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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

Wed, 07 Dec 2011 10:59:48 -0500

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/2011/Dec/07/t132327372715jjrtec70svof9.htm/, Retrieved Thu, 02 May 2024 23:31:18 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=152527, Retrieved Thu, 02 May 2024 23:31:18 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W83

Estimated Impact

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

-       [Standard Deviation-Mean Plot] [] [2011-12-07 15:59:48] [f7653f7e39425878158499028a118a95] [Current]

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Dataseries X:

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Histogram

Boxplots

5.82
5.85
5.87
5.88
5.9
5.91
5.94
5.97
5.98
6
6.01
6.02
6.11
6.13
6.15
6.15
6.16
6.18
6.21
6.22
6.23
6.26
6.28
6.28
6.29
6.32
6.36
6.37
6.38
6.38
6.4
6.41
6.42
6.43
6.44
6.47
6.47
6.48
6.51
6.54
6.56
6.57
6.6
6.62
6.65
6.71
6.76
6.78
6.8
6.83
6.86
6.86
6.87
6.88
6.9
6.92
6.93
6.94
6.96
6.98
6.99
7.01
7.06
7.07
7.08
7.08
7.1
7.11
7.22
7.24
7.25
7.26

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' @ jenkins.wessa.net

\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' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152527&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152527&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152527&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' @ jenkins.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	5.855	0.0264575131106458	0.0599999999999996
2	5.93	0.0316227766016836	0.0699999999999994
3	6.0025	0.017078251276599	0.0399999999999991
4	6.135	0.0191485421551268	0.04
5	6.1925	0.0275378527364304	0.0599999999999996
6	6.2625	0.023629078131263	0.0499999999999998
7	6.335	0.0369684550213648	0.0800000000000001
8	6.3925	0.0150000000000002	0.0300000000000002
9	6.44	0.0216024689946928	0.0499999999999998
10	6.5	0.0316227766016838	0.0700000000000003
11	6.5875	0.0275378527364306	0.0600000000000005
12	6.725	0.0580229839517639	0.13
13	6.8375	0.0287228132326904	0.0600000000000005
14	6.8925	0.0221735578260834	0.0499999999999998
15	6.9525	0.0221735578260836	0.0500000000000007
16	7.0325	0.0386221007541882	0.0800000000000001
17	7.0925	0.015	0.0300000000000002
18	7.2425	0.0170782512765994	0.04

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 5.855 & 0.0264575131106458 & 0.0599999999999996 \tabularnewline
2 & 5.93 & 0.0316227766016836 & 0.0699999999999994 \tabularnewline
3 & 6.0025 & 0.017078251276599 & 0.0399999999999991 \tabularnewline
4 & 6.135 & 0.0191485421551268 & 0.04 \tabularnewline
5 & 6.1925 & 0.0275378527364304 & 0.0599999999999996 \tabularnewline
6 & 6.2625 & 0.023629078131263 & 0.0499999999999998 \tabularnewline
7 & 6.335 & 0.0369684550213648 & 0.0800000000000001 \tabularnewline
8 & 6.3925 & 0.0150000000000002 & 0.0300000000000002 \tabularnewline
9 & 6.44 & 0.0216024689946928 & 0.0499999999999998 \tabularnewline
10 & 6.5 & 0.0316227766016838 & 0.0700000000000003 \tabularnewline
11 & 6.5875 & 0.0275378527364306 & 0.0600000000000005 \tabularnewline
12 & 6.725 & 0.0580229839517639 & 0.13 \tabularnewline
13 & 6.8375 & 0.0287228132326904 & 0.0600000000000005 \tabularnewline
14 & 6.8925 & 0.0221735578260834 & 0.0499999999999998 \tabularnewline
15 & 6.9525 & 0.0221735578260836 & 0.0500000000000007 \tabularnewline
16 & 7.0325 & 0.0386221007541882 & 0.0800000000000001 \tabularnewline
17 & 7.0925 & 0.015 & 0.0300000000000002 \tabularnewline
18 & 7.2425 & 0.0170782512765994 & 0.04 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152527&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]5.855[/C][C]0.0264575131106458[/C][C]0.0599999999999996[/C][/ROW]
[ROW][C]2[/C][C]5.93[/C][C]0.0316227766016836[/C][C]0.0699999999999994[/C][/ROW]
[ROW][C]3[/C][C]6.0025[/C][C]0.017078251276599[/C][C]0.0399999999999991[/C][/ROW]
[ROW][C]4[/C][C]6.135[/C][C]0.0191485421551268[/C][C]0.04[/C][/ROW]
[ROW][C]5[/C][C]6.1925[/C][C]0.0275378527364304[/C][C]0.0599999999999996[/C][/ROW]
[ROW][C]6[/C][C]6.2625[/C][C]0.023629078131263[/C][C]0.0499999999999998[/C][/ROW]
[ROW][C]7[/C][C]6.335[/C][C]0.0369684550213648[/C][C]0.0800000000000001[/C][/ROW]
[ROW][C]8[/C][C]6.3925[/C][C]0.0150000000000002[/C][C]0.0300000000000002[/C][/ROW]
[ROW][C]9[/C][C]6.44[/C][C]0.0216024689946928[/C][C]0.0499999999999998[/C][/ROW]
[ROW][C]10[/C][C]6.5[/C][C]0.0316227766016838[/C][C]0.0700000000000003[/C][/ROW]
[ROW][C]11[/C][C]6.5875[/C][C]0.0275378527364306[/C][C]0.0600000000000005[/C][/ROW]
[ROW][C]12[/C][C]6.725[/C][C]0.0580229839517639[/C][C]0.13[/C][/ROW]
[ROW][C]13[/C][C]6.8375[/C][C]0.0287228132326904[/C][C]0.0600000000000005[/C][/ROW]
[ROW][C]14[/C][C]6.8925[/C][C]0.0221735578260834[/C][C]0.0499999999999998[/C][/ROW]
[ROW][C]15[/C][C]6.9525[/C][C]0.0221735578260836[/C][C]0.0500000000000007[/C][/ROW]
[ROW][C]16[/C][C]7.0325[/C][C]0.0386221007541882[/C][C]0.0800000000000001[/C][/ROW]
[ROW][C]17[/C][C]7.0925[/C][C]0.015[/C][C]0.0300000000000002[/C][/ROW]
[ROW][C]18[/C][C]7.2425[/C][C]0.0170782512765994[/C][C]0.04[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152527&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152527&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	5.855	0.0264575131106458	0.0599999999999996
2	5.93	0.0316227766016836	0.0699999999999994
3	6.0025	0.017078251276599	0.0399999999999991
4	6.135	0.0191485421551268	0.04
5	6.1925	0.0275378527364304	0.0599999999999996
6	6.2625	0.023629078131263	0.0499999999999998
7	6.335	0.0369684550213648	0.0800000000000001
8	6.3925	0.0150000000000002	0.0300000000000002
9	6.44	0.0216024689946928	0.0499999999999998
10	6.5	0.0316227766016838	0.0700000000000003
11	6.5875	0.0275378527364306	0.0600000000000005
12	6.725	0.0580229839517639	0.13
13	6.8375	0.0287228132326904	0.0600000000000005
14	6.8925	0.0221735578260834	0.0499999999999998
15	6.9525	0.0221735578260836	0.0500000000000007
16	7.0325	0.0386221007541882	0.0800000000000001
17	7.0925	0.015	0.0300000000000002
18	7.2425	0.0170782512765994	0.04

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	0.0234317011325284
beta	0.000495949678238771
S.D.	0.00622536314610174
T-STAT	0.079665983589942
p-value	0.937490833424899

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.0234317011325284 \tabularnewline
beta & 0.000495949678238771 \tabularnewline
S.D. & 0.00622536314610174 \tabularnewline
T-STAT & 0.079665983589942 \tabularnewline
p-value & 0.937490833424899 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152527&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.0234317011325284[/C][/ROW]
[ROW][C]beta[/C][C]0.000495949678238771[/C][/ROW]
[ROW][C]S.D.[/C][C]0.00622536314610174[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.079665983589942[/C][/ROW]
[ROW][C]p-value[/C][C]0.937490833424899[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152527&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152527&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	0.0234317011325284
beta	0.000495949678238771
S.D.	0.00622536314610174
T-STAT	0.079665983589942
p-value	0.937490833424899

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-3.31220172028071
beta	-0.200065353118623
S.D.	1.37025796434062
T-STAT	-0.146005612319061
p-value	0.885740630712986
Lambda	1.20006535311862

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.31220172028071 \tabularnewline
beta & -0.200065353118623 \tabularnewline
S.D. & 1.37025796434062 \tabularnewline
T-STAT & -0.146005612319061 \tabularnewline
p-value & 0.885740630712986 \tabularnewline
Lambda & 1.20006535311862 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152527&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.31220172028071[/C][/ROW]
[ROW][C]beta[/C][C]-0.200065353118623[/C][/ROW]
[ROW][C]S.D.[/C][C]1.37025796434062[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.146005612319061[/C][/ROW]
[ROW][C]p-value[/C][C]0.885740630712986[/C][/ROW]
[ROW][C]Lambda[/C][C]1.20006535311862[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152527&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152527&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	-3.31220172028071
beta	-0.200065353118623
S.D.	1.37025796434062
T-STAT	-0.146005612319061
p-value	0.885740630712986
Lambda	1.20006535311862

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

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code