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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

Sun, 15 Jan 2012 12:52:10 -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/Jan/15/t132664998955qpuwntyhsmusb.htm/, Retrieved Fri, 03 May 2024 08:29:59 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=161111, Retrieved Fri, 03 May 2024 08:29:59 +0000

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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] [] [2012-01-15 17:52:10] [618e20b48371a4632e04cdc6ff96552f] [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	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=161111&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=161111&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161111&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	100.375	0.359397644214128	0.799999999999997
2	99.375	0.298607881119483	0.700000000000003
3	99.125	0.359397644214128	0.799999999999997
4	99.975	0.170782512765995	0.400000000000006
5	100.175	0.0500000000000043	0.100000000000009
6	100	0.182574185835055	0.400000000000006
7	99.85	0.0577350269189675	0.100000000000009
8	99.925	0.0499999999999972	0.0999999999999943
9	100.325	0.221735578260834	0.5
10	101.35	0.264575131106457	0.599999999999994
11	102.3	0.496655480858376	1.09999999999999
12	102.3	0.439696865275765	1
13	101.5	0.163299316185548	0.400000000000006
14	101.95	0.0577350269189593	0.0999999999999943
15	103.225	0.84212033977732	1.90000000000001
16	104.75	0.341565025531987	0.799999999999997
17	106.125	0.250000000000004	0.600000000000009
18	107.7	0.697614984548542	1.59999999999999

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 100.375 & 0.359397644214128 & 0.799999999999997 \tabularnewline
2 & 99.375 & 0.298607881119483 & 0.700000000000003 \tabularnewline
3 & 99.125 & 0.359397644214128 & 0.799999999999997 \tabularnewline
4 & 99.975 & 0.170782512765995 & 0.400000000000006 \tabularnewline
5 & 100.175 & 0.0500000000000043 & 0.100000000000009 \tabularnewline
6 & 100 & 0.182574185835055 & 0.400000000000006 \tabularnewline
7 & 99.85 & 0.0577350269189675 & 0.100000000000009 \tabularnewline
8 & 99.925 & 0.0499999999999972 & 0.0999999999999943 \tabularnewline
9 & 100.325 & 0.221735578260834 & 0.5 \tabularnewline
10 & 101.35 & 0.264575131106457 & 0.599999999999994 \tabularnewline
11 & 102.3 & 0.496655480858376 & 1.09999999999999 \tabularnewline
12 & 102.3 & 0.439696865275765 & 1 \tabularnewline
13 & 101.5 & 0.163299316185548 & 0.400000000000006 \tabularnewline
14 & 101.95 & 0.0577350269189593 & 0.0999999999999943 \tabularnewline
15 & 103.225 & 0.84212033977732 & 1.90000000000001 \tabularnewline
16 & 104.75 & 0.341565025531987 & 0.799999999999997 \tabularnewline
17 & 106.125 & 0.250000000000004 & 0.600000000000009 \tabularnewline
18 & 107.7 & 0.697614984548542 & 1.59999999999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161111&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]100.375[/C][C]0.359397644214128[/C][C]0.799999999999997[/C][/ROW]
[ROW][C]2[/C][C]99.375[/C][C]0.298607881119483[/C][C]0.700000000000003[/C][/ROW]
[ROW][C]3[/C][C]99.125[/C][C]0.359397644214128[/C][C]0.799999999999997[/C][/ROW]
[ROW][C]4[/C][C]99.975[/C][C]0.170782512765995[/C][C]0.400000000000006[/C][/ROW]
[ROW][C]5[/C][C]100.175[/C][C]0.0500000000000043[/C][C]0.100000000000009[/C][/ROW]
[ROW][C]6[/C][C]100[/C][C]0.182574185835055[/C][C]0.400000000000006[/C][/ROW]
[ROW][C]7[/C][C]99.85[/C][C]0.0577350269189675[/C][C]0.100000000000009[/C][/ROW]
[ROW][C]8[/C][C]99.925[/C][C]0.0499999999999972[/C][C]0.0999999999999943[/C][/ROW]
[ROW][C]9[/C][C]100.325[/C][C]0.221735578260834[/C][C]0.5[/C][/ROW]
[ROW][C]10[/C][C]101.35[/C][C]0.264575131106457[/C][C]0.599999999999994[/C][/ROW]
[ROW][C]11[/C][C]102.3[/C][C]0.496655480858376[/C][C]1.09999999999999[/C][/ROW]
[ROW][C]12[/C][C]102.3[/C][C]0.439696865275765[/C][C]1[/C][/ROW]
[ROW][C]13[/C][C]101.5[/C][C]0.163299316185548[/C][C]0.400000000000006[/C][/ROW]
[ROW][C]14[/C][C]101.95[/C][C]0.0577350269189593[/C][C]0.0999999999999943[/C][/ROW]
[ROW][C]15[/C][C]103.225[/C][C]0.84212033977732[/C][C]1.90000000000001[/C][/ROW]
[ROW][C]16[/C][C]104.75[/C][C]0.341565025531987[/C][C]0.799999999999997[/C][/ROW]
[ROW][C]17[/C][C]106.125[/C][C]0.250000000000004[/C][C]0.600000000000009[/C][/ROW]
[ROW][C]18[/C][C]107.7[/C][C]0.697614984548542[/C][C]1.59999999999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161111&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161111&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	100.375	0.359397644214128	0.799999999999997
2	99.375	0.298607881119483	0.700000000000003
3	99.125	0.359397644214128	0.799999999999997
4	99.975	0.170782512765995	0.400000000000006
5	100.175	0.0500000000000043	0.100000000000009
6	100	0.182574185835055	0.400000000000006
7	99.85	0.0577350269189675	0.100000000000009
8	99.925	0.0499999999999972	0.0999999999999943
9	100.325	0.221735578260834	0.5
10	101.35	0.264575131106457	0.599999999999994
11	102.3	0.496655480858376	1.09999999999999
12	102.3	0.439696865275765	1
13	101.5	0.163299316185548	0.400000000000006
14	101.95	0.0577350269189593	0.0999999999999943
15	103.225	0.84212033977732	1.90000000000001
16	104.75	0.341565025531987	0.799999999999997
17	106.125	0.250000000000004	0.600000000000009
18	107.7	0.697614984548542	1.59999999999999

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-4.73034696403698
beta	0.0494173100384889
S.D.	0.0191597151280772
T-STAT	2.57922989502445
p-value	0.0201733995094798

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -4.73034696403698 \tabularnewline
beta & 0.0494173100384889 \tabularnewline
S.D. & 0.0191597151280772 \tabularnewline
T-STAT & 2.57922989502445 \tabularnewline
p-value & 0.0201733995094798 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161111&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.73034696403698[/C][/ROW]
[ROW][C]beta[/C][C]0.0494173100384889[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0191597151280772[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.57922989502445[/C][/ROW]
[ROW][C]p-value[/C][C]0.0201733995094798[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161111&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161111&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	-4.73034696403698
beta	0.0494173100384889
S.D.	0.0191597151280772
T-STAT	2.57922989502445
p-value	0.0201733995094798

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-83.3085364396438
beta	17.6943021932635
S.D.	8.34290027979164
T-STAT	2.12088142011274
p-value	0.0499065708472197
Lambda	-16.6943021932635

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -83.3085364396438 \tabularnewline
beta & 17.6943021932635 \tabularnewline
S.D. & 8.34290027979164 \tabularnewline
T-STAT & 2.12088142011274 \tabularnewline
p-value & 0.0499065708472197 \tabularnewline
Lambda & -16.6943021932635 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161111&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-83.3085364396438[/C][/ROW]
[ROW][C]beta[/C][C]17.6943021932635[/C][/ROW]
[ROW][C]S.D.[/C][C]8.34290027979164[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.12088142011274[/C][/ROW]
[ROW][C]p-value[/C][C]0.0499065708472197[/C][/ROW]
[ROW][C]Lambda[/C][C]-16.6943021932635[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161111&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161111&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	-83.3085364396438
beta	17.6943021932635
S.D.	8.34290027979164
T-STAT	2.12088142011274
p-value	0.0499065708472197
Lambda	-16.6943021932635

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par2 = grey ; par3 = FALSE ; par4 = Unknown ;

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')

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code