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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, 29 Dec 2009 07:21:57 -0700

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/2009/Dec/29/t12620966184xmpo3ohpmf0gd7.htm/, Retrieved Fri, 03 May 2024 12:29:19 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=71126, Retrieved Fri, 03 May 2024 12:29:19 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W83

Estimated Impact

145

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

-       [Standard Deviation-Mean Plot] [] [2009-12-29 14:21:57] [ab5cffebaafedfca74d2c063d2ba2ba4] [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=71126&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=71126&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71126&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	108.975	6.91538140669045	14.7
2	118.275	2.70354705279318	5.7
3	120.55	13.9325757369794	30.4
4	109.125	8.23463215126618	17.2
5	121.325	1.56710986638886	3.69999999999999
6	122.9	14.1734493566904	32.4
7	112.45	8.99499861033896	19.2
8	124.25	2.33023603954621	5.7
9	124.825	12.9461384203939	30.1
10	112	7.3851201750547	15.7
11	121.725	3.64817305876060	8.3
12	124.35	14.9321800149878	31.2
13	112.9	7.26223106214612	15.5
14	120.025	3.83959633294959	8.9
15	121.55	15.1200749557225	30.8
16	109.325	9.28309395262879	20.4
17	120.775	2.98258836136222	6.9
18	121.35	14.4988505291512	30.8
19	111.925	9.39090872422188	20.3
20	126.925	3.34203032102743	7.10000000000001
21	126.2	15.0412765415705	32.4
22	117.35	12.1998633872133	25.8
23	131.15	5.46046396075157	12.8
24	131.675	13.7376308001052	31.2
25	122.5	7.26957128492916	16.7
26	135.6	2.86705423736628	5.79999999999998
27	134.65	15.5611696218504	32.7

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 108.975 & 6.91538140669045 & 14.7 \tabularnewline
2 & 118.275 & 2.70354705279318 & 5.7 \tabularnewline
3 & 120.55 & 13.9325757369794 & 30.4 \tabularnewline
4 & 109.125 & 8.23463215126618 & 17.2 \tabularnewline
5 & 121.325 & 1.56710986638886 & 3.69999999999999 \tabularnewline
6 & 122.9 & 14.1734493566904 & 32.4 \tabularnewline
7 & 112.45 & 8.99499861033896 & 19.2 \tabularnewline
8 & 124.25 & 2.33023603954621 & 5.7 \tabularnewline
9 & 124.825 & 12.9461384203939 & 30.1 \tabularnewline
10 & 112 & 7.3851201750547 & 15.7 \tabularnewline
11 & 121.725 & 3.64817305876060 & 8.3 \tabularnewline
12 & 124.35 & 14.9321800149878 & 31.2 \tabularnewline
13 & 112.9 & 7.26223106214612 & 15.5 \tabularnewline
14 & 120.025 & 3.83959633294959 & 8.9 \tabularnewline
15 & 121.55 & 15.1200749557225 & 30.8 \tabularnewline
16 & 109.325 & 9.28309395262879 & 20.4 \tabularnewline
17 & 120.775 & 2.98258836136222 & 6.9 \tabularnewline
18 & 121.35 & 14.4988505291512 & 30.8 \tabularnewline
19 & 111.925 & 9.39090872422188 & 20.3 \tabularnewline
20 & 126.925 & 3.34203032102743 & 7.10000000000001 \tabularnewline
21 & 126.2 & 15.0412765415705 & 32.4 \tabularnewline
22 & 117.35 & 12.1998633872133 & 25.8 \tabularnewline
23 & 131.15 & 5.46046396075157 & 12.8 \tabularnewline
24 & 131.675 & 13.7376308001052 & 31.2 \tabularnewline
25 & 122.5 & 7.26957128492916 & 16.7 \tabularnewline
26 & 135.6 & 2.86705423736628 & 5.79999999999998 \tabularnewline
27 & 134.65 & 15.5611696218504 & 32.7 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71126&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]108.975[/C][C]6.91538140669045[/C][C]14.7[/C][/ROW]
[ROW][C]2[/C][C]118.275[/C][C]2.70354705279318[/C][C]5.7[/C][/ROW]
[ROW][C]3[/C][C]120.55[/C][C]13.9325757369794[/C][C]30.4[/C][/ROW]
[ROW][C]4[/C][C]109.125[/C][C]8.23463215126618[/C][C]17.2[/C][/ROW]
[ROW][C]5[/C][C]121.325[/C][C]1.56710986638886[/C][C]3.69999999999999[/C][/ROW]
[ROW][C]6[/C][C]122.9[/C][C]14.1734493566904[/C][C]32.4[/C][/ROW]
[ROW][C]7[/C][C]112.45[/C][C]8.99499861033896[/C][C]19.2[/C][/ROW]
[ROW][C]8[/C][C]124.25[/C][C]2.33023603954621[/C][C]5.7[/C][/ROW]
[ROW][C]9[/C][C]124.825[/C][C]12.9461384203939[/C][C]30.1[/C][/ROW]
[ROW][C]10[/C][C]112[/C][C]7.3851201750547[/C][C]15.7[/C][/ROW]
[ROW][C]11[/C][C]121.725[/C][C]3.64817305876060[/C][C]8.3[/C][/ROW]
[ROW][C]12[/C][C]124.35[/C][C]14.9321800149878[/C][C]31.2[/C][/ROW]
[ROW][C]13[/C][C]112.9[/C][C]7.26223106214612[/C][C]15.5[/C][/ROW]
[ROW][C]14[/C][C]120.025[/C][C]3.83959633294959[/C][C]8.9[/C][/ROW]
[ROW][C]15[/C][C]121.55[/C][C]15.1200749557225[/C][C]30.8[/C][/ROW]
[ROW][C]16[/C][C]109.325[/C][C]9.28309395262879[/C][C]20.4[/C][/ROW]
[ROW][C]17[/C][C]120.775[/C][C]2.98258836136222[/C][C]6.9[/C][/ROW]
[ROW][C]18[/C][C]121.35[/C][C]14.4988505291512[/C][C]30.8[/C][/ROW]
[ROW][C]19[/C][C]111.925[/C][C]9.39090872422188[/C][C]20.3[/C][/ROW]
[ROW][C]20[/C][C]126.925[/C][C]3.34203032102743[/C][C]7.10000000000001[/C][/ROW]
[ROW][C]21[/C][C]126.2[/C][C]15.0412765415705[/C][C]32.4[/C][/ROW]
[ROW][C]22[/C][C]117.35[/C][C]12.1998633872133[/C][C]25.8[/C][/ROW]
[ROW][C]23[/C][C]131.15[/C][C]5.46046396075157[/C][C]12.8[/C][/ROW]
[ROW][C]24[/C][C]131.675[/C][C]13.7376308001052[/C][C]31.2[/C][/ROW]
[ROW][C]25[/C][C]122.5[/C][C]7.26957128492916[/C][C]16.7[/C][/ROW]
[ROW][C]26[/C][C]135.6[/C][C]2.86705423736628[/C][C]5.79999999999998[/C][/ROW]
[ROW][C]27[/C][C]134.65[/C][C]15.5611696218504[/C][C]32.7[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71126&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71126&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	108.975	6.91538140669045	14.7
2	118.275	2.70354705279318	5.7
3	120.55	13.9325757369794	30.4
4	109.125	8.23463215126618	17.2
5	121.325	1.56710986638886	3.69999999999999
6	122.9	14.1734493566904	32.4
7	112.45	8.99499861033896	19.2
8	124.25	2.33023603954621	5.7
9	124.825	12.9461384203939	30.1
10	112	7.3851201750547	15.7
11	121.725	3.64817305876060	8.3
12	124.35	14.9321800149878	31.2
13	112.9	7.26223106214612	15.5
14	120.025	3.83959633294959	8.9
15	121.55	15.1200749557225	30.8
16	109.325	9.28309395262879	20.4
17	120.775	2.98258836136222	6.9
18	121.35	14.4988505291512	30.8
19	111.925	9.39090872422188	20.3
20	126.925	3.34203032102743	7.10000000000001
21	126.2	15.0412765415705	32.4
22	117.35	12.1998633872133	25.8
23	131.15	5.46046396075157	12.8
24	131.675	13.7376308001052	31.2
25	122.5	7.26957128492916	16.7
26	135.6	2.86705423736628	5.79999999999998
27	134.65	15.5611696218504	32.7

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	0.73255075053498
beta	0.0661146143379665
S.D.	0.127892264736737
T-STAT	0.516955536553066
p-value	0.609730775777023

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.73255075053498 \tabularnewline
beta & 0.0661146143379665 \tabularnewline
S.D. & 0.127892264736737 \tabularnewline
T-STAT & 0.516955536553066 \tabularnewline
p-value & 0.609730775777023 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71126&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.73255075053498[/C][/ROW]
[ROW][C]beta[/C][C]0.0661146143379665[/C][/ROW]
[ROW][C]S.D.[/C][C]0.127892264736737[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.516955536553066[/C][/ROW]
[ROW][C]p-value[/C][C]0.609730775777023[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71126&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71126&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	0.73255075053498
beta	0.0661146143379665
S.D.	0.127892264736737
T-STAT	0.516955536553066
p-value	0.609730775777023

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	4.09681935315628
beta	-0.443875216777925
S.D.	2.23363046406787
T-STAT	-0.198723658151377
p-value	0.84408619424399
Lambda	1.44387521677793

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 4.09681935315628 \tabularnewline
beta & -0.443875216777925 \tabularnewline
S.D. & 2.23363046406787 \tabularnewline
T-STAT & -0.198723658151377 \tabularnewline
p-value & 0.84408619424399 \tabularnewline
Lambda & 1.44387521677793 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71126&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]4.09681935315628[/C][/ROW]
[ROW][C]beta[/C][C]-0.443875216777925[/C][/ROW]
[ROW][C]S.D.[/C][C]2.23363046406787[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.198723658151377[/C][/ROW]
[ROW][C]p-value[/C][C]0.84408619424399[/C][/ROW]
[ROW][C]Lambda[/C][C]1.44387521677793[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71126&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71126&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	4.09681935315628
beta	-0.443875216777925
S.D.	2.23363046406787
T-STAT	-0.198723658151377
p-value	0.84408619424399
Lambda	1.44387521677793

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