ROW]
[ROW][C]4[/C][C]348[/C][C]4.39696865275764[/C][C]10[/C][/ROW]
[ROW][C]5[/C][C]358.75[/C][C]11.4418821295566[/C][C]24[/C][/ROW]
[ROW][C]6[/C][C]352.5[/C][C]4.50924975282289[/C][C]10[/C][/ROW]
[ROW][C]7[/C][C]345.25[/C][C]3.77491721763537[/C][C]7[/C][/ROW]
[ROW][C]8[/C][C]369.5[/C][C]8.85061203156784[/C][C]18[/C][/ROW]
[ROW][C]9[/C][C]365.75[/C][C]5.61990510002912[/C][C]13[/C][/ROW]
[ROW][C]10[/C][C]357[/C][C]8.60232526704263[/C][C]21[/C][/ROW]
[ROW][C]11[/C][C]372.5[/C][C]14.8884742894182[/C][C]32[/C][/ROW]
[ROW][C]12[/C][C]362[/C][C]6.58280588604383[/C][C]16[/C][/ROW]
[ROW][C]13[/C][C]358.25[/C][C]7.36545993132812[/C][C]15[/C][/ROW]
[ROW][C]14[/C][C]371.5[/C][C]19.1224126790180[/C][C]41[/C][/ROW]
[ROW][C]15[/C][C]344.75[/C][C]6.07590871118606[/C][C]14[/C][/ROW]
[ROW][C]16[/C][C]336.5[/C][C]15.0222057856583[/C][C]34[/C][/ROW]
[ROW][C]17[/C][C]333[/C][C]19.6129209111409[/C][C]43[/C][/ROW]
[ROW][C]18[/C][C]309.5[/C][C]5.91607978309962[/C][C]13[/C][/ROW]
[ROW][C]19[/C][C]283.25[/C][C]13.7446959466795[/C][C]27[/C][/ROW]
[ROW][C]20[/C][C]276.5[/C][C]16.3401346383682[/C][C]36[/C][/ROW]
[ROW][C]21[/C][C]261[/C][C]3.91578004149024[/C][C]9[/C][/ROW]
[ROW][C]22[/C][C]233.75[/C][C]13.6717470232106[/C][C]26[/C][/ROW]
[ROW][C]23[/C][C]225.75[/C][C]17.1731379388470[/C][C]37[/C][/ROW]
[ROW][C]24[/C][C]213.25[/C][C]2.98607881119482[/C][C]7[/C][/ROW]
[ROW][C]25[/C][C]187[/C][C]16.9901932498329[/C][C]37[/C][/ROW]
[ROW][C]26[/C][C]170.5[/C][C]22.4870333006972[/C][C]51[/C][/ROW]
[ROW][C]27[/C][C]141[/C][C]3.74165738677394[/C][C]9[/C][/ROW]
[ROW][C]28[/C][C]119.75[/C][C]13.3260396717604[/C][C]31[/C][/ROW]
[ROW][C]29[/C][C]108[/C][C]26.9196334794266[/C][C]61[/C][/ROW]
[ROW][C]30[/C][C]61.75[/C][C]3.30403793359983[/C][C]7[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78581&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78581&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	354.25	1.70782512765993	4
2	361.25	12.5266382827424	26
3	348	1.41421356237310	3
4	348	4.39696865275764	10
5	358.75	11.4418821295566	24
6	352.5	4.50924975282289	10
7	345.25	3.77491721763537	7
8	369.5	8.85061203156784	18
9	365.75	5.61990510002912	13
10	357	8.60232526704263	21
11	372.5	14.8884742894182	32
12	362	6.58280588604383	16
13	358.25	7.36545993132812	15
14	371.5	19.1224126790180	41
15	344.75	6.07590871118606	14
16	336.5	15.0222057856583	34
17	333	19.6129209111409	43
18	309.5	5.91607978309962	13
19	283.25	13.7446959466795	27
20	276.5	16.3401346383682	36
21	261	3.91578004149024	9
22	233.75	13.6717470232106	26
23	225.75	17.1731379388470	37
24	213.25	2.98607881119482	7
25	187	16.9901932498329	37
26	170.5	22.4870333006972	51
27	141	3.74165738677394	9
28	119.75	13.3260396717604	31
29	108	26.9196334794266	61
30	61.75	3.30403793359983	7

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	15.7344740590558
beta	-0.0185408902052449
S.D.	0.0133557928134081
T-STAT	-1.38822834887281
p-value	0.176014661128088

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 15.7344740590558 \tabularnewline
beta & -0.0185408902052449 \tabularnewline
S.D. & 0.0133557928134081 \tabularnewline
T-STAT & -1.38822834887281 \tabularnewline
p-value & 0.176014661128088 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78581&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]15.7344740590558[/C][/ROW]
[ROW][C]beta[/C][C]-0.0185408902052449[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0133557928134081[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.38822834887281[/C][/ROW]
[ROW][C]p-value[/C][C]0.176014661128088[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78581&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78581&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	15.7344740590558
beta	-0.0185408902052449
S.D.	0.0133557928134081
T-STAT	-1.38822834887281
p-value	0.176014661128088

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	2.99089087234818
beta	-0.161335334836302
S.D.	0.325502695384741
T-STAT	-0.49564976611209
p-value	0.624009537981624
Lambda	1.16133533483630

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 2.99089087234818 \tabularnewline
beta & -0.161335334836302 \tabularnewline
S.D. & 0.325502695384741 \tabularnewline
T-STAT & -0.49564976611209 \tabularnewline
p-value & 0.624009537981624 \tabularnewline
Lambda & 1.16133533483630 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78581&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.99089087234818[/C][/ROW]
[ROW][C]beta[/C][C]-0.161335334836302[/C][/ROW]
[ROW][C]S.D.[/C][C]0.325502695384741[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.49564976611209[/C][/ROW]
[ROW][C]p-value[/C][C]0.624009537981624[/C][/ROW]
[ROW][C]Lambda[/C][C]1.16133533483630[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78581&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78581&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	2.99089087234818
beta	-0.161335334836302
S.D.	0.325502695384741
T-STAT	-0.49564976611209
p-value	0.624009537981624
Lambda	1.16133533483630

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