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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

Thu, 28 May 2009 04:30:00 -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/28/t12435066518c8nfc8d1mxao6r.htm/, Retrieved Mon, 06 May 2024 08:23:18 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=40578, Retrieved Mon, 06 May 2024 08:23:18 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

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] [Opgave 8 oefening...] [2009-05-28 10:30:00] [c0b80eb26a0ae341c828c46b0228b15b] [Current]

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Dataseries X:

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Histogram

Boxplots

5.29
5.29
5.29
5.31
5.33
5.34
5.34
5.37
5.41
5.41
5.38
5.44
5.44
5.46
5.46
5.45
5.46
5.46
5.48
5.47
5.48
5.51
5.55
5.58
5.59
5.6
5.6
5.67
5.71
5.7
5.73
5.72
5.75
5.75
5.77
5.83
5.85
5.87
5.86
5.87
5.93
5.97
5.98
5.99
5.99
6.03
6.06
6.07
6.08
6.08
6.1
6.13
6.14
6.14
6.16
6.2
6.19
6.32
6.32
6.33
6.32
6.33
6.38
6.42
6.46
6.47
6.42
6.48
6.47
6.49
6.48
6.51
6.51
6.52
6.57
6.59
6.62
6.63
6.61
6.64

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	'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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40578&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40578&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40578&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	'George Udny Yule' @ 72.249.76.132

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	5.295	0.00999999999999979	0.0199999999999996
2	5.345	0.0173205080756888	0.04
3	5.41	0.024494897427832	0.0600000000000005
4	5.4525	0.00957427107756318	0.0199999999999996
5	5.4675	0.00957427107756356	0.0200000000000005
6	5.53	0.0439696865275763	0.0999999999999996
7	5.615	0.0369684550213648	0.08
8	5.715	0.0129099444873581	0.0300000000000002
9	5.775	0.0378593889720019	0.08
10	5.8625	0.00957427107756356	0.0200000000000005
11	5.9675	0.0262995563967661	0.0600000000000005
12	6.0375	0.0359397644214129	0.08
13	6.0975	0.0236290781312629	0.0499999999999998
14	6.16	0.0282842712474621	0.0600000000000005
15	6.29	0.0668331255192113	0.140000000000000
16	6.3625	0.0464578662158877	0.0999999999999996
17	6.4575	0.0262995563967659	0.0600000000000005
18	6.4875	0.0170782512765993	0.04
19	6.5475	0.0386221007541884	0.08
20	6.625	0.0129099444873578	0.0299999999999994

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 5.295 & 0.00999999999999979 & 0.0199999999999996 \tabularnewline
2 & 5.345 & 0.0173205080756888 & 0.04 \tabularnewline
3 & 5.41 & 0.024494897427832 & 0.0600000000000005 \tabularnewline
4 & 5.4525 & 0.00957427107756318 & 0.0199999999999996 \tabularnewline
5 & 5.4675 & 0.00957427107756356 & 0.0200000000000005 \tabularnewline
6 & 5.53 & 0.0439696865275763 & 0.0999999999999996 \tabularnewline
7 & 5.615 & 0.0369684550213648 & 0.08 \tabularnewline
8 & 5.715 & 0.0129099444873581 & 0.0300000000000002 \tabularnewline
9 & 5.775 & 0.0378593889720019 & 0.08 \tabularnewline
10 & 5.8625 & 0.00957427107756356 & 0.0200000000000005 \tabularnewline
11 & 5.9675 & 0.0262995563967661 & 0.0600000000000005 \tabularnewline
12 & 6.0375 & 0.0359397644214129 & 0.08 \tabularnewline
13 & 6.0975 & 0.0236290781312629 & 0.0499999999999998 \tabularnewline
14 & 6.16 & 0.0282842712474621 & 0.0600000000000005 \tabularnewline
15 & 6.29 & 0.0668331255192113 & 0.140000000000000 \tabularnewline
16 & 6.3625 & 0.0464578662158877 & 0.0999999999999996 \tabularnewline
17 & 6.4575 & 0.0262995563967659 & 0.0600000000000005 \tabularnewline
18 & 6.4875 & 0.0170782512765993 & 0.04 \tabularnewline
19 & 6.5475 & 0.0386221007541884 & 0.08 \tabularnewline
20 & 6.625 & 0.0129099444873578 & 0.0299999999999994 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40578&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]5.295[/C][C]0.00999999999999979[/C][C]0.0199999999999996[/C][/ROW]
[ROW][C]2[/C][C]5.345[/C][C]0.0173205080756888[/C][C]0.04[/C][/ROW]
[ROW][C]3[/C][C]5.41[/C][C]0.024494897427832[/C][C]0.0600000000000005[/C][/ROW]
[ROW][C]4[/C][C]5.4525[/C][C]0.00957427107756318[/C][C]0.0199999999999996[/C][/ROW]
[ROW][C]5[/C][C]5.4675[/C][C]0.00957427107756356[/C][C]0.0200000000000005[/C][/ROW]
[ROW][C]6[/C][C]5.53[/C][C]0.0439696865275763[/C][C]0.0999999999999996[/C][/ROW]
[ROW][C]7[/C][C]5.615[/C][C]0.0369684550213648[/C][C]0.08[/C][/ROW]
[ROW][C]8[/C][C]5.715[/C][C]0.0129099444873581[/C][C]0.0300000000000002[/C][/ROW]
[ROW][C]9[/C][C]5.775[/C][C]0.0378593889720019[/C][C]0.08[/C][/ROW]
[ROW][C]10[/C][C]5.8625[/C][C]0.00957427107756356[/C][C]0.0200000000000005[/C][/ROW]
[ROW][C]11[/C][C]5.9675[/C][C]0.0262995563967661[/C][C]0.0600000000000005[/C][/ROW]
[ROW][C]12[/C][C]6.0375[/C][C]0.0359397644214129[/C][C]0.08[/C][/ROW]
[ROW][C]13[/C][C]6.0975[/C][C]0.0236290781312629[/C][C]0.0499999999999998[/C][/ROW]
[ROW][C]14[/C][C]6.16[/C][C]0.0282842712474621[/C][C]0.0600000000000005[/C][/ROW]
[ROW][C]15[/C][C]6.29[/C][C]0.0668331255192113[/C][C]0.140000000000000[/C][/ROW]
[ROW][C]16[/C][C]6.3625[/C][C]0.0464578662158877[/C][C]0.0999999999999996[/C][/ROW]
[ROW][C]17[/C][C]6.4575[/C][C]0.0262995563967659[/C][C]0.0600000000000005[/C][/ROW]
[ROW][C]18[/C][C]6.4875[/C][C]0.0170782512765993[/C][C]0.04[/C][/ROW]
[ROW][C]19[/C][C]6.5475[/C][C]0.0386221007541884[/C][C]0.08[/C][/ROW]
[ROW][C]20[/C][C]6.625[/C][C]0.0129099444873578[/C][C]0.0299999999999994[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40578&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40578&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	5.295	0.00999999999999979	0.0199999999999996
2	5.345	0.0173205080756888	0.04
3	5.41	0.024494897427832	0.0600000000000005
4	5.4525	0.00957427107756318	0.0199999999999996
5	5.4675	0.00957427107756356	0.0200000000000005
6	5.53	0.0439696865275763	0.0999999999999996
7	5.615	0.0369684550213648	0.08
8	5.715	0.0129099444873581	0.0300000000000002
9	5.775	0.0378593889720019	0.08
10	5.8625	0.00957427107756356	0.0200000000000005
11	5.9675	0.0262995563967661	0.0600000000000005
12	6.0375	0.0359397644214129	0.08
13	6.0975	0.0236290781312629	0.0499999999999998
14	6.16	0.0282842712474621	0.0600000000000005
15	6.29	0.0668331255192113	0.140000000000000
16	6.3625	0.0464578662158877	0.0999999999999996
17	6.4575	0.0262995563967659	0.0600000000000005
18	6.4875	0.0170782512765993	0.04
19	6.5475	0.0386221007541884	0.08
20	6.625	0.0129099444873578	0.0299999999999994

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-0.0407209649574238
beta	0.0113841224281848
S.D.	0.00781640034516968
T-STAT	1.45644055133638
p-value	0.162493561627541

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.0407209649574238 \tabularnewline
beta & 0.0113841224281848 \tabularnewline
S.D. & 0.00781640034516968 \tabularnewline
T-STAT & 1.45644055133638 \tabularnewline
p-value & 0.162493561627541 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40578&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.0407209649574238[/C][/ROW]
[ROW][C]beta[/C][C]0.0113841224281848[/C][/ROW]
[ROW][C]S.D.[/C][C]0.00781640034516968[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.45644055133638[/C][/ROW]
[ROW][C]p-value[/C][C]0.162493561627541[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40578&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40578&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	-0.0407209649574238
beta	0.0113841224281848
S.D.	0.00781640034516968
T-STAT	1.45644055133638
p-value	0.162493561627541

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-9.09608706930961
beta	2.98884128258888
S.D.	1.78760019561491
T-STAT	1.67198531859679
p-value	0.111819897348192
Lambda	-1.98884128258888

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -9.09608706930961 \tabularnewline
beta & 2.98884128258888 \tabularnewline
S.D. & 1.78760019561491 \tabularnewline
T-STAT & 1.67198531859679 \tabularnewline
p-value & 0.111819897348192 \tabularnewline
Lambda & -1.98884128258888 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40578&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-9.09608706930961[/C][/ROW]
[ROW][C]beta[/C][C]2.98884128258888[/C][/ROW]
[ROW][C]S.D.[/C][C]1.78760019561491[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.67198531859679[/C][/ROW]
[ROW][C]p-value[/C][C]0.111819897348192[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.98884128258888[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40578&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40578&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	-9.09608706930961
beta	2.98884128258888
S.D.	1.78760019561491
T-STAT	1.67198531859679
p-value	0.111819897348192
Lambda	-1.98884128258888

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