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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

Sun, 21 Aug 2011 08:41:36 -0400

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/2011/Aug/21/t1313930514x01bxvmymm8mlie.htm/, Retrieved Wed, 15 May 2024 09:41:05 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=124234, Retrieved Wed, 15 May 2024 09:41:05 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Blij Arnaud

Estimated Impact

195

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

-       [Standard Deviation-Mean Plot] [Tijdreeks 2 - Sta...] [2011-08-21 12:41:36] [084e0343a0486ff05530df6c705c8bb4] [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' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124234&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124234&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124234&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' @ jenkins.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	662.5	56.7890834580027	120
2	692.5	35.939764421413	80
3	705	58.022983951764	140
4	640	61.6441400296898	150
5	707.5	37.7491721763537	90
6	790	84.8528137423857	200
7	642.5	59.6517672272443	130
8	742.5	57.373048260195	130
9	807.5	92.8708781050336	210
10	662.5	35.939764421413	80
11	730	40.8248290463863	90
12	827.5	103.400515794974	210
13	692.5	60.7590871118606	110
14	730	63.7704215656966	140
15	880	155.56349186104	330
16	670	121.1060141639	260
17	755	83.8649708360608	200
18	917.5	160.701586799882	350
19	695	94.6924847422786	190
20	755	101.488915650922	230
21	922.5	227.797424626941	510
22	730	117.473401244707	270
23	735	110.302614051829	230
24	905	233.309522594628	520
25	712.5	112.657297440808	260
26	720	149.888847706114	320
27	905	221.885856541902	460

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 662.5 & 56.7890834580027 & 120 \tabularnewline
2 & 692.5 & 35.939764421413 & 80 \tabularnewline
3 & 705 & 58.022983951764 & 140 \tabularnewline
4 & 640 & 61.6441400296898 & 150 \tabularnewline
5 & 707.5 & 37.7491721763537 & 90 \tabularnewline
6 & 790 & 84.8528137423857 & 200 \tabularnewline
7 & 642.5 & 59.6517672272443 & 130 \tabularnewline
8 & 742.5 & 57.373048260195 & 130 \tabularnewline
9 & 807.5 & 92.8708781050336 & 210 \tabularnewline
10 & 662.5 & 35.939764421413 & 80 \tabularnewline
11 & 730 & 40.8248290463863 & 90 \tabularnewline
12 & 827.5 & 103.400515794974 & 210 \tabularnewline
13 & 692.5 & 60.7590871118606 & 110 \tabularnewline
14 & 730 & 63.7704215656966 & 140 \tabularnewline
15 & 880 & 155.56349186104 & 330 \tabularnewline
16 & 670 & 121.1060141639 & 260 \tabularnewline
17 & 755 & 83.8649708360608 & 200 \tabularnewline
18 & 917.5 & 160.701586799882 & 350 \tabularnewline
19 & 695 & 94.6924847422786 & 190 \tabularnewline
20 & 755 & 101.488915650922 & 230 \tabularnewline
21 & 922.5 & 227.797424626941 & 510 \tabularnewline
22 & 730 & 117.473401244707 & 270 \tabularnewline
23 & 735 & 110.302614051829 & 230 \tabularnewline
24 & 905 & 233.309522594628 & 520 \tabularnewline
25 & 712.5 & 112.657297440808 & 260 \tabularnewline
26 & 720 & 149.888847706114 & 320 \tabularnewline
27 & 905 & 221.885856541902 & 460 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124234&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]662.5[/C][C]56.7890834580027[/C][C]120[/C][/ROW]
[ROW][C]2[/C][C]692.5[/C][C]35.939764421413[/C][C]80[/C][/ROW]
[ROW][C]3[/C][C]705[/C][C]58.022983951764[/C][C]140[/C][/ROW]
[ROW][C]4[/C][C]640[/C][C]61.6441400296898[/C][C]150[/C][/ROW]
[ROW][C]5[/C][C]707.5[/C][C]37.7491721763537[/C][C]90[/C][/ROW]
[ROW][C]6[/C][C]790[/C][C]84.8528137423857[/C][C]200[/C][/ROW]
[ROW][C]7[/C][C]642.5[/C][C]59.6517672272443[/C][C]130[/C][/ROW]
[ROW][C]8[/C][C]742.5[/C][C]57.373048260195[/C][C]130[/C][/ROW]
[ROW][C]9[/C][C]807.5[/C][C]92.8708781050336[/C][C]210[/C][/ROW]
[ROW][C]10[/C][C]662.5[/C][C]35.939764421413[/C][C]80[/C][/ROW]
[ROW][C]11[/C][C]730[/C][C]40.8248290463863[/C][C]90[/C][/ROW]
[ROW][C]12[/C][C]827.5[/C][C]103.400515794974[/C][C]210[/C][/ROW]
[ROW][C]13[/C][C]692.5[/C][C]60.7590871118606[/C][C]110[/C][/ROW]
[ROW][C]14[/C][C]730[/C][C]63.7704215656966[/C][C]140[/C][/ROW]
[ROW][C]15[/C][C]880[/C][C]155.56349186104[/C][C]330[/C][/ROW]
[ROW][C]16[/C][C]670[/C][C]121.1060141639[/C][C]260[/C][/ROW]
[ROW][C]17[/C][C]755[/C][C]83.8649708360608[/C][C]200[/C][/ROW]
[ROW][C]18[/C][C]917.5[/C][C]160.701586799882[/C][C]350[/C][/ROW]
[ROW][C]19[/C][C]695[/C][C]94.6924847422786[/C][C]190[/C][/ROW]
[ROW][C]20[/C][C]755[/C][C]101.488915650922[/C][C]230[/C][/ROW]
[ROW][C]21[/C][C]922.5[/C][C]227.797424626941[/C][C]510[/C][/ROW]
[ROW][C]22[/C][C]730[/C][C]117.473401244707[/C][C]270[/C][/ROW]
[ROW][C]23[/C][C]735[/C][C]110.302614051829[/C][C]230[/C][/ROW]
[ROW][C]24[/C][C]905[/C][C]233.309522594628[/C][C]520[/C][/ROW]
[ROW][C]25[/C][C]712.5[/C][C]112.657297440808[/C][C]260[/C][/ROW]
[ROW][C]26[/C][C]720[/C][C]149.888847706114[/C][C]320[/C][/ROW]
[ROW][C]27[/C][C]905[/C][C]221.885856541902[/C][C]460[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124234&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124234&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	662.5	56.7890834580027	120
2	692.5	35.939764421413	80
3	705	58.022983951764	140
4	640	61.6441400296898	150
5	707.5	37.7491721763537	90
6	790	84.8528137423857	200
7	642.5	59.6517672272443	130
8	742.5	57.373048260195	130
9	807.5	92.8708781050336	210
10	662.5	35.939764421413	80
11	730	40.8248290463863	90
12	827.5	103.400515794974	210
13	692.5	60.7590871118606	110
14	730	63.7704215656966	140
15	880	155.56349186104	330
16	670	121.1060141639	260
17	755	83.8649708360608	200
18	917.5	160.701586799882	350
19	695	94.6924847422786	190
20	755	101.488915650922	230
21	922.5	227.797424626941	510
22	730	117.473401244707	270
23	735	110.302614051829	230
24	905	233.309522594628	520
25	712.5	112.657297440808	260
26	720	149.888847706114	320
27	905	221.885856541902	460

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-301.08652604745
beta	0.534529476314462
S.D.	0.0791593504929152
T-STAT	6.75257531783693
p-value	4.4618375957398e-07

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -301.08652604745 \tabularnewline
beta & 0.534529476314462 \tabularnewline
S.D. & 0.0791593504929152 \tabularnewline
T-STAT & 6.75257531783693 \tabularnewline
p-value & 4.4618375957398e-07 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124234&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-301.08652604745[/C][/ROW]
[ROW][C]beta[/C][C]0.534529476314462[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0791593504929152[/C][/ROW]
[ROW][C]T-STAT[/C][C]6.75257531783693[/C][/ROW]
[ROW][C]p-value[/C][C]4.4618375957398e-07[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124234&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124234&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	-301.08652604745
beta	0.534529476314462
S.D.	0.0791593504929152
T-STAT	6.75257531783693
p-value	4.4618375957398e-07

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-19.8878117148916
beta	3.68077168028318
S.D.	0.67166438670444
T-STAT	5.48007569426615
p-value	1.08201272340809e-05
Lambda	-2.68077168028318

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -19.8878117148916 \tabularnewline
beta & 3.68077168028318 \tabularnewline
S.D. & 0.67166438670444 \tabularnewline
T-STAT & 5.48007569426615 \tabularnewline
p-value & 1.08201272340809e-05 \tabularnewline
Lambda & -2.68077168028318 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124234&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-19.8878117148916[/C][/ROW]
[ROW][C]beta[/C][C]3.68077168028318[/C][/ROW]
[ROW][C]S.D.[/C][C]0.67166438670444[/C][/ROW]
[ROW][C]T-STAT[/C][C]5.48007569426615[/C][/ROW]
[ROW][C]p-value[/C][C]1.08201272340809e-05[/C][/ROW]
[ROW][C]Lambda[/C][C]-2.68077168028318[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124234&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124234&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	-19.8878117148916
beta	3.68077168028318
S.D.	0.67166438670444
T-STAT	5.48007569426615
p-value	1.08201272340809e-05
Lambda	-2.68077168028318

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

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code