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Author

*The author of this computation has been verified*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Thu, 29 Nov 2012 08:22:34 -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/2012/Nov/29/t1354195381ymgu74r54kj00sr.htm/, Retrieved Sun, 28 Apr 2024 14:19:26 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=194500, Retrieved Sun, 28 Apr 2024 14:19:26 +0000

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Estimated Impact

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

-     [Variance Reduction Matrix] [Workshop 9 - vari...] [2012-11-29 11:54:34] [9f87ad58f325f963ff5b3a15384d509e]
- RM D    [Standard Deviation-Mean Plot] [Workshop 9 - stan...] [2012-11-29 13:22:34] [3353489d44052879174bf0d9e8b7362f] [Current]

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Boxplots

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net
R Framework error message	Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

\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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
R Framework error message & Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values. \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=194500&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=194500&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=194500&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	3 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net
R Framework error message	Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	8.5325	0.530833392797675	1.57
2	7.06583333333333	0.389158961055372	1.17
3	7.9525	0.524805158649812	1.61
4	7.2675	0.538974194018769	1.76
5	6.37083333333333	0.392601077508208	1.1
6	5.63666666666667	0.22720968822707	0.82
7	4.57166666666667	0.446620305147109	1.28
8	4.89666666666667	0.626713408959547	1.77
9	5.485	0.169464396904429	0.56
10	5.0775	0.221159136452383	0.79
11	4.7875	0.453273447470529	1.36
12	4.08	0.192967260529769	0.63
13	4.03583333333333	0.279006625315058	0.870000000000001
14	3.38416666666667	0.18951892845419	0.55
15	3.89	0.183352616065825	0.64
16	4.34166666666667	0.187753868539413	0.62
17	4.35416666666667	0.325784600711277	1.08
18	3.475	0.328010531981687	1.14
19	4.04583333333333	0.283499505637963	0.98
20	3.435	0.77988926952951	2.52

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 8.5325 & 0.530833392797675 & 1.57 \tabularnewline
2 & 7.06583333333333 & 0.389158961055372 & 1.17 \tabularnewline
3 & 7.9525 & 0.524805158649812 & 1.61 \tabularnewline
4 & 7.2675 & 0.538974194018769 & 1.76 \tabularnewline
5 & 6.37083333333333 & 0.392601077508208 & 1.1 \tabularnewline
6 & 5.63666666666667 & 0.22720968822707 & 0.82 \tabularnewline
7 & 4.57166666666667 & 0.446620305147109 & 1.28 \tabularnewline
8 & 4.89666666666667 & 0.626713408959547 & 1.77 \tabularnewline
9 & 5.485 & 0.169464396904429 & 0.56 \tabularnewline
10 & 5.0775 & 0.221159136452383 & 0.79 \tabularnewline
11 & 4.7875 & 0.453273447470529 & 1.36 \tabularnewline
12 & 4.08 & 0.192967260529769 & 0.63 \tabularnewline
13 & 4.03583333333333 & 0.279006625315058 & 0.870000000000001 \tabularnewline
14 & 3.38416666666667 & 0.18951892845419 & 0.55 \tabularnewline
15 & 3.89 & 0.183352616065825 & 0.64 \tabularnewline
16 & 4.34166666666667 & 0.187753868539413 & 0.62 \tabularnewline
17 & 4.35416666666667 & 0.325784600711277 & 1.08 \tabularnewline
18 & 3.475 & 0.328010531981687 & 1.14 \tabularnewline
19 & 4.04583333333333 & 0.283499505637963 & 0.98 \tabularnewline
20 & 3.435 & 0.77988926952951 & 2.52 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=194500&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]8.5325[/C][C]0.530833392797675[/C][C]1.57[/C][/ROW]
[ROW][C]2[/C][C]7.06583333333333[/C][C]0.389158961055372[/C][C]1.17[/C][/ROW]
[ROW][C]3[/C][C]7.9525[/C][C]0.524805158649812[/C][C]1.61[/C][/ROW]
[ROW][C]4[/C][C]7.2675[/C][C]0.538974194018769[/C][C]1.76[/C][/ROW]
[ROW][C]5[/C][C]6.37083333333333[/C][C]0.392601077508208[/C][C]1.1[/C][/ROW]
[ROW][C]6[/C][C]5.63666666666667[/C][C]0.22720968822707[/C][C]0.82[/C][/ROW]
[ROW][C]7[/C][C]4.57166666666667[/C][C]0.446620305147109[/C][C]1.28[/C][/ROW]
[ROW][C]8[/C][C]4.89666666666667[/C][C]0.626713408959547[/C][C]1.77[/C][/ROW]
[ROW][C]9[/C][C]5.485[/C][C]0.169464396904429[/C][C]0.56[/C][/ROW]
[ROW][C]10[/C][C]5.0775[/C][C]0.221159136452383[/C][C]0.79[/C][/ROW]
[ROW][C]11[/C][C]4.7875[/C][C]0.453273447470529[/C][C]1.36[/C][/ROW]
[ROW][C]12[/C][C]4.08[/C][C]0.192967260529769[/C][C]0.63[/C][/ROW]
[ROW][C]13[/C][C]4.03583333333333[/C][C]0.279006625315058[/C][C]0.870000000000001[/C][/ROW]
[ROW][C]14[/C][C]3.38416666666667[/C][C]0.18951892845419[/C][C]0.55[/C][/ROW]
[ROW][C]15[/C][C]3.89[/C][C]0.183352616065825[/C][C]0.64[/C][/ROW]
[ROW][C]16[/C][C]4.34166666666667[/C][C]0.187753868539413[/C][C]0.62[/C][/ROW]
[ROW][C]17[/C][C]4.35416666666667[/C][C]0.325784600711277[/C][C]1.08[/C][/ROW]
[ROW][C]18[/C][C]3.475[/C][C]0.328010531981687[/C][C]1.14[/C][/ROW]
[ROW][C]19[/C][C]4.04583333333333[/C][C]0.283499505637963[/C][C]0.98[/C][/ROW]
[ROW][C]20[/C][C]3.435[/C][C]0.77988926952951[/C][C]2.52[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=194500&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=194500&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	8.5325	0.530833392797675	1.57
2	7.06583333333333	0.389158961055372	1.17
3	7.9525	0.524805158649812	1.61
4	7.2675	0.538974194018769	1.76
5	6.37083333333333	0.392601077508208	1.1
6	5.63666666666667	0.22720968822707	0.82
7	4.57166666666667	0.446620305147109	1.28
8	4.89666666666667	0.626713408959547	1.77
9	5.485	0.169464396904429	0.56
10	5.0775	0.221159136452383	0.79
11	4.7875	0.453273447470529	1.36
12	4.08	0.192967260529769	0.63
13	4.03583333333333	0.279006625315058	0.870000000000001
14	3.38416666666667	0.18951892845419	0.55
15	3.89	0.183352616065825	0.64
16	4.34166666666667	0.187753868539413	0.62
17	4.35416666666667	0.325784600711277	1.08
18	3.475	0.328010531981687	1.14
19	4.04583333333333	0.283499505637963	0.98
20	3.435	0.77988926952951	2.52

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	0.17907364802687
beta	0.0359263132378033
S.D.	0.0248260087849804
T-STAT	1.44712400406216
p-value	0.165054032714069

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.17907364802687 \tabularnewline
beta & 0.0359263132378033 \tabularnewline
S.D. & 0.0248260087849804 \tabularnewline
T-STAT & 1.44712400406216 \tabularnewline
p-value & 0.165054032714069 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=194500&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.17907364802687[/C][/ROW]
[ROW][C]beta[/C][C]0.0359263132378033[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0248260087849804[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.44712400406216[/C][/ROW]
[ROW][C]p-value[/C][C]0.165054032714069[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=194500&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=194500&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	0.17907364802687
beta	0.0359263132378033
S.D.	0.0248260087849804
T-STAT	1.44712400406216
p-value	0.165054032714069

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-2.05185072317158
beta	0.586598464428491
S.D.	0.36485894293054
T-STAT	1.60774040432432
p-value	0.125290971693747
Lambda	0.413401535571509

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.05185072317158 \tabularnewline
beta & 0.586598464428491 \tabularnewline
S.D. & 0.36485894293054 \tabularnewline
T-STAT & 1.60774040432432 \tabularnewline
p-value & 0.125290971693747 \tabularnewline
Lambda & 0.413401535571509 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=194500&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.05185072317158[/C][/ROW]
[ROW][C]beta[/C][C]0.586598464428491[/C][/ROW]
[ROW][C]S.D.[/C][C]0.36485894293054[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.60774040432432[/C][/ROW]
[ROW][C]p-value[/C][C]0.125290971693747[/C][/ROW]
[ROW][C]Lambda[/C][C]0.413401535571509[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=194500&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=194500&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	-2.05185072317158
beta	0.586598464428491
S.D.	0.36485894293054
T-STAT	1.60774040432432
p-value	0.125290971693747
Lambda	0.413401535571509

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = 12 ;

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