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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, 12 Aug 2008 06:59:06 -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/2008/Aug/12/t1218545993fxxmv0ioai2wvn3.htm/, Retrieved Wed, 15 May 2024 11:06:23 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=14001, Retrieved Wed, 15 May 2024 11:06:23 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

263

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

-       [Standard Deviation-Mean Plot] [Spreidingsgrafiek...] [2008-08-12 12:59:06] [a3a2988ef7dc4a3ac06bf68b078ac3cb] [Current]

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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=14001&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=14001&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14001&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	126.916666666667	13.4533424933146	44
2	142.166666666667	17.4399402278653	56
3	172.333333333333	16.6533279957291	53
4	199.083333333333	21.4792006510033	70
5	225.666666666667	27.8121403619921	92
6	242.083333333333	33.1483122656434	114
7	287.5	40.0261278303424	131
8	330.833333333333	46.0589214205483	142
9	370.5	56.2195372058181	166
10	382.666666666667	63.6272287815857	195
11	433.083333333333	66.6243994799248	217

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 126.916666666667 & 13.4533424933146 & 44 \tabularnewline
2 & 142.166666666667 & 17.4399402278653 & 56 \tabularnewline
3 & 172.333333333333 & 16.6533279957291 & 53 \tabularnewline
4 & 199.083333333333 & 21.4792006510033 & 70 \tabularnewline
5 & 225.666666666667 & 27.8121403619921 & 92 \tabularnewline
6 & 242.083333333333 & 33.1483122656434 & 114 \tabularnewline
7 & 287.5 & 40.0261278303424 & 131 \tabularnewline
8 & 330.833333333333 & 46.0589214205483 & 142 \tabularnewline
9 & 370.5 & 56.2195372058181 & 166 \tabularnewline
10 & 382.666666666667 & 63.6272287815857 & 195 \tabularnewline
11 & 433.083333333333 & 66.6243994799248 & 217 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14001&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]126.916666666667[/C][C]13.4533424933146[/C][C]44[/C][/ROW]
[ROW][C]2[/C][C]142.166666666667[/C][C]17.4399402278653[/C][C]56[/C][/ROW]
[ROW][C]3[/C][C]172.333333333333[/C][C]16.6533279957291[/C][C]53[/C][/ROW]
[ROW][C]4[/C][C]199.083333333333[/C][C]21.4792006510033[/C][C]70[/C][/ROW]
[ROW][C]5[/C][C]225.666666666667[/C][C]27.8121403619921[/C][C]92[/C][/ROW]
[ROW][C]6[/C][C]242.083333333333[/C][C]33.1483122656434[/C][C]114[/C][/ROW]
[ROW][C]7[/C][C]287.5[/C][C]40.0261278303424[/C][C]131[/C][/ROW]
[ROW][C]8[/C][C]330.833333333333[/C][C]46.0589214205483[/C][C]142[/C][/ROW]
[ROW][C]9[/C][C]370.5[/C][C]56.2195372058181[/C][C]166[/C][/ROW]
[ROW][C]10[/C][C]382.666666666667[/C][C]63.6272287815857[/C][C]195[/C][/ROW]
[ROW][C]11[/C][C]433.083333333333[/C][C]66.6243994799248[/C][C]217[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14001&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14001&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	126.916666666667	13.4533424933146	44
2	142.166666666667	17.4399402278653	56
3	172.333333333333	16.6533279957291	53
4	199.083333333333	21.4792006510033	70
5	225.666666666667	27.8121403619921	92
6	242.083333333333	33.1483122656434	114
7	287.5	40.0261278303424	131
8	330.833333333333	46.0589214205483	142
9	370.5	56.2195372058181	166
10	382.666666666667	63.6272287815857	195
11	433.083333333333	66.6243994799248	217

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-12.3418918561987
beta	0.184804012976581
S.D.	0.00878765837561067
T-STAT	21.0299496267957
p-value	5.82813357638148e-09

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -12.3418918561987 \tabularnewline
beta & 0.184804012976581 \tabularnewline
S.D. & 0.00878765837561067 \tabularnewline
T-STAT & 21.0299496267957 \tabularnewline
p-value & 5.82813357638148e-09 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14001&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-12.3418918561987[/C][/ROW]
[ROW][C]beta[/C][C]0.184804012976581[/C][/ROW]
[ROW][C]S.D.[/C][C]0.00878765837561067[/C][/ROW]
[ROW][C]T-STAT[/C][C]21.0299496267957[/C][/ROW]
[ROW][C]p-value[/C][C]5.82813357638148e-09[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14001&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14001&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	-12.3418918561987
beta	0.184804012976581
S.D.	0.00878765837561067
T-STAT	21.0299496267957
p-value	5.82813357638148e-09

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-4.01682578877474
beta	1.35843166920308
S.D.	0.0698993165726499
T-STAT	19.4341194708420
p-value	1.16933775109486e-08
Lambda	-0.358431669203082

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -4.01682578877474 \tabularnewline
beta & 1.35843166920308 \tabularnewline
S.D. & 0.0698993165726499 \tabularnewline
T-STAT & 19.4341194708420 \tabularnewline
p-value & 1.16933775109486e-08 \tabularnewline
Lambda & -0.358431669203082 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14001&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.01682578877474[/C][/ROW]
[ROW][C]beta[/C][C]1.35843166920308[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0698993165726499[/C][/ROW]
[ROW][C]T-STAT[/C][C]19.4341194708420[/C][/ROW]
[ROW][C]p-value[/C][C]1.16933775109486e-08[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.358431669203082[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14001&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14001&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	-4.01682578877474
beta	1.35843166920308
S.D.	0.0698993165726499
T-STAT	19.4341194708420
p-value	1.16933775109486e-08
Lambda	-0.358431669203082

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