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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

Fri, 24 Dec 2010 14:24:35 +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/24/t1293201115yru15fk3q5fv6wq.htm/, Retrieved Tue, 30 Apr 2024 02:04:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115004, Retrieved Tue, 30 Apr 2024 02:04:47 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

127

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

-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
- RMPD  [Bivariate Explorative Data Analysis] [Ws4 part 1.1 s090...] [2009-10-27 21:56:53] [e0fc65a5811681d807296d590d5b45de]
-  M D    [Bivariate Explorative Data Analysis] [Paper; bivariate ...] [2009-12-19 19:10:37] [e0fc65a5811681d807296d590d5b45de]
- RMPD      [Cross Correlation Function] [cross correlation...] [2010-12-08 19:50:23] [74be16979710d4c4e7c6647856088456]
- RMPD          [Standard Deviation-Mean Plot] [] [2010-12-24 14:24:35] [6b31f806e9ccc1f74a26091056f791cb] [Current]

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Boxplots

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	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115004&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115004&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115004&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	'George Udny Yule' @ 72.249.76.132

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	15.5758333333333	1.04410429932971	3.21
2	20.9216666666667	1.94566573478467	6.07
3	25.9758333333333	2.67647820952471	9.17
4	41.5641666666667	7.64243471240241	22.04
5	53.26	8.52715981704662	27.79
6	96.3916666666667	17.7816963263470	52.79
7	45.2141666666667	25.8980281658428	78.42
8	47.1116666666667	5.87419291683908	20.55
9	55.8341666666667	4.73194455191777	14.69
10	62.2758333333333	6.12028142302049	20.37
11	83.1416666666667	4.36330115505416	16.1
12	102.599166666667	9.01734435642913	29.34
13	160.0675	16.5579155061587	48.6
14	183.946666666667	13.3119777461935	42.82
15	161.879166666667	38.9356217967168	104.2
16	125.229166666667	20.5625177350941	61

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 15.5758333333333 & 1.04410429932971 & 3.21 \tabularnewline
2 & 20.9216666666667 & 1.94566573478467 & 6.07 \tabularnewline
3 & 25.9758333333333 & 2.67647820952471 & 9.17 \tabularnewline
4 & 41.5641666666667 & 7.64243471240241 & 22.04 \tabularnewline
5 & 53.26 & 8.52715981704662 & 27.79 \tabularnewline
6 & 96.3916666666667 & 17.7816963263470 & 52.79 \tabularnewline
7 & 45.2141666666667 & 25.8980281658428 & 78.42 \tabularnewline
8 & 47.1116666666667 & 5.87419291683908 & 20.55 \tabularnewline
9 & 55.8341666666667 & 4.73194455191777 & 14.69 \tabularnewline
10 & 62.2758333333333 & 6.12028142302049 & 20.37 \tabularnewline
11 & 83.1416666666667 & 4.36330115505416 & 16.1 \tabularnewline
12 & 102.599166666667 & 9.01734435642913 & 29.34 \tabularnewline
13 & 160.0675 & 16.5579155061587 & 48.6 \tabularnewline
14 & 183.946666666667 & 13.3119777461935 & 42.82 \tabularnewline
15 & 161.879166666667 & 38.9356217967168 & 104.2 \tabularnewline
16 & 125.229166666667 & 20.5625177350941 & 61 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115004&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]15.5758333333333[/C][C]1.04410429932971[/C][C]3.21[/C][/ROW]
[ROW][C]2[/C][C]20.9216666666667[/C][C]1.94566573478467[/C][C]6.07[/C][/ROW]
[ROW][C]3[/C][C]25.9758333333333[/C][C]2.67647820952471[/C][C]9.17[/C][/ROW]
[ROW][C]4[/C][C]41.5641666666667[/C][C]7.64243471240241[/C][C]22.04[/C][/ROW]
[ROW][C]5[/C][C]53.26[/C][C]8.52715981704662[/C][C]27.79[/C][/ROW]
[ROW][C]6[/C][C]96.3916666666667[/C][C]17.7816963263470[/C][C]52.79[/C][/ROW]
[ROW][C]7[/C][C]45.2141666666667[/C][C]25.8980281658428[/C][C]78.42[/C][/ROW]
[ROW][C]8[/C][C]47.1116666666667[/C][C]5.87419291683908[/C][C]20.55[/C][/ROW]
[ROW][C]9[/C][C]55.8341666666667[/C][C]4.73194455191777[/C][C]14.69[/C][/ROW]
[ROW][C]10[/C][C]62.2758333333333[/C][C]6.12028142302049[/C][C]20.37[/C][/ROW]
[ROW][C]11[/C][C]83.1416666666667[/C][C]4.36330115505416[/C][C]16.1[/C][/ROW]
[ROW][C]12[/C][C]102.599166666667[/C][C]9.01734435642913[/C][C]29.34[/C][/ROW]
[ROW][C]13[/C][C]160.0675[/C][C]16.5579155061587[/C][C]48.6[/C][/ROW]
[ROW][C]14[/C][C]183.946666666667[/C][C]13.3119777461935[/C][C]42.82[/C][/ROW]
[ROW][C]15[/C][C]161.879166666667[/C][C]38.9356217967168[/C][C]104.2[/C][/ROW]
[ROW][C]16[/C][C]125.229166666667[/C][C]20.5625177350941[/C][C]61[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115004&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115004&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	15.5758333333333	1.04410429932971	3.21
2	20.9216666666667	1.94566573478467	6.07
3	25.9758333333333	2.67647820952471	9.17
4	41.5641666666667	7.64243471240241	22.04
5	53.26	8.52715981704662	27.79
6	96.3916666666667	17.7816963263470	52.79
7	45.2141666666667	25.8980281658428	78.42
8	47.1116666666667	5.87419291683908	20.55
9	55.8341666666667	4.73194455191777	14.69
10	62.2758333333333	6.12028142302049	20.37
11	83.1416666666667	4.36330115505416	16.1
12	102.599166666667	9.01734435642913	29.34
13	160.0675	16.5579155061587	48.6
14	183.946666666667	13.3119777461935	42.82
15	161.879166666667	38.9356217967168	104.2
16	125.229166666667	20.5625177350941	61

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	1.88693023596635
beta	0.120844020705815
S.D.	0.0399201278522898
T-STAT	3.02714513222390
p-value	0.0090510223167977

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.88693023596635 \tabularnewline
beta & 0.120844020705815 \tabularnewline
S.D. & 0.0399201278522898 \tabularnewline
T-STAT & 3.02714513222390 \tabularnewline
p-value & 0.0090510223167977 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115004&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.88693023596635[/C][/ROW]
[ROW][C]beta[/C][C]0.120844020705815[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0399201278522898[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.02714513222390[/C][/ROW]
[ROW][C]p-value[/C][C]0.0090510223167977[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115004&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115004&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	1.88693023596635
beta	0.120844020705815
S.D.	0.0399201278522898
T-STAT	3.02714513222390
p-value	0.0090510223167977

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-2.34988015684401
beta	1.06174686080364
S.D.	0.209880041347868
T-STAT	5.05882719473946
p-value	0.000174450376680521
Lambda	-0.0617468608036396

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.34988015684401 \tabularnewline
beta & 1.06174686080364 \tabularnewline
S.D. & 0.209880041347868 \tabularnewline
T-STAT & 5.05882719473946 \tabularnewline
p-value & 0.000174450376680521 \tabularnewline
Lambda & -0.0617468608036396 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115004&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.34988015684401[/C][/ROW]
[ROW][C]beta[/C][C]1.06174686080364[/C][/ROW]
[ROW][C]S.D.[/C][C]0.209880041347868[/C][/ROW]
[ROW][C]T-STAT[/C][C]5.05882719473946[/C][/ROW]
[ROW][C]p-value[/C][C]0.000174450376680521[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.0617468608036396[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115004&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115004&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	-2.34988015684401
beta	1.06174686080364
S.D.	0.209880041347868
T-STAT	5.05882719473946
p-value	0.000174450376680521
Lambda	-0.0617468608036396

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')

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code