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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

Fri, 23 Dec 2016 11:11:12 +0100

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/2016/Dec/23/t1482487896qsmj2dq8tl4k3k0.htm/, Retrieved Fri, 17 May 2024 19:11:28 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302831, Retrieved Fri, 17 May 2024 19:11:28 +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] [standard deviatio...] [2016-12-23 10:11:12] [bd7223969ac5b08f41438741a34686d6] [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	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302831&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

1 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=302831&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302831&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	Big Analytics Cloud Computing Center

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	1914.16666666667	104.551712592672	350
2	1822.08333333333	73.3750742088314	220
3	1921.66666666667	207.346145955077	680
4	2124.16666666667	216.971231160989	685
5	1736.66666666667	101.8093881484	350
6	1415.41666666667	144.496906750996	410
7	1200.41666666667	116.725364021967	410
8	1391.25	163.833687844495	525
9	2125	422.868988953058	1465
10	3092.08333333333	579.601972882854	1970

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 1914.16666666667 & 104.551712592672 & 350 \tabularnewline
2 & 1822.08333333333 & 73.3750742088314 & 220 \tabularnewline
3 & 1921.66666666667 & 207.346145955077 & 680 \tabularnewline
4 & 2124.16666666667 & 216.971231160989 & 685 \tabularnewline
5 & 1736.66666666667 & 101.8093881484 & 350 \tabularnewline
6 & 1415.41666666667 & 144.496906750996 & 410 \tabularnewline
7 & 1200.41666666667 & 116.725364021967 & 410 \tabularnewline
8 & 1391.25 & 163.833687844495 & 525 \tabularnewline
9 & 2125 & 422.868988953058 & 1465 \tabularnewline
10 & 3092.08333333333 & 579.601972882854 & 1970 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302831&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]1914.16666666667[/C][C]104.551712592672[/C][C]350[/C][/ROW]
[ROW][C]2[/C][C]1822.08333333333[/C][C]73.3750742088314[/C][C]220[/C][/ROW]
[ROW][C]3[/C][C]1921.66666666667[/C][C]207.346145955077[/C][C]680[/C][/ROW]
[ROW][C]4[/C][C]2124.16666666667[/C][C]216.971231160989[/C][C]685[/C][/ROW]
[ROW][C]5[/C][C]1736.66666666667[/C][C]101.8093881484[/C][C]350[/C][/ROW]
[ROW][C]6[/C][C]1415.41666666667[/C][C]144.496906750996[/C][C]410[/C][/ROW]
[ROW][C]7[/C][C]1200.41666666667[/C][C]116.725364021967[/C][C]410[/C][/ROW]
[ROW][C]8[/C][C]1391.25[/C][C]163.833687844495[/C][C]525[/C][/ROW]
[ROW][C]9[/C][C]2125[/C][C]422.868988953058[/C][C]1465[/C][/ROW]
[ROW][C]10[/C][C]3092.08333333333[/C][C]579.601972882854[/C][C]1970[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302831&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302831&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	1914.16666666667	104.551712592672	350
2	1822.08333333333	73.3750742088314	220
3	1921.66666666667	207.346145955077	680
4	2124.16666666667	216.971231160989	685
5	1736.66666666667	101.8093881484	350
6	1415.41666666667	144.496906750996	410
7	1200.41666666667	116.725364021967	410
8	1391.25	163.833687844495	525
9	2125	422.868988953058	1465
10	3092.08333333333	579.601972882854	1970

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-259.235305501025
beta	0.252038335950715
S.D.	0.0619204574255347
T-STAT	4.07035649330943
p-value	0.00358165195703497

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -259.235305501025 \tabularnewline
beta & 0.252038335950715 \tabularnewline
S.D. & 0.0619204574255347 \tabularnewline
T-STAT & 4.07035649330943 \tabularnewline
p-value & 0.00358165195703497 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302831&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-259.235305501025[/C][/ROW]
[ROW][C]beta[/C][C]0.252038335950715[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0619204574255347[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.07035649330943[/C][/ROW]
[ROW][C]p-value[/C][C]0.00358165195703497[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302831&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302831&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	-259.235305501025
beta	0.252038335950715
S.D.	0.0619204574255347
T-STAT	4.07035649330943
p-value	0.00358165195703497

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-7.01870599490842
beta	1.62220085830056
S.D.	0.639223176401995
T-STAT	2.53776915197516
p-value	0.034831537525716
Lambda	-0.62220085830056

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -7.01870599490842 \tabularnewline
beta & 1.62220085830056 \tabularnewline
S.D. & 0.639223176401995 \tabularnewline
T-STAT & 2.53776915197516 \tabularnewline
p-value & 0.034831537525716 \tabularnewline
Lambda & -0.62220085830056 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302831&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-7.01870599490842[/C][/ROW]
[ROW][C]beta[/C][C]1.62220085830056[/C][/ROW]
[ROW][C]S.D.[/C][C]0.639223176401995[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.53776915197516[/C][/ROW]
[ROW][C]p-value[/C][C]0.034831537525716[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.62220085830056[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302831&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302831&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	-7.01870599490842
beta	1.62220085830056
S.D.	0.639223176401995
T-STAT	2.53776915197516
p-value	0.034831537525716
Lambda	-0.62220085830056

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 <- '12'
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

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code