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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, 19 Dec 2008 03:25:45 -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/2008/Dec/19/t1229682576nlh6utu8w67lamy.htm/, Retrieved Wed, 15 May 2024 21:55:08 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35027, Retrieved Wed, 15 May 2024 21:55:08 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

228

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

-     [Box-Cox Linearity Plot] [Box-Cox] [2008-11-11 14:29:04] [adb6b6905cde49db36d59ca44433140d]
- RM D  [Box-Cox Normality Plot] [Box-Cox Normality...] [2008-11-11 14:44:37] [adb6b6905cde49db36d59ca44433140d]
F    D    [Box-Cox Normality Plot] [Box-Cox Normality...] [2008-11-11 23:46:30] [b591abfa820a394aeb0c5ebd9cfa1091]
F RMPD      [Maximum-likelihood Fitting - Normal Distribution] [Normal Distribution ] [2008-11-12 15:48:53] [b478325fa744e3f2fc16a7222294469c]
F   PD        [Maximum-likelihood Fitting - Normal Distribution] [task 8 maximum li...] [2008-11-12 20:17:58] [1eab65e90adf64584b8e6f0da23ff414]
- RMPD          [Box-Cox Normality Plot] [4.2.1] [2008-12-18 18:51:19] [1eab65e90adf64584b8e6f0da23ff414]
- RMP               [Standard Deviation-Mean Plot] [4.2.2] [2008-12-19 10:25:45] [0458bd763b171003ec052ce63099d477] [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	4 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 4 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35027&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35027&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35027&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	4 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	99.6833333333333	6.97708370092383	20.4
2	103.408333333333	6.03617252800803	22.3
3	103.3	8.3314300856892	26.2
4	101.466666666667	8.7222112848159	29.6
5	101.658333333333	7.40410921943574	22.6
6	106.441666666667	7.06199280828311	21.7
7	109.333333333333	7.34380794625752	24.8

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 99.6833333333333 & 6.97708370092383 & 20.4 \tabularnewline
2 & 103.408333333333 & 6.03617252800803 & 22.3 \tabularnewline
3 & 103.3 & 8.3314300856892 & 26.2 \tabularnewline
4 & 101.466666666667 & 8.7222112848159 & 29.6 \tabularnewline
5 & 101.658333333333 & 7.40410921943574 & 22.6 \tabularnewline
6 & 106.441666666667 & 7.06199280828311 & 21.7 \tabularnewline
7 & 109.333333333333 & 7.34380794625752 & 24.8 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35027&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]99.6833333333333[/C][C]6.97708370092383[/C][C]20.4[/C][/ROW]
[ROW][C]2[/C][C]103.408333333333[/C][C]6.03617252800803[/C][C]22.3[/C][/ROW]
[ROW][C]3[/C][C]103.3[/C][C]8.3314300856892[/C][C]26.2[/C][/ROW]
[ROW][C]4[/C][C]101.466666666667[/C][C]8.7222112848159[/C][C]29.6[/C][/ROW]
[ROW][C]5[/C][C]101.658333333333[/C][C]7.40410921943574[/C][C]22.6[/C][/ROW]
[ROW][C]6[/C][C]106.441666666667[/C][C]7.06199280828311[/C][C]21.7[/C][/ROW]
[ROW][C]7[/C][C]109.333333333333[/C][C]7.34380794625752[/C][C]24.8[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35027&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35027&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	99.6833333333333	6.97708370092383	20.4
2	103.408333333333	6.03617252800803	22.3
3	103.3	8.3314300856892	26.2
4	101.466666666667	8.7222112848159	29.6
5	101.658333333333	7.40410921943574	22.6
6	106.441666666667	7.06199280828311	21.7
7	109.333333333333	7.34380794625752	24.8

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	11.3708699841039
beta	-0.0382181177438696
S.D.	0.12020488923586
T-STAT	-0.317941458012411
p-value	0.763379152296642

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 11.3708699841039 \tabularnewline
beta & -0.0382181177438696 \tabularnewline
S.D. & 0.12020488923586 \tabularnewline
T-STAT & -0.317941458012411 \tabularnewline
p-value & 0.763379152296642 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35027&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]11.3708699841039[/C][/ROW]
[ROW][C]beta[/C][C]-0.0382181177438696[/C][/ROW]
[ROW][C]S.D.[/C][C]0.12020488923586[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.317941458012411[/C][/ROW]
[ROW][C]p-value[/C][C]0.763379152296642[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35027&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35027&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	11.3708699841039
beta	-0.0382181177438696
S.D.	0.12020488923586
T-STAT	-0.317941458012411
p-value	0.763379152296642

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	4.20308663762745
beta	-0.475489054907425
S.D.	1.71217677847554
T-STAT	-0.277710258008980
p-value	0.792351689520825
Lambda	1.47548905490742

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 4.20308663762745 \tabularnewline
beta & -0.475489054907425 \tabularnewline
S.D. & 1.71217677847554 \tabularnewline
T-STAT & -0.277710258008980 \tabularnewline
p-value & 0.792351689520825 \tabularnewline
Lambda & 1.47548905490742 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35027&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]4.20308663762745[/C][/ROW]
[ROW][C]beta[/C][C]-0.475489054907425[/C][/ROW]
[ROW][C]S.D.[/C][C]1.71217677847554[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.277710258008980[/C][/ROW]
[ROW][C]p-value[/C][C]0.792351689520825[/C][/ROW]
[ROW][C]Lambda[/C][C]1.47548905490742[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35027&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35027&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	4.20308663762745
beta	-0.475489054907425
S.D.	1.71217677847554
T-STAT	-0.277710258008980
p-value	0.792351689520825
Lambda	1.47548905490742

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