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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, 26 Jan 2010 11:07:50 -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/2010/Jan/26/t1264529319upgtck1gib5zsfn.htm/, Retrieved Thu, 02 May 2024 19:02:40 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72647, Retrieved Thu, 02 May 2024 19:02:40 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W83

Estimated Impact

118

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

-       [Standard Deviation-Mean Plot] [] [2010-01-26 18:07:50] [a0577a728571d1f3a39246738c9fa77a] [Current]

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Dataseries X:

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Histogram

Boxplots

1.61
1.58
1.69
1.78
1.76
1.83
1.8
1.57
1.45
1.4
1.55
1.58
1.58
1.59
1.8
1.99
2.06
2.06
2.08
2
1.85
1.77
1.7
1.66
1.67
1.73
1.91
2.02
2.07
2.15
2.1
1.68
1.68
1.65
1.72
1.73
1.76
1.84
1.99
2.05
2.12
2.13
2.08
1.88
1.81
1.81
1.88
1.87
1.87
1.9
2.01
2.05
2.16
2.18
2.15
2.12
2.04
2.04
2.06
1.93
1.86
1.94
2.35
2.46
2.59
2.66
2.41
2.18
2.13
2.11
2.12
2.16
2.07
2.2
2.29
2.32
2.37
2.38
2.38
2.28
2.22
2.25
2.3
2.3
2.23
2.27
2.3
2.32
2.41
2.43
2.45
2.47
2.46
2.5
2.46
2.43
2.37
2.45
2.53
2.56
2.62
2.67
2.62
2.6
2.53
2.49
2.48
2.44

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	'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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72647&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72647&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72647&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	'Gwilym Jenkins' @ 72.249.127.135

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	1.665	0.089628864398325	0.2
2	1.74	0.116904519445001	0.26
3	1.495	0.0842614977317637	0.18
4	1.74	0.195106808355492	0.41
5	2.05	0.0346410161513776	0.08
6	1.745	0.0834665601703262	0.19
7	1.8325	0.161322658049017	0.35
8	2	0.215870331449229	0.47
9	1.695	0.0369684550213648	0.08
10	1.91	0.133416640641263	0.29
11	2.0525	0.117011395456454	0.25
12	1.8425	0.0377491721763537	0.0699999999999998
13	1.9575	0.0861684396980703	0.180000000000000
14	2.1525	0.0250000000000000	0.06
15	2.0175	0.0590903263374528	0.13
16	2.1525	0.296802403404465	0.6
17	2.46	0.214320632075713	0.48
18	2.13	0.0216024689946930	0.0500000000000003
19	2.22	0.112249721603218	0.25
20	2.3525	0.0485626742811116	0.1
21	2.2675	0.0394757309410899	0.0799999999999996
22	2.28	0.0391578004149024	0.0899999999999999
23	2.44	0.0258198889747161	0.06
24	2.4625	0.0287228132326901	0.0699999999999998
25	2.4775	0.0853912563829966	0.19
26	2.6275	0.0298607881119481	0.0699999999999998
27	2.485	0.0369684550213647	0.0899999999999999

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 1.665 & 0.089628864398325 & 0.2 \tabularnewline
2 & 1.74 & 0.116904519445001 & 0.26 \tabularnewline
3 & 1.495 & 0.0842614977317637 & 0.18 \tabularnewline
4 & 1.74 & 0.195106808355492 & 0.41 \tabularnewline
5 & 2.05 & 0.0346410161513776 & 0.08 \tabularnewline
6 & 1.745 & 0.0834665601703262 & 0.19 \tabularnewline
7 & 1.8325 & 0.161322658049017 & 0.35 \tabularnewline
8 & 2 & 0.215870331449229 & 0.47 \tabularnewline
9 & 1.695 & 0.0369684550213648 & 0.08 \tabularnewline
10 & 1.91 & 0.133416640641263 & 0.29 \tabularnewline
11 & 2.0525 & 0.117011395456454 & 0.25 \tabularnewline
12 & 1.8425 & 0.0377491721763537 & 0.0699999999999998 \tabularnewline
13 & 1.9575 & 0.0861684396980703 & 0.180000000000000 \tabularnewline
14 & 2.1525 & 0.0250000000000000 & 0.06 \tabularnewline
15 & 2.0175 & 0.0590903263374528 & 0.13 \tabularnewline
16 & 2.1525 & 0.296802403404465 & 0.6 \tabularnewline
17 & 2.46 & 0.214320632075713 & 0.48 \tabularnewline
18 & 2.13 & 0.0216024689946930 & 0.0500000000000003 \tabularnewline
19 & 2.22 & 0.112249721603218 & 0.25 \tabularnewline
20 & 2.3525 & 0.0485626742811116 & 0.1 \tabularnewline
21 & 2.2675 & 0.0394757309410899 & 0.0799999999999996 \tabularnewline
22 & 2.28 & 0.0391578004149024 & 0.0899999999999999 \tabularnewline
23 & 2.44 & 0.0258198889747161 & 0.06 \tabularnewline
24 & 2.4625 & 0.0287228132326901 & 0.0699999999999998 \tabularnewline
25 & 2.4775 & 0.0853912563829966 & 0.19 \tabularnewline
26 & 2.6275 & 0.0298607881119481 & 0.0699999999999998 \tabularnewline
27 & 2.485 & 0.0369684550213647 & 0.0899999999999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72647&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]1.665[/C][C]0.089628864398325[/C][C]0.2[/C][/ROW]
[ROW][C]2[/C][C]1.74[/C][C]0.116904519445001[/C][C]0.26[/C][/ROW]
[ROW][C]3[/C][C]1.495[/C][C]0.0842614977317637[/C][C]0.18[/C][/ROW]
[ROW][C]4[/C][C]1.74[/C][C]0.195106808355492[/C][C]0.41[/C][/ROW]
[ROW][C]5[/C][C]2.05[/C][C]0.0346410161513776[/C][C]0.08[/C][/ROW]
[ROW][C]6[/C][C]1.745[/C][C]0.0834665601703262[/C][C]0.19[/C][/ROW]
[ROW][C]7[/C][C]1.8325[/C][C]0.161322658049017[/C][C]0.35[/C][/ROW]
[ROW][C]8[/C][C]2[/C][C]0.215870331449229[/C][C]0.47[/C][/ROW]
[ROW][C]9[/C][C]1.695[/C][C]0.0369684550213648[/C][C]0.08[/C][/ROW]
[ROW][C]10[/C][C]1.91[/C][C]0.133416640641263[/C][C]0.29[/C][/ROW]
[ROW][C]11[/C][C]2.0525[/C][C]0.117011395456454[/C][C]0.25[/C][/ROW]
[ROW][C]12[/C][C]1.8425[/C][C]0.0377491721763537[/C][C]0.0699999999999998[/C][/ROW]
[ROW][C]13[/C][C]1.9575[/C][C]0.0861684396980703[/C][C]0.180000000000000[/C][/ROW]
[ROW][C]14[/C][C]2.1525[/C][C]0.0250000000000000[/C][C]0.06[/C][/ROW]
[ROW][C]15[/C][C]2.0175[/C][C]0.0590903263374528[/C][C]0.13[/C][/ROW]
[ROW][C]16[/C][C]2.1525[/C][C]0.296802403404465[/C][C]0.6[/C][/ROW]
[ROW][C]17[/C][C]2.46[/C][C]0.214320632075713[/C][C]0.48[/C][/ROW]
[ROW][C]18[/C][C]2.13[/C][C]0.0216024689946930[/C][C]0.0500000000000003[/C][/ROW]
[ROW][C]19[/C][C]2.22[/C][C]0.112249721603218[/C][C]0.25[/C][/ROW]
[ROW][C]20[/C][C]2.3525[/C][C]0.0485626742811116[/C][C]0.1[/C][/ROW]
[ROW][C]21[/C][C]2.2675[/C][C]0.0394757309410899[/C][C]0.0799999999999996[/C][/ROW]
[ROW][C]22[/C][C]2.28[/C][C]0.0391578004149024[/C][C]0.0899999999999999[/C][/ROW]
[ROW][C]23[/C][C]2.44[/C][C]0.0258198889747161[/C][C]0.06[/C][/ROW]
[ROW][C]24[/C][C]2.4625[/C][C]0.0287228132326901[/C][C]0.0699999999999998[/C][/ROW]
[ROW][C]25[/C][C]2.4775[/C][C]0.0853912563829966[/C][C]0.19[/C][/ROW]
[ROW][C]26[/C][C]2.6275[/C][C]0.0298607881119481[/C][C]0.0699999999999998[/C][/ROW]
[ROW][C]27[/C][C]2.485[/C][C]0.0369684550213647[/C][C]0.0899999999999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72647&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72647&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	1.665	0.089628864398325	0.2
2	1.74	0.116904519445001	0.26
3	1.495	0.0842614977317637	0.18
4	1.74	0.195106808355492	0.41
5	2.05	0.0346410161513776	0.08
6	1.745	0.0834665601703262	0.19
7	1.8325	0.161322658049017	0.35
8	2	0.215870331449229	0.47
9	1.695	0.0369684550213648	0.08
10	1.91	0.133416640641263	0.29
11	2.0525	0.117011395456454	0.25
12	1.8425	0.0377491721763537	0.0699999999999998
13	1.9575	0.0861684396980703	0.180000000000000
14	2.1525	0.0250000000000000	0.06
15	2.0175	0.0590903263374528	0.13
16	2.1525	0.296802403404465	0.6
17	2.46	0.214320632075713	0.48
18	2.13	0.0216024689946930	0.0500000000000003
19	2.22	0.112249721603218	0.25
20	2.3525	0.0485626742811116	0.1
21	2.2675	0.0394757309410899	0.0799999999999996
22	2.28	0.0391578004149024	0.0899999999999999
23	2.44	0.0258198889747161	0.06
24	2.4625	0.0287228132326901	0.0699999999999998
25	2.4775	0.0853912563829966	0.19
26	2.6275	0.0298607881119481	0.0699999999999998
27	2.485	0.0369684550213647	0.0899999999999999

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	0.190387496458426
beta	-0.0477319304152374
S.D.	0.0462033685812659
T-STAT	-1.03308334177589
p-value	0.311455808363215

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.190387496458426 \tabularnewline
beta & -0.0477319304152374 \tabularnewline
S.D. & 0.0462033685812659 \tabularnewline
T-STAT & -1.03308334177589 \tabularnewline
p-value & 0.311455808363215 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72647&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.190387496458426[/C][/ROW]
[ROW][C]beta[/C][C]-0.0477319304152374[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0462033685812659[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.03308334177589[/C][/ROW]
[ROW][C]p-value[/C][C]0.311455808363215[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72647&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72647&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	0.190387496458426
beta	-0.0477319304152374
S.D.	0.0462033685812659
T-STAT	-1.03308334177589
p-value	0.311455808363215

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-1.46970469589062
beta	-1.67102353579082
S.D.	0.972682526007041
T-STAT	-1.71795369106767
p-value	0.0981686039565131
Lambda	2.67102353579082

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.46970469589062 \tabularnewline
beta & -1.67102353579082 \tabularnewline
S.D. & 0.972682526007041 \tabularnewline
T-STAT & -1.71795369106767 \tabularnewline
p-value & 0.0981686039565131 \tabularnewline
Lambda & 2.67102353579082 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72647&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.46970469589062[/C][/ROW]
[ROW][C]beta[/C][C]-1.67102353579082[/C][/ROW]
[ROW][C]S.D.[/C][C]0.972682526007041[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.71795369106767[/C][/ROW]
[ROW][C]p-value[/C][C]0.0981686039565131[/C][/ROW]
[ROW][C]Lambda[/C][C]2.67102353579082[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72647&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72647&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	-1.46970469589062
beta	-1.67102353579082
S.D.	0.972682526007041
T-STAT	-1.71795369106767
p-value	0.0981686039565131
Lambda	2.67102353579082

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