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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

Fri, 22 May 2009 04:52:35 -0600

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/May/22/t1242989578d8i75nxjfbh4adx.htm/, Retrieved Sun, 05 May 2024 17:25:28 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=40293, Retrieved Sun, 05 May 2024 17:25:28 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

184

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

-       [Standard Deviation-Mean Plot] [] [2009-05-22 10:52:35] [06deb41b065a40f2c80cc8da489fa5fe] [Current]

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Dataseries X:

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Histogram

Boxplots

4.43
4.43
4.44
4.44
4.44
4.45
4.47
4.48
4.48
4.5
4.52
4.52
4.53
4.53
4.63
4.66
4.67
4.68
4.69
4.69
4.7
4.71
4.72
4.72
4.72
4.73
4.74
4.76
4.81
4.82
4.83
4.83
4.84
4.89
4.92
4.95
4.95
5.01
5.05
5.08
5.11
5.14
5.17
5.18
5.2
5.22
5.24
5.28
5.29
5.33
5.4
5.43
5.46
5.46
5.46
5.47
5.49
5.5
5.54
5.55
5.55
5.56
5.6
5.61
5.63
5.64
5.66
5.67
5.69
5.77
5.77
5.78
5.8
5.82
5.85
5.87
5.88
5.9
5.91
5.94
5.97
5.98
6
6.01
6.02

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=40293&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=40293&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40293&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	4.435	0.00577350269189665	0.0100000000000007
2	4.46	0.0182574185835055	0.04
3	4.505	0.0191485421551264	0.0399999999999991
4	4.5875	0.0675154303350969	0.13
5	4.6825	0.00957427107756364	0.0200000000000005
6	4.7125	0.00957427107756318	0.0199999999999996
7	4.7375	0.0170782512765993	0.04
8	4.8225	0.00957427107756356	0.0200000000000005
9	4.9	0.0469041575982344	0.110000000000000
10	5.0225	0.0561990510002911	0.13
11	5.15	0.0316227766016836	0.0699999999999994
12	5.235	0.0341565025531988	0.08
13	5.3625	0.0639661368746516	0.140000000000000
14	5.4625	0.00499999999999989	0.00999999999999979
15	5.52	0.0294392028877594	0.0599999999999996
16	5.58	0.0294392028877597	0.0600000000000005
17	5.65	0.0182574185835056	0.04
18	5.7525	0.0419324854180302	0.0899999999999999
19	5.835	0.0310912635102961	0.0700000000000003
20	5.9075	0.0250000000000002	0.0600000000000005
21	5.99	0.0182574185835055	0.04

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 4.435 & 0.00577350269189665 & 0.0100000000000007 \tabularnewline
2 & 4.46 & 0.0182574185835055 & 0.04 \tabularnewline
3 & 4.505 & 0.0191485421551264 & 0.0399999999999991 \tabularnewline
4 & 4.5875 & 0.0675154303350969 & 0.13 \tabularnewline
5 & 4.6825 & 0.00957427107756364 & 0.0200000000000005 \tabularnewline
6 & 4.7125 & 0.00957427107756318 & 0.0199999999999996 \tabularnewline
7 & 4.7375 & 0.0170782512765993 & 0.04 \tabularnewline
8 & 4.8225 & 0.00957427107756356 & 0.0200000000000005 \tabularnewline
9 & 4.9 & 0.0469041575982344 & 0.110000000000000 \tabularnewline
10 & 5.0225 & 0.0561990510002911 & 0.13 \tabularnewline
11 & 5.15 & 0.0316227766016836 & 0.0699999999999994 \tabularnewline
12 & 5.235 & 0.0341565025531988 & 0.08 \tabularnewline
13 & 5.3625 & 0.0639661368746516 & 0.140000000000000 \tabularnewline
14 & 5.4625 & 0.00499999999999989 & 0.00999999999999979 \tabularnewline
15 & 5.52 & 0.0294392028877594 & 0.0599999999999996 \tabularnewline
16 & 5.58 & 0.0294392028877597 & 0.0600000000000005 \tabularnewline
17 & 5.65 & 0.0182574185835056 & 0.04 \tabularnewline
18 & 5.7525 & 0.0419324854180302 & 0.0899999999999999 \tabularnewline
19 & 5.835 & 0.0310912635102961 & 0.0700000000000003 \tabularnewline
20 & 5.9075 & 0.0250000000000002 & 0.0600000000000005 \tabularnewline
21 & 5.99 & 0.0182574185835055 & 0.04 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40293&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]4.435[/C][C]0.00577350269189665[/C][C]0.0100000000000007[/C][/ROW]
[ROW][C]2[/C][C]4.46[/C][C]0.0182574185835055[/C][C]0.04[/C][/ROW]
[ROW][C]3[/C][C]4.505[/C][C]0.0191485421551264[/C][C]0.0399999999999991[/C][/ROW]
[ROW][C]4[/C][C]4.5875[/C][C]0.0675154303350969[/C][C]0.13[/C][/ROW]
[ROW][C]5[/C][C]4.6825[/C][C]0.00957427107756364[/C][C]0.0200000000000005[/C][/ROW]
[ROW][C]6[/C][C]4.7125[/C][C]0.00957427107756318[/C][C]0.0199999999999996[/C][/ROW]
[ROW][C]7[/C][C]4.7375[/C][C]0.0170782512765993[/C][C]0.04[/C][/ROW]
[ROW][C]8[/C][C]4.8225[/C][C]0.00957427107756356[/C][C]0.0200000000000005[/C][/ROW]
[ROW][C]9[/C][C]4.9[/C][C]0.0469041575982344[/C][C]0.110000000000000[/C][/ROW]
[ROW][C]10[/C][C]5.0225[/C][C]0.0561990510002911[/C][C]0.13[/C][/ROW]
[ROW][C]11[/C][C]5.15[/C][C]0.0316227766016836[/C][C]0.0699999999999994[/C][/ROW]
[ROW][C]12[/C][C]5.235[/C][C]0.0341565025531988[/C][C]0.08[/C][/ROW]
[ROW][C]13[/C][C]5.3625[/C][C]0.0639661368746516[/C][C]0.140000000000000[/C][/ROW]
[ROW][C]14[/C][C]5.4625[/C][C]0.00499999999999989[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]15[/C][C]5.52[/C][C]0.0294392028877594[/C][C]0.0599999999999996[/C][/ROW]
[ROW][C]16[/C][C]5.58[/C][C]0.0294392028877597[/C][C]0.0600000000000005[/C][/ROW]
[ROW][C]17[/C][C]5.65[/C][C]0.0182574185835056[/C][C]0.04[/C][/ROW]
[ROW][C]18[/C][C]5.7525[/C][C]0.0419324854180302[/C][C]0.0899999999999999[/C][/ROW]
[ROW][C]19[/C][C]5.835[/C][C]0.0310912635102961[/C][C]0.0700000000000003[/C][/ROW]
[ROW][C]20[/C][C]5.9075[/C][C]0.0250000000000002[/C][C]0.0600000000000005[/C][/ROW]
[ROW][C]21[/C][C]5.99[/C][C]0.0182574185835055[/C][C]0.04[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40293&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40293&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	4.435	0.00577350269189665	0.0100000000000007
2	4.46	0.0182574185835055	0.04
3	4.505	0.0191485421551264	0.0399999999999991
4	4.5875	0.0675154303350969	0.13
5	4.6825	0.00957427107756364	0.0200000000000005
6	4.7125	0.00957427107756318	0.0199999999999996
7	4.7375	0.0170782512765993	0.04
8	4.8225	0.00957427107756356	0.0200000000000005
9	4.9	0.0469041575982344	0.110000000000000
10	5.0225	0.0561990510002911	0.13
11	5.15	0.0316227766016836	0.0699999999999994
12	5.235	0.0341565025531988	0.08
13	5.3625	0.0639661368746516	0.140000000000000
14	5.4625	0.00499999999999989	0.00999999999999979
15	5.52	0.0294392028877594	0.0599999999999996
16	5.58	0.0294392028877597	0.0600000000000005
17	5.65	0.0182574185835056	0.04
18	5.7525	0.0419324854180302	0.0899999999999999
19	5.835	0.0310912635102961	0.0700000000000003
20	5.9075	0.0250000000000002	0.0600000000000005
21	5.99	0.0182574185835055	0.04

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	0.00635626129268047
beta	0.00419425803367686
S.D.	0.00814644743734422
T-STAT	0.51485731245867
p-value	0.612590481428428

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.00635626129268047 \tabularnewline
beta & 0.00419425803367686 \tabularnewline
S.D. & 0.00814644743734422 \tabularnewline
T-STAT & 0.51485731245867 \tabularnewline
p-value & 0.612590481428428 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40293&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.00635626129268047[/C][/ROW]
[ROW][C]beta[/C][C]0.00419425803367686[/C][/ROW]
[ROW][C]S.D.[/C][C]0.00814644743734422[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.51485731245867[/C][/ROW]
[ROW][C]p-value[/C][C]0.612590481428428[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40293&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40293&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	0.00635626129268047
beta	0.00419425803367686
S.D.	0.00814644743734422
T-STAT	0.51485731245867
p-value	0.612590481428428

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-6.89247260151906
beta	1.88389823448504
S.D.	1.65656580934092
T-STAT	1.13723114642488
p-value	0.269580930673617
Lambda	-0.88389823448504

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -6.89247260151906 \tabularnewline
beta & 1.88389823448504 \tabularnewline
S.D. & 1.65656580934092 \tabularnewline
T-STAT & 1.13723114642488 \tabularnewline
p-value & 0.269580930673617 \tabularnewline
Lambda & -0.88389823448504 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40293&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-6.89247260151906[/C][/ROW]
[ROW][C]beta[/C][C]1.88389823448504[/C][/ROW]
[ROW][C]S.D.[/C][C]1.65656580934092[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.13723114642488[/C][/ROW]
[ROW][C]p-value[/C][C]0.269580930673617[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.88389823448504[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40293&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40293&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	-6.89247260151906
beta	1.88389823448504
S.D.	1.65656580934092
T-STAT	1.13723114642488
p-value	0.269580930673617
Lambda	-0.88389823448504

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