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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

Mon, 12 May 2008 13:55:45 -0600

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/May/12/t1210622231oocxn68jdpxg1nb.htm/, Retrieved Tue, 14 May 2024 08:56:19 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=12434, Retrieved Tue, 14 May 2024 08:56:19 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

150

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

-       [Standard Deviation-Mean Plot] [Jan-PIeter Onzea-...] [2008-05-12 19:55:45] [1140c1f194cb83f4b6ccae47f83794fa] [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	'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=12434&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=12434&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12434&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	470.5	6.85565460040104	15
2	488.25	37.9594081443147	70
3	515.75	6.39661368746516	14
4	513.75	4.99165971062398	10
5	539.25	41.0233673248146	79
6	561.25	13.3759734848222	31
7	555.5	8.2663978450915	18
8	571.25	36.8272996566406	74
9	603.25	10.1447851956888	19
10	584.25	8.05708797684788	18
11	596.5	33.0807093837683	62
12	608	15.3405779986718	33
13	584.25	8.80814017448254	19
14	598	28.9712501168544	53
15	582.75	28.0401497856199	63
16	542	15.9791530856092	35
17	532.5	32.3882694814033	66
18	523.25	14.4539498638492	32

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 470.5 & 6.85565460040104 & 15 \tabularnewline
2 & 488.25 & 37.9594081443147 & 70 \tabularnewline
3 & 515.75 & 6.39661368746516 & 14 \tabularnewline
4 & 513.75 & 4.99165971062398 & 10 \tabularnewline
5 & 539.25 & 41.0233673248146 & 79 \tabularnewline
6 & 561.25 & 13.3759734848222 & 31 \tabularnewline
7 & 555.5 & 8.2663978450915 & 18 \tabularnewline
8 & 571.25 & 36.8272996566406 & 74 \tabularnewline
9 & 603.25 & 10.1447851956888 & 19 \tabularnewline
10 & 584.25 & 8.05708797684788 & 18 \tabularnewline
11 & 596.5 & 33.0807093837683 & 62 \tabularnewline
12 & 608 & 15.3405779986718 & 33 \tabularnewline
13 & 584.25 & 8.80814017448254 & 19 \tabularnewline
14 & 598 & 28.9712501168544 & 53 \tabularnewline
15 & 582.75 & 28.0401497856199 & 63 \tabularnewline
16 & 542 & 15.9791530856092 & 35 \tabularnewline
17 & 532.5 & 32.3882694814033 & 66 \tabularnewline
18 & 523.25 & 14.4539498638492 & 32 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12434&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]470.5[/C][C]6.85565460040104[/C][C]15[/C][/ROW]
[ROW][C]2[/C][C]488.25[/C][C]37.9594081443147[/C][C]70[/C][/ROW]
[ROW][C]3[/C][C]515.75[/C][C]6.39661368746516[/C][C]14[/C][/ROW]
[ROW][C]4[/C][C]513.75[/C][C]4.99165971062398[/C][C]10[/C][/ROW]
[ROW][C]5[/C][C]539.25[/C][C]41.0233673248146[/C][C]79[/C][/ROW]
[ROW][C]6[/C][C]561.25[/C][C]13.3759734848222[/C][C]31[/C][/ROW]
[ROW][C]7[/C][C]555.5[/C][C]8.2663978450915[/C][C]18[/C][/ROW]
[ROW][C]8[/C][C]571.25[/C][C]36.8272996566406[/C][C]74[/C][/ROW]
[ROW][C]9[/C][C]603.25[/C][C]10.1447851956888[/C][C]19[/C][/ROW]
[ROW][C]10[/C][C]584.25[/C][C]8.05708797684788[/C][C]18[/C][/ROW]
[ROW][C]11[/C][C]596.5[/C][C]33.0807093837683[/C][C]62[/C][/ROW]
[ROW][C]12[/C][C]608[/C][C]15.3405779986718[/C][C]33[/C][/ROW]
[ROW][C]13[/C][C]584.25[/C][C]8.80814017448254[/C][C]19[/C][/ROW]
[ROW][C]14[/C][C]598[/C][C]28.9712501168544[/C][C]53[/C][/ROW]
[ROW][C]15[/C][C]582.75[/C][C]28.0401497856199[/C][C]63[/C][/ROW]
[ROW][C]16[/C][C]542[/C][C]15.9791530856092[/C][C]35[/C][/ROW]
[ROW][C]17[/C][C]532.5[/C][C]32.3882694814033[/C][C]66[/C][/ROW]
[ROW][C]18[/C][C]523.25[/C][C]14.4539498638492[/C][C]32[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12434&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12434&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	470.5	6.85565460040104	15
2	488.25	37.9594081443147	70
3	515.75	6.39661368746516	14
4	513.75	4.99165971062398	10
5	539.25	41.0233673248146	79
6	561.25	13.3759734848222	31
7	555.5	8.2663978450915	18
8	571.25	36.8272996566406	74
9	603.25	10.1447851956888	19
10	584.25	8.05708797684788	18
11	596.5	33.0807093837683	62
12	608	15.3405779986718	33
13	584.25	8.80814017448254	19
14	598	28.9712501168544	53
15	582.75	28.0401497856199	63
16	542	15.9791530856092	35
17	532.5	32.3882694814033	66
18	523.25	14.4539498638492	32

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	6.70437952262672
beta	0.0230968748135391
S.D.	0.0772446655199938
T-STAT	0.299009318741380
p-value	0.768781753165195

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 6.70437952262672 \tabularnewline
beta & 0.0230968748135391 \tabularnewline
S.D. & 0.0772446655199938 \tabularnewline
T-STAT & 0.299009318741380 \tabularnewline
p-value & 0.768781753165195 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12434&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]6.70437952262672[/C][/ROW]
[ROW][C]beta[/C][C]0.0230968748135391[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0772446655199938[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.299009318741380[/C][/ROW]
[ROW][C]p-value[/C][C]0.768781753165195[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12434&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12434&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	6.70437952262672
beta	0.0230968748135391
S.D.	0.0772446655199938
T-STAT	0.299009318741380
p-value	0.768781753165195

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-8.58043777629464
beta	1.79421367062771
S.D.	2.30221174315159
T-STAT	0.779343462201063
p-value	0.447152357554196
Lambda	-0.794213670627709

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -8.58043777629464 \tabularnewline
beta & 1.79421367062771 \tabularnewline
S.D. & 2.30221174315159 \tabularnewline
T-STAT & 0.779343462201063 \tabularnewline
p-value & 0.447152357554196 \tabularnewline
Lambda & -0.794213670627709 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12434&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-8.58043777629464[/C][/ROW]
[ROW][C]beta[/C][C]1.79421367062771[/C][/ROW]
[ROW][C]S.D.[/C][C]2.30221174315159[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.779343462201063[/C][/ROW]
[ROW][C]p-value[/C][C]0.447152357554196[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.794213670627709[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12434&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12434&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	-8.58043777629464
beta	1.79421367062771
S.D.	2.30221174315159
T-STAT	0.779343462201063
p-value	0.447152357554196
Lambda	-0.794213670627709

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

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code