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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, 16 Aug 2015 00:01:39 +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/2015/Aug/16/t143967971702bj98dbixuqw8h.htm/, Retrieved Sun, 19 May 2024 12:57:06 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=280103, Retrieved Sun, 19 May 2024 12:57:06 +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] [] [2015-08-15 23:01:39] [f898ec974b62c60a8bec4044c4c271e3] [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	'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280103&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280103&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280103&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	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	5421177.66666667	183714.587644349	547976
2	5515939	194933.534405961	631488
3	5659892.33333333	191204.979917714	611182
4	5840668.16666667	195628.122641744	674388
5	5663634.16666667	322152.643100027	1157442
6	5154792.5	384092.45584234	1326468
7	4637084.83333333	315868.804968666	1136850
8	3929973.66666667	440250.122490992	1599312
9	3426375.33333333	491598.31613761	1642212
10	2731514.5	544063.75947953	1874444

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 5421177.66666667 & 183714.587644349 & 547976 \tabularnewline
2 & 5515939 & 194933.534405961 & 631488 \tabularnewline
3 & 5659892.33333333 & 191204.979917714 & 611182 \tabularnewline
4 & 5840668.16666667 & 195628.122641744 & 674388 \tabularnewline
5 & 5663634.16666667 & 322152.643100027 & 1157442 \tabularnewline
6 & 5154792.5 & 384092.45584234 & 1326468 \tabularnewline
7 & 4637084.83333333 & 315868.804968666 & 1136850 \tabularnewline
8 & 3929973.66666667 & 440250.122490992 & 1599312 \tabularnewline
9 & 3426375.33333333 & 491598.31613761 & 1642212 \tabularnewline
10 & 2731514.5 & 544063.75947953 & 1874444 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280103&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]5421177.66666667[/C][C]183714.587644349[/C][C]547976[/C][/ROW]
[ROW][C]2[/C][C]5515939[/C][C]194933.534405961[/C][C]631488[/C][/ROW]
[ROW][C]3[/C][C]5659892.33333333[/C][C]191204.979917714[/C][C]611182[/C][/ROW]
[ROW][C]4[/C][C]5840668.16666667[/C][C]195628.122641744[/C][C]674388[/C][/ROW]
[ROW][C]5[/C][C]5663634.16666667[/C][C]322152.643100027[/C][C]1157442[/C][/ROW]
[ROW][C]6[/C][C]5154792.5[/C][C]384092.45584234[/C][C]1326468[/C][/ROW]
[ROW][C]7[/C][C]4637084.83333333[/C][C]315868.804968666[/C][C]1136850[/C][/ROW]
[ROW][C]8[/C][C]3929973.66666667[/C][C]440250.122490992[/C][C]1599312[/C][/ROW]
[ROW][C]9[/C][C]3426375.33333333[/C][C]491598.31613761[/C][C]1642212[/C][/ROW]
[ROW][C]10[/C][C]2731514.5[/C][C]544063.75947953[/C][C]1874444[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280103&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280103&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	5421177.66666667	183714.587644349	547976
2	5515939	194933.534405961	631488
3	5659892.33333333	191204.979917714	611182
4	5840668.16666667	195628.122641744	674388
5	5663634.16666667	322152.643100027	1157442
6	5154792.5	384092.45584234	1326468
7	4637084.83333333	315868.804968666	1136850
8	3929973.66666667	440250.122490992	1599312
9	3426375.33333333	491598.31613761	1642212
10	2731514.5	544063.75947953	1874444

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	869264.937184961
beta	-0.113151792219188
S.D.	0.0185894327362386
T-STAT	-6.08688784777213
p-value	0.000293686871073618

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 869264.937184961 \tabularnewline
beta & -0.113151792219188 \tabularnewline
S.D. & 0.0185894327362386 \tabularnewline
T-STAT & -6.08688784777213 \tabularnewline
p-value & 0.000293686871073618 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280103&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]869264.937184961[/C][/ROW]
[ROW][C]beta[/C][C]-0.113151792219188[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0185894327362386[/C][/ROW]
[ROW][C]T-STAT[/C][C]-6.08688784777213[/C][/ROW]
[ROW][C]p-value[/C][C]0.000293686871073618[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280103&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280103&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	869264.937184961
beta	-0.113151792219188
S.D.	0.0185894327362386
T-STAT	-6.08688784777213
p-value	0.000293686871073618

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	33.8981904944784
beta	-1.38589065989076
S.D.	0.316605261909548
T-STAT	-4.3773456307454
p-value	0.00235715681397516
Lambda	2.38589065989076

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 33.8981904944784 \tabularnewline
beta & -1.38589065989076 \tabularnewline
S.D. & 0.316605261909548 \tabularnewline
T-STAT & -4.3773456307454 \tabularnewline
p-value & 0.00235715681397516 \tabularnewline
Lambda & 2.38589065989076 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280103&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]33.8981904944784[/C][/ROW]
[ROW][C]beta[/C][C]-1.38589065989076[/C][/ROW]
[ROW][C]S.D.[/C][C]0.316605261909548[/C][/ROW]
[ROW][C]T-STAT[/C][C]-4.3773456307454[/C][/ROW]
[ROW][C]p-value[/C][C]0.00235715681397516[/C][/ROW]
[ROW][C]Lambda[/C][C]2.38589065989076[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280103&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280103&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	33.8981904944784
beta	-1.38589065989076
S.D.	0.316605261909548
T-STAT	-4.3773456307454
p-value	0.00235715681397516
Lambda	2.38589065989076

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