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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

Sat, 13 Dec 2008 15:13:56 -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/13/t1229206507y37juauzp7ql7e6.htm/, Retrieved Sun, 19 May 2024 05:14:24 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=33226, Retrieved Sun, 19 May 2024 05:14:24 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Van Dooren Leen

Estimated Impact

156

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

-       [Standard Deviation-Mean Plot] [paper ] [2008-12-13 22:13:56] [d175f84d503eb4f2a43145d5e67795b5] [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	'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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33226&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33226&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33226&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	'Gwilym Jenkins' @ 72.249.127.135

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	513.75	4.99165971062398	10
2	539.25	41.0233673248146	79
3	561.25	13.3759734848222	31
4	555.5	8.2663978450915	18
5	571.25	36.8272996566406	74
6	603.25	10.1447851956888	19
7	584.25	8.05708797684788	18
8	596.5	33.0807093837683	62
9	608	15.3405779986718	33
10	584.25	8.80814017448254	19
11	598	28.9712501168544	53
12	582.75	28.0401497856199	63
13	542	15.9791530856092	35
14	532.5	32.3882694814033	66
15	523.25	14.4539498638492	32
16	502	12.7279220613579	27
17	502.25	33.4900482730816	65

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 513.75 & 4.99165971062398 & 10 \tabularnewline
2 & 539.25 & 41.0233673248146 & 79 \tabularnewline
3 & 561.25 & 13.3759734848222 & 31 \tabularnewline
4 & 555.5 & 8.2663978450915 & 18 \tabularnewline
5 & 571.25 & 36.8272996566406 & 74 \tabularnewline
6 & 603.25 & 10.1447851956888 & 19 \tabularnewline
7 & 584.25 & 8.05708797684788 & 18 \tabularnewline
8 & 596.5 & 33.0807093837683 & 62 \tabularnewline
9 & 608 & 15.3405779986718 & 33 \tabularnewline
10 & 584.25 & 8.80814017448254 & 19 \tabularnewline
11 & 598 & 28.9712501168544 & 53 \tabularnewline
12 & 582.75 & 28.0401497856199 & 63 \tabularnewline
13 & 542 & 15.9791530856092 & 35 \tabularnewline
14 & 532.5 & 32.3882694814033 & 66 \tabularnewline
15 & 523.25 & 14.4539498638492 & 32 \tabularnewline
16 & 502 & 12.7279220613579 & 27 \tabularnewline
17 & 502.25 & 33.4900482730816 & 65 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33226&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]513.75[/C][C]4.99165971062398[/C][C]10[/C][/ROW]
[ROW][C]2[/C][C]539.25[/C][C]41.0233673248146[/C][C]79[/C][/ROW]
[ROW][C]3[/C][C]561.25[/C][C]13.3759734848222[/C][C]31[/C][/ROW]
[ROW][C]4[/C][C]555.5[/C][C]8.2663978450915[/C][C]18[/C][/ROW]
[ROW][C]5[/C][C]571.25[/C][C]36.8272996566406[/C][C]74[/C][/ROW]
[ROW][C]6[/C][C]603.25[/C][C]10.1447851956888[/C][C]19[/C][/ROW]
[ROW][C]7[/C][C]584.25[/C][C]8.05708797684788[/C][C]18[/C][/ROW]
[ROW][C]8[/C][C]596.5[/C][C]33.0807093837683[/C][C]62[/C][/ROW]
[ROW][C]9[/C][C]608[/C][C]15.3405779986718[/C][C]33[/C][/ROW]
[ROW][C]10[/C][C]584.25[/C][C]8.80814017448254[/C][C]19[/C][/ROW]
[ROW][C]11[/C][C]598[/C][C]28.9712501168544[/C][C]53[/C][/ROW]
[ROW][C]12[/C][C]582.75[/C][C]28.0401497856199[/C][C]63[/C][/ROW]
[ROW][C]13[/C][C]542[/C][C]15.9791530856092[/C][C]35[/C][/ROW]
[ROW][C]14[/C][C]532.5[/C][C]32.3882694814033[/C][C]66[/C][/ROW]
[ROW][C]15[/C][C]523.25[/C][C]14.4539498638492[/C][C]32[/C][/ROW]
[ROW][C]16[/C][C]502[/C][C]12.7279220613579[/C][C]27[/C][/ROW]
[ROW][C]17[/C][C]502.25[/C][C]33.4900482730816[/C][C]65[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33226&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33226&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	513.75	4.99165971062398	10
2	539.25	41.0233673248146	79
3	561.25	13.3759734848222	31
4	555.5	8.2663978450915	18
5	571.25	36.8272996566406	74
6	603.25	10.1447851956888	19
7	584.25	8.05708797684788	18
8	596.5	33.0807093837683	62
9	608	15.3405779986718	33
10	584.25	8.80814017448254	19
11	598	28.9712501168544	53
12	582.75	28.0401497856199	63
13	542	15.9791530856092	35
14	532.5	32.3882694814033	66
15	523.25	14.4539498638492	32
16	502	12.7279220613579	27
17	502.25	33.4900482730816	65

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	23.9724157323382
beta	-0.00648045537163383
S.D.	0.0859317295747389
T-STAT	-0.0754139990397548
p-value	0.940881929679497

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 23.9724157323382 \tabularnewline
beta & -0.00648045537163383 \tabularnewline
S.D. & 0.0859317295747389 \tabularnewline
T-STAT & -0.0754139990397548 \tabularnewline
p-value & 0.940881929679497 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33226&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]23.9724157323382[/C][/ROW]
[ROW][C]beta[/C][C]-0.00648045537163383[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0859317295747389[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.0754139990397548[/C][/ROW]
[ROW][C]p-value[/C][C]0.940881929679497[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33226&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33226&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	23.9724157323382
beta	-0.00648045537163383
S.D.	0.0859317295747389
T-STAT	-0.0754139990397548
p-value	0.940881929679497

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	0.762999804942924
beta	0.326925904789293
S.D.	2.58131029496017
T-STAT	0.126651145128733
p-value	0.900898636984372
Lambda	0.673074095210707

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.762999804942924 \tabularnewline
beta & 0.326925904789293 \tabularnewline
S.D. & 2.58131029496017 \tabularnewline
T-STAT & 0.126651145128733 \tabularnewline
p-value & 0.900898636984372 \tabularnewline
Lambda & 0.673074095210707 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33226&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.762999804942924[/C][/ROW]
[ROW][C]beta[/C][C]0.326925904789293[/C][/ROW]
[ROW][C]S.D.[/C][C]2.58131029496017[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.126651145128733[/C][/ROW]
[ROW][C]p-value[/C][C]0.900898636984372[/C][/ROW]
[ROW][C]Lambda[/C][C]0.673074095210707[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33226&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33226&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	0.762999804942924
beta	0.326925904789293
S.D.	2.58131029496017
T-STAT	0.126651145128733
p-value	0.900898636984372
Lambda	0.673074095210707

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