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Author's title

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

Mon, 21 Dec 2009 14:15:15 -0700

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/2009/Dec/21/t1261430155kdo8rcgkajo38ii.htm/, Retrieved Sun, 05 May 2024 11:57:49 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=70392, Retrieved Sun, 05 May 2024 11:57:49 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

106

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

-       [Standard Deviation-Mean Plot] [Paper] [2009-12-21 21:15:15] [e339dd08bcbfc073ac7494f09a949034] [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=70392&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=70392&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70392&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	22.2833333333333	2.00540935139604	5.2
2	21.1	1.74011493873250	4
3	21.75	1.29884564132925	3.3
4	20.35	2.03936264553414	4.5
5	20.0166666666667	1.84001811585285	4.6
6	19.6166666666667	1.07222510074455	2.70000000000000
7	17.5833333333333	0.870440501508671	2.3
8	17.35	4.38622844822291	10.3
9	19.4333333333333	2.16764080665286	5.6
10	21.3833333333333	2.0173414848921	4.9

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 22.2833333333333 & 2.00540935139604 & 5.2 \tabularnewline
2 & 21.1 & 1.74011493873250 & 4 \tabularnewline
3 & 21.75 & 1.29884564132925 & 3.3 \tabularnewline
4 & 20.35 & 2.03936264553414 & 4.5 \tabularnewline
5 & 20.0166666666667 & 1.84001811585285 & 4.6 \tabularnewline
6 & 19.6166666666667 & 1.07222510074455 & 2.70000000000000 \tabularnewline
7 & 17.5833333333333 & 0.870440501508671 & 2.3 \tabularnewline
8 & 17.35 & 4.38622844822291 & 10.3 \tabularnewline
9 & 19.4333333333333 & 2.16764080665286 & 5.6 \tabularnewline
10 & 21.3833333333333 & 2.0173414848921 & 4.9 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70392&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]22.2833333333333[/C][C]2.00540935139604[/C][C]5.2[/C][/ROW]
[ROW][C]2[/C][C]21.1[/C][C]1.74011493873250[/C][C]4[/C][/ROW]
[ROW][C]3[/C][C]21.75[/C][C]1.29884564132925[/C][C]3.3[/C][/ROW]
[ROW][C]4[/C][C]20.35[/C][C]2.03936264553414[/C][C]4.5[/C][/ROW]
[ROW][C]5[/C][C]20.0166666666667[/C][C]1.84001811585285[/C][C]4.6[/C][/ROW]
[ROW][C]6[/C][C]19.6166666666667[/C][C]1.07222510074455[/C][C]2.70000000000000[/C][/ROW]
[ROW][C]7[/C][C]17.5833333333333[/C][C]0.870440501508671[/C][C]2.3[/C][/ROW]
[ROW][C]8[/C][C]17.35[/C][C]4.38622844822291[/C][C]10.3[/C][/ROW]
[ROW][C]9[/C][C]19.4333333333333[/C][C]2.16764080665286[/C][C]5.6[/C][/ROW]
[ROW][C]10[/C][C]21.3833333333333[/C][C]2.0173414848921[/C][C]4.9[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70392&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70392&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	22.2833333333333	2.00540935139604	5.2
2	21.1	1.74011493873250	4
3	21.75	1.29884564132925	3.3
4	20.35	2.03936264553414	4.5
5	20.0166666666667	1.84001811585285	4.6
6	19.6166666666667	1.07222510074455	2.70000000000000
7	17.5833333333333	0.870440501508671	2.3
8	17.35	4.38622844822291	10.3
9	19.4333333333333	2.16764080665286	5.6
10	21.3833333333333	2.0173414848921	4.9

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	5.79421825975929
beta	-0.191692111994990
S.D.	0.194557540145543
T-STAT	-0.98527207864363
p-value	0.353347303062261

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 5.79421825975929 \tabularnewline
beta & -0.191692111994990 \tabularnewline
S.D. & 0.194557540145543 \tabularnewline
T-STAT & -0.98527207864363 \tabularnewline
p-value & 0.353347303062261 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70392&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]5.79421825975929[/C][/ROW]
[ROW][C]beta[/C][C]-0.191692111994990[/C][/ROW]
[ROW][C]S.D.[/C][C]0.194557540145543[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.98527207864363[/C][/ROW]
[ROW][C]p-value[/C][C]0.353347303062261[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70392&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70392&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	5.79421825975929
beta	-0.191692111994990
S.D.	0.194557540145543
T-STAT	-0.98527207864363
p-value	0.353347303062261

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	2.24223878691950
beta	-0.557372196673194
S.D.	1.84385433729463
T-STAT	-0.302286457991573
p-value	0.770143601394463
Lambda	1.55737219667319

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 2.24223878691950 \tabularnewline
beta & -0.557372196673194 \tabularnewline
S.D. & 1.84385433729463 \tabularnewline
T-STAT & -0.302286457991573 \tabularnewline
p-value & 0.770143601394463 \tabularnewline
Lambda & 1.55737219667319 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70392&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.24223878691950[/C][/ROW]
[ROW][C]beta[/C][C]-0.557372196673194[/C][/ROW]
[ROW][C]S.D.[/C][C]1.84385433729463[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.302286457991573[/C][/ROW]
[ROW][C]p-value[/C][C]0.770143601394463[/C][/ROW]
[ROW][C]Lambda[/C][C]1.55737219667319[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70392&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70392&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	2.24223878691950
beta	-0.557372196673194
S.D.	1.84385433729463
T-STAT	-0.302286457991573
p-value	0.770143601394463
Lambda	1.55737219667319

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 1 ; par2 = 2 ; par3 = 1 ; par4 = 1 ;

Parameters (R input):

par1 = 6 ;

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