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Author

*Unverified author*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Wed, 19 Nov 2014 18:55:29 +0000

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/2014/Nov/19/t1416423340v8z2351z7i7mvlv.htm/, Retrieved Sun, 19 May 2024 16:09:52 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=256670, Retrieved Sun, 19 May 2024 16:09:52 +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)

-       [Standard Deviation-Mean Plot] [] [2014-11-19 18:55:29] [76c30f62b7052b57088120e90a652e05] [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	'Herman Ole Andreas Wold' @ wold.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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=256670&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=256670&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=256670&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	39.7	1.77951304200522	4.1
2	43.425	1.5305227865014	3.6
3	48.05	1.44798710859823	3.3
4	54.65	3.10966236109324	7
5	65.025	3.41211078366456	7.4
6	73.675	2.29836898691224	5.19999999999999
7	78.7	1.40712472794703	3
8	84.1	1.36626010212795	3.2
9	89.375	1.95341581168304	4.3
10	93.75	1.69213868619961	3.60000000000001
11	99.05	1.3699148392023	3.19999999999999
12	102.575	0.865544144839921	1.90000000000001
13	105.125	0.298607881119483	0.700000000000003
14	100.575	1.5283433296656	3.39999999999999
15	100	0.816496580927727	1.8
16	95.7	1.50554530541816	3.40000000000001
17	89.525	2.81469358900751	5.69999999999999
18	83.075	1.34752860204648	3.2

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 39.7 & 1.77951304200522 & 4.1 \tabularnewline
2 & 43.425 & 1.5305227865014 & 3.6 \tabularnewline
3 & 48.05 & 1.44798710859823 & 3.3 \tabularnewline
4 & 54.65 & 3.10966236109324 & 7 \tabularnewline
5 & 65.025 & 3.41211078366456 & 7.4 \tabularnewline
6 & 73.675 & 2.29836898691224 & 5.19999999999999 \tabularnewline
7 & 78.7 & 1.40712472794703 & 3 \tabularnewline
8 & 84.1 & 1.36626010212795 & 3.2 \tabularnewline
9 & 89.375 & 1.95341581168304 & 4.3 \tabularnewline
10 & 93.75 & 1.69213868619961 & 3.60000000000001 \tabularnewline
11 & 99.05 & 1.3699148392023 & 3.19999999999999 \tabularnewline
12 & 102.575 & 0.865544144839921 & 1.90000000000001 \tabularnewline
13 & 105.125 & 0.298607881119483 & 0.700000000000003 \tabularnewline
14 & 100.575 & 1.5283433296656 & 3.39999999999999 \tabularnewline
15 & 100 & 0.816496580927727 & 1.8 \tabularnewline
16 & 95.7 & 1.50554530541816 & 3.40000000000001 \tabularnewline
17 & 89.525 & 2.81469358900751 & 5.69999999999999 \tabularnewline
18 & 83.075 & 1.34752860204648 & 3.2 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=256670&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]39.7[/C][C]1.77951304200522[/C][C]4.1[/C][/ROW]
[ROW][C]2[/C][C]43.425[/C][C]1.5305227865014[/C][C]3.6[/C][/ROW]
[ROW][C]3[/C][C]48.05[/C][C]1.44798710859823[/C][C]3.3[/C][/ROW]
[ROW][C]4[/C][C]54.65[/C][C]3.10966236109324[/C][C]7[/C][/ROW]
[ROW][C]5[/C][C]65.025[/C][C]3.41211078366456[/C][C]7.4[/C][/ROW]
[ROW][C]6[/C][C]73.675[/C][C]2.29836898691224[/C][C]5.19999999999999[/C][/ROW]
[ROW][C]7[/C][C]78.7[/C][C]1.40712472794703[/C][C]3[/C][/ROW]
[ROW][C]8[/C][C]84.1[/C][C]1.36626010212795[/C][C]3.2[/C][/ROW]
[ROW][C]9[/C][C]89.375[/C][C]1.95341581168304[/C][C]4.3[/C][/ROW]
[ROW][C]10[/C][C]93.75[/C][C]1.69213868619961[/C][C]3.60000000000001[/C][/ROW]
[ROW][C]11[/C][C]99.05[/C][C]1.3699148392023[/C][C]3.19999999999999[/C][/ROW]
[ROW][C]12[/C][C]102.575[/C][C]0.865544144839921[/C][C]1.90000000000001[/C][/ROW]
[ROW][C]13[/C][C]105.125[/C][C]0.298607881119483[/C][C]0.700000000000003[/C][/ROW]
[ROW][C]14[/C][C]100.575[/C][C]1.5283433296656[/C][C]3.39999999999999[/C][/ROW]
[ROW][C]15[/C][C]100[/C][C]0.816496580927727[/C][C]1.8[/C][/ROW]
[ROW][C]16[/C][C]95.7[/C][C]1.50554530541816[/C][C]3.40000000000001[/C][/ROW]
[ROW][C]17[/C][C]89.525[/C][C]2.81469358900751[/C][C]5.69999999999999[/C][/ROW]
[ROW][C]18[/C][C]83.075[/C][C]1.34752860204648[/C][C]3.2[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=256670&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=256670&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	39.7	1.77951304200522	4.1
2	43.425	1.5305227865014	3.6
3	48.05	1.44798710859823	3.3
4	54.65	3.10966236109324	7
5	65.025	3.41211078366456	7.4
6	73.675	2.29836898691224	5.19999999999999
7	78.7	1.40712472794703	3
8	84.1	1.36626010212795	3.2
9	89.375	1.95341581168304	4.3
10	93.75	1.69213868619961	3.60000000000001
11	99.05	1.3699148392023	3.19999999999999
12	102.575	0.865544144839921	1.90000000000001
13	105.125	0.298607881119483	0.700000000000003
14	100.575	1.5283433296656	3.39999999999999
15	100	0.816496580927727	1.8
16	95.7	1.50554530541816	3.40000000000001
17	89.525	2.81469358900751	5.69999999999999
18	83.075	1.34752860204648	3.2

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	3.00439657017093
beta	-0.0162753381353782
S.D.	0.00824182656400133
T-STAT	-1.97472465708823
p-value	0.065816074033778

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 3.00439657017093 \tabularnewline
beta & -0.0162753381353782 \tabularnewline
S.D. & 0.00824182656400133 \tabularnewline
T-STAT & -1.97472465708823 \tabularnewline
p-value & 0.065816074033778 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=256670&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.00439657017093[/C][/ROW]
[ROW][C]beta[/C][C]-0.0162753381353782[/C][/ROW]
[ROW][C]S.D.[/C][C]0.00824182656400133[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.97472465708823[/C][/ROW]
[ROW][C]p-value[/C][C]0.065816074033778[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=256670&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=256670&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	3.00439657017093
beta	-0.0162753381353782
S.D.	0.00824182656400133
T-STAT	-1.97472465708823
p-value	0.065816074033778

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	3.57106653705008
beta	-0.728074367490823
S.D.	0.403135179942806
T-STAT	-1.80603034345481
p-value	0.0897599145975161
Lambda	1.72807436749082

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 3.57106653705008 \tabularnewline
beta & -0.728074367490823 \tabularnewline
S.D. & 0.403135179942806 \tabularnewline
T-STAT & -1.80603034345481 \tabularnewline
p-value & 0.0897599145975161 \tabularnewline
Lambda & 1.72807436749082 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=256670&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.57106653705008[/C][/ROW]
[ROW][C]beta[/C][C]-0.728074367490823[/C][/ROW]
[ROW][C]S.D.[/C][C]0.403135179942806[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.80603034345481[/C][/ROW]
[ROW][C]p-value[/C][C]0.0897599145975161[/C][/ROW]
[ROW][C]Lambda[/C][C]1.72807436749082[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=256670&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=256670&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	3.57106653705008
beta	-0.728074367490823
S.D.	0.403135179942806
T-STAT	-1.80603034345481
p-value	0.0897599145975161
Lambda	1.72807436749082

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')

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Dataset

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Figures (Output of Computation)

Input Parameters & R Code