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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

Tue, 20 Dec 2011 08:36:10 -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/2011/Dec/20/t1324388194yx8vyol3lr57jmw.htm/, Retrieved Mon, 06 May 2024 04:49:21 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=157958, Retrieved Mon, 06 May 2024 04:49:21 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

146

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

-     [Spectral Analysis] [Paper] [2011-12-20 12:55:33] [43239ed98a62e091c70785d80176537f]
- RMP     [Standard Deviation-Mean Plot] [paper] [2011-12-20 13:36:10] [6e647d331a8f33aa61a2d78ef323178e] [Current]

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Boxplots

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	'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157958&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157958&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157958&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	'Gertrude Mary Cox' @ cox.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	597	29.3484809374069	64
2	588.25	23.0271578793389	51
3	570	22.464787260659	55
4	541	24.3447461820136	55
5	507.5	23.5301225382841	55
6	469.25	24.5407823836161	57
7	473.75	27.1830216618143	65
8	501.75	30.0818328342318	65
9	549.25	30.1482448355898	70
10	583.75	29.4660821963151	65
11	596.25	23.5566692608838	56
12	578	31.5489038372704	75
13	522.25	21.6390850083824	48
14	511.5	24.0069434400411	53
15	564.75	23.6836793312751	56
16	561.25	24.1988291727789	52

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 597 & 29.3484809374069 & 64 \tabularnewline
2 & 588.25 & 23.0271578793389 & 51 \tabularnewline
3 & 570 & 22.464787260659 & 55 \tabularnewline
4 & 541 & 24.3447461820136 & 55 \tabularnewline
5 & 507.5 & 23.5301225382841 & 55 \tabularnewline
6 & 469.25 & 24.5407823836161 & 57 \tabularnewline
7 & 473.75 & 27.1830216618143 & 65 \tabularnewline
8 & 501.75 & 30.0818328342318 & 65 \tabularnewline
9 & 549.25 & 30.1482448355898 & 70 \tabularnewline
10 & 583.75 & 29.4660821963151 & 65 \tabularnewline
11 & 596.25 & 23.5566692608838 & 56 \tabularnewline
12 & 578 & 31.5489038372704 & 75 \tabularnewline
13 & 522.25 & 21.6390850083824 & 48 \tabularnewline
14 & 511.5 & 24.0069434400411 & 53 \tabularnewline
15 & 564.75 & 23.6836793312751 & 56 \tabularnewline
16 & 561.25 & 24.1988291727789 & 52 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157958&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]597[/C][C]29.3484809374069[/C][C]64[/C][/ROW]
[ROW][C]2[/C][C]588.25[/C][C]23.0271578793389[/C][C]51[/C][/ROW]
[ROW][C]3[/C][C]570[/C][C]22.464787260659[/C][C]55[/C][/ROW]
[ROW][C]4[/C][C]541[/C][C]24.3447461820136[/C][C]55[/C][/ROW]
[ROW][C]5[/C][C]507.5[/C][C]23.5301225382841[/C][C]55[/C][/ROW]
[ROW][C]6[/C][C]469.25[/C][C]24.5407823836161[/C][C]57[/C][/ROW]
[ROW][C]7[/C][C]473.75[/C][C]27.1830216618143[/C][C]65[/C][/ROW]
[ROW][C]8[/C][C]501.75[/C][C]30.0818328342318[/C][C]65[/C][/ROW]
[ROW][C]9[/C][C]549.25[/C][C]30.1482448355898[/C][C]70[/C][/ROW]
[ROW][C]10[/C][C]583.75[/C][C]29.4660821963151[/C][C]65[/C][/ROW]
[ROW][C]11[/C][C]596.25[/C][C]23.5566692608838[/C][C]56[/C][/ROW]
[ROW][C]12[/C][C]578[/C][C]31.5489038372704[/C][C]75[/C][/ROW]
[ROW][C]13[/C][C]522.25[/C][C]21.6390850083824[/C][C]48[/C][/ROW]
[ROW][C]14[/C][C]511.5[/C][C]24.0069434400411[/C][C]53[/C][/ROW]
[ROW][C]15[/C][C]564.75[/C][C]23.6836793312751[/C][C]56[/C][/ROW]
[ROW][C]16[/C][C]561.25[/C][C]24.1988291727789[/C][C]52[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157958&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157958&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	597	29.3484809374069	64
2	588.25	23.0271578793389	51
3	570	22.464787260659	55
4	541	24.3447461820136	55
5	507.5	23.5301225382841	55
6	469.25	24.5407823836161	57
7	473.75	27.1830216618143	65
8	501.75	30.0818328342318	65
9	549.25	30.1482448355898	70
10	583.75	29.4660821963151	65
11	596.25	23.5566692608838	56
12	578	31.5489038372704	75
13	522.25	21.6390850083824	48
14	511.5	24.0069434400411	53
15	564.75	23.6836793312751	56
16	561.25	24.1988291727789	52

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	21.6165084177119
beta	0.00767658012466428
S.D.	0.0204377697790969
T-STAT	0.375607525069377
p-value	0.712838540122474

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 21.6165084177119 \tabularnewline
beta & 0.00767658012466428 \tabularnewline
S.D. & 0.0204377697790969 \tabularnewline
T-STAT & 0.375607525069377 \tabularnewline
p-value & 0.712838540122474 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157958&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]21.6165084177119[/C][/ROW]
[ROW][C]beta[/C][C]0.00767658012466428[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0204377697790969[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.375607525069377[/C][/ROW]
[ROW][C]p-value[/C][C]0.712838540122474[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157958&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157958&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	21.6165084177119
beta	0.00767658012466428
S.D.	0.0204377697790969
T-STAT	0.375607525069377
p-value	0.712838540122474

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	2.43794614216295
beta	0.127855285275246
S.D.	0.413110865118434
T-STAT	0.309493881838696
p-value	0.761504329232279
Lambda	0.872144714724754

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 2.43794614216295 \tabularnewline
beta & 0.127855285275246 \tabularnewline
S.D. & 0.413110865118434 \tabularnewline
T-STAT & 0.309493881838696 \tabularnewline
p-value & 0.761504329232279 \tabularnewline
Lambda & 0.872144714724754 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157958&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.43794614216295[/C][/ROW]
[ROW][C]beta[/C][C]0.127855285275246[/C][/ROW]
[ROW][C]S.D.[/C][C]0.413110865118434[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.309493881838696[/C][/ROW]
[ROW][C]p-value[/C][C]0.761504329232279[/C][/ROW]
[ROW][C]Lambda[/C][C]0.872144714724754[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157958&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157958&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	2.43794614216295
beta	0.127855285275246
S.D.	0.413110865118434
T-STAT	0.309493881838696
p-value	0.761504329232279
Lambda	0.872144714724754

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code