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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, 04 Aug 2010 11:18:18 +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/04/t1280920695k6js258ro0j6p9e.htm/, Retrieved Fri, 03 May 2024 03:54:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78296, Retrieved Fri, 03 May 2024 03:54:47 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Bogaerts Yannik

Estimated Impact

153

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

-       [Standard Deviation-Mean Plot] [Tijdreeks A stap 26] [2010-08-04 11:18:18] [1596366c2ece8f787477cc7d1246d4c7] [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	2 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78296&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78296&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78296&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	440.25	1.70782512765993	4
2	447.25	12.5266382827424	26
3	434	1.4142135623731	3
4	438.75	2.06155281280883	5
5	442.25	17.6517232397671	39
6	407.75	4.19324854180304	10
7	411.5	3	6
8	419.25	18.0069431053691	39
9	395.5	6.2449979983984	15
10	395.75	8.77021474461525	19
11	388.75	16.7605688049859	34
12	365	4.96655480858378	11
13	357	11.8883696667513	26
14	347.25	24.5950537032686	50
15	302.5	8.81286937760152	20
16	296.75	8.84590300647707	18
17	297	23.137271518771	48
18	257	9.69535971483266	21
19	252.75	8.26135582092915	19
20	255.75	20.271079563424	40
21	220.75	9.74251849711699	22
22	209.5	11.8180652674906	28
23	210.25	20.8865985742054	42
24	176.5	10.2794292967395	25
25	159.75	13.4505266315735	29
26	147.25	23.2289331079439	47
27	109.5	12.0415945787923	26
28	83	11.4017542509914	24
29	79.5	23.6149670054113	48
30	36.5	8.50490054811538	19

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 440.25 & 1.70782512765993 & 4 \tabularnewline
2 & 447.25 & 12.5266382827424 & 26 \tabularnewline
3 & 434 & 1.4142135623731 & 3 \tabularnewline
4 & 438.75 & 2.06155281280883 & 5 \tabularnewline
5 & 442.25 & 17.6517232397671 & 39 \tabularnewline
6 & 407.75 & 4.19324854180304 & 10 \tabularnewline
7 & 411.5 & 3 & 6 \tabularnewline
8 & 419.25 & 18.0069431053691 & 39 \tabularnewline
9 & 395.5 & 6.2449979983984 & 15 \tabularnewline
10 & 395.75 & 8.77021474461525 & 19 \tabularnewline
11 & 388.75 & 16.7605688049859 & 34 \tabularnewline
12 & 365 & 4.96655480858378 & 11 \tabularnewline
13 & 357 & 11.8883696667513 & 26 \tabularnewline
14 & 347.25 & 24.5950537032686 & 50 \tabularnewline
15 & 302.5 & 8.81286937760152 & 20 \tabularnewline
16 & 296.75 & 8.84590300647707 & 18 \tabularnewline
17 & 297 & 23.137271518771 & 48 \tabularnewline
18 & 257 & 9.69535971483266 & 21 \tabularnewline
19 & 252.75 & 8.26135582092915 & 19 \tabularnewline
20 & 255.75 & 20.271079563424 & 40 \tabularnewline
21 & 220.75 & 9.74251849711699 & 22 \tabularnewline
22 & 209.5 & 11.8180652674906 & 28 \tabularnewline
23 & 210.25 & 20.8865985742054 & 42 \tabularnewline
24 & 176.5 & 10.2794292967395 & 25 \tabularnewline
25 & 159.75 & 13.4505266315735 & 29 \tabularnewline
26 & 147.25 & 23.2289331079439 & 47 \tabularnewline
27 & 109.5 & 12.0415945787923 & 26 \tabularnewline
28 & 83 & 11.4017542509914 & 24 \tabularnewline
29 & 79.5 & 23.6149670054113 & 48 \tabularnewline
30 & 36.5 & 8.50490054811538 & 19 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78296&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]440.25[/C][C]1.70782512765993[/C][C]4[/C][/ROW]
[ROW][C]2[/C][C]447.25[/C][C]12.5266382827424[/C][C]26[/C][/ROW]
[ROW][C]3[/C][C]434[/C][C]1.4142135623731[/C][C]3[/C][/ROW]
[ROW][C]4[/C][C]438.75[/C][C]2.06155281280883[/C][C]5[/C][/ROW]
[ROW][C]5[/C][C]442.25[/C][C]17.6517232397671[/C][C]39[/C][/ROW]
[ROW][C]6[/C][C]407.75[/C][C]4.19324854180304[/C][C]10[/C][/ROW]
[ROW][C]7[/C][C]411.5[/C][C]3[/C][C]6[/C][/ROW]
[ROW][C]8[/C][C]419.25[/C][C]18.0069431053691[/C][C]39[/C][/ROW]
[ROW][C]9[/C][C]395.5[/C][C]6.2449979983984[/C][C]15[/C][/ROW]
[ROW][C]10[/C][C]395.75[/C][C]8.77021474461525[/C][C]19[/C][/ROW]
[ROW][C]11[/C][C]388.75[/C][C]16.7605688049859[/C][C]34[/C][/ROW]
[ROW][C]12[/C][C]365[/C][C]4.96655480858378[/C][C]11[/C][/ROW]
[ROW][C]13[/C][C]357[/C][C]11.8883696667513[/C][C]26[/C][/ROW]
[ROW][C]14[/C][C]347.25[/C][C]24.5950537032686[/C][C]50[/C][/ROW]
[ROW][C]15[/C][C]302.5[/C][C]8.81286937760152[/C][C]20[/C][/ROW]
[ROW][C]16[/C][C]296.75[/C][C]8.84590300647707[/C][C]18[/C][/ROW]
[ROW][C]17[/C][C]297[/C][C]23.137271518771[/C][C]48[/C][/ROW]
[ROW][C]18[/C][C]257[/C][C]9.69535971483266[/C][C]21[/C][/ROW]
[ROW][C]19[/C][C]252.75[/C][C]8.26135582092915[/C][C]19[/C][/ROW]
[ROW][C]20[/C][C]255.75[/C][C]20.271079563424[/C][C]40[/C][/ROW]
[ROW][C]21[/C][C]220.75[/C][C]9.74251849711699[/C][C]22[/C][/ROW]
[ROW][C]22[/C][C]209.5[/C][C]11.8180652674906[/C][C]28[/C][/ROW]
[ROW][C]23[/C][C]210.25[/C][C]20.8865985742054[/C][C]42[/C][/ROW]
[ROW][C]24[/C][C]176.5[/C][C]10.2794292967395[/C][C]25[/C][/ROW]
[ROW][C]25[/C][C]159.75[/C][C]13.4505266315735[/C][C]29[/C][/ROW]
[ROW][C]26[/C][C]147.25[/C][C]23.2289331079439[/C][C]47[/C][/ROW]
[ROW][C]27[/C][C]109.5[/C][C]12.0415945787923[/C][C]26[/C][/ROW]
[ROW][C]28[/C][C]83[/C][C]11.4017542509914[/C][C]24[/C][/ROW]
[ROW][C]29[/C][C]79.5[/C][C]23.6149670054113[/C][C]48[/C][/ROW]
[ROW][C]30[/C][C]36.5[/C][C]8.50490054811538[/C][C]19[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78296&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78296&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	440.25	1.70782512765993	4
2	447.25	12.5266382827424	26
3	434	1.4142135623731	3
4	438.75	2.06155281280883	5
5	442.25	17.6517232397671	39
6	407.75	4.19324854180304	10
7	411.5	3	6
8	419.25	18.0069431053691	39
9	395.5	6.2449979983984	15
10	395.75	8.77021474461525	19
11	388.75	16.7605688049859	34
12	365	4.96655480858378	11
13	357	11.8883696667513	26
14	347.25	24.5950537032686	50
15	302.5	8.81286937760152	20
16	296.75	8.84590300647707	18
17	297	23.137271518771	48
18	257	9.69535971483266	21
19	252.75	8.26135582092915	19
20	255.75	20.271079563424	40
21	220.75	9.74251849711699	22
22	209.5	11.8180652674906	28
23	210.25	20.8865985742054	42
24	176.5	10.2794292967395	25
25	159.75	13.4505266315735	29
26	147.25	23.2289331079439	47
27	109.5	12.0415945787923	26
28	83	11.4017542509914	24
29	79.5	23.6149670054113	48
30	36.5	8.50490054811538	19

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	17.5041692964709
beta	-0.0190499229022239
S.D.	0.00977168693149113
T-STAT	-1.94950196785694
p-value	0.0613157199362863

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 17.5041692964709 \tabularnewline
beta & -0.0190499229022239 \tabularnewline
S.D. & 0.00977168693149113 \tabularnewline
T-STAT & -1.94950196785694 \tabularnewline
p-value & 0.0613157199362863 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78296&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]17.5041692964709[/C][/ROW]
[ROW][C]beta[/C][C]-0.0190499229022239[/C][/ROW]
[ROW][C]S.D.[/C][C]0.00977168693149113[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.94950196785694[/C][/ROW]
[ROW][C]p-value[/C][C]0.0613157199362863[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78296&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78296&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	17.5041692964709
beta	-0.0190499229022239
S.D.	0.00977168693149113
T-STAT	-1.94950196785694
p-value	0.0613157199362863

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	4.64084197730159
beta	-0.431531189433701
S.D.	0.224186798809605
T-STAT	-1.92487332762259
p-value	0.0644598685863708
Lambda	1.4315311894337

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 4.64084197730159 \tabularnewline
beta & -0.431531189433701 \tabularnewline
S.D. & 0.224186798809605 \tabularnewline
T-STAT & -1.92487332762259 \tabularnewline
p-value & 0.0644598685863708 \tabularnewline
Lambda & 1.4315311894337 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78296&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]4.64084197730159[/C][/ROW]
[ROW][C]beta[/C][C]-0.431531189433701[/C][/ROW]
[ROW][C]S.D.[/C][C]0.224186798809605[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.92487332762259[/C][/ROW]
[ROW][C]p-value[/C][C]0.0644598685863708[/C][/ROW]
[ROW][C]Lambda[/C][C]1.4315311894337[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78296&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78296&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	4.64084197730159
beta	-0.431531189433701
S.D.	0.224186798809605
T-STAT	-1.92487332762259
p-value	0.0644598685863708
Lambda	1.4315311894337

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