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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

Sun, 21 Dec 2008 15:00:36 -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/21/t1229896878u8i6lhe2gw84r8o.htm/, Retrieved Fri, 17 May 2024 05:46:24 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35861, Retrieved Fri, 17 May 2024 05:46:24 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

152

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

-     [Box-Cox Linearity Plot] [Box cox linearity...] [2008-12-21 21:47:51] [c5e27150943bc3d623392efb0d98f8d3]
-    D  [Box-Cox Linearity Plot] [Box cox linearity...] [2008-12-21 21:49:45] [c5e27150943bc3d623392efb0d98f8d3]
- RMPD    [Standard Deviation-Mean Plot] [standard deviatio...] [2008-12-21 21:56:51] [c5e27150943bc3d623392efb0d98f8d3]
-    D      [Standard Deviation-Mean Plot] [standard deviatio...] [2008-12-21 21:58:39] [c5e27150943bc3d623392efb0d98f8d3]
-    D          [Standard Deviation-Mean Plot] [standard deviatio...] [2008-12-21 22:00:36] [25d75405d700c34901b109463a9659f5] [Current]

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Dataseries X:

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Histogram

Boxplots

8,3
8,4
8,4
8,4
8,6
8,9
8,8
8,3
7,5
7,2
7,5
8,8
9,3
9,3
8,7
8,2
8,3
8,5
8,6
8,6
8,2
8,1
8
8,6
8,7
8,8
8,5
8,4
8,5
8,7
8,7
8,6
8,5
8,3
8,1
8,2
8,1
8,1
7,9
7,9
7,9
8
8
7,9
8
7,7
7,2
7,5
7,3
7
7
7
7,2
7,3
7,1
6,8
6,6
6,2
6,2
6,8

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35861&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]2 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=35861&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35861&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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	8.375	0.0499999999999998	0.0999999999999996
2	8.65	0.264575131106459	0.6
3	7.75	0.714142842854285	1.6
4	8.875	0.531507290636733	1.10000000000000
5	8.5	0.141421356237309	0.299999999999999
6	8.225	0.262995563967658	0.6
7	8.6	0.182574185835055	0.4
8	8.625	0.0957427107756335	0.199999999999999
9	8.275	0.170782512765994	0.4
10	8	0.115470053837925	0.199999999999999
11	7.95	0.0577350269189624	0.0999999999999996
12	7.6	0.336650164612069	0.8
13	7.075	0.15	0.3
14	7.1	0.216024689946929	0.5
15	6.45	0.3	0.6

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 8.375 & 0.0499999999999998 & 0.0999999999999996 \tabularnewline
2 & 8.65 & 0.264575131106459 & 0.6 \tabularnewline
3 & 7.75 & 0.714142842854285 & 1.6 \tabularnewline
4 & 8.875 & 0.531507290636733 & 1.10000000000000 \tabularnewline
5 & 8.5 & 0.141421356237309 & 0.299999999999999 \tabularnewline
6 & 8.225 & 0.262995563967658 & 0.6 \tabularnewline
7 & 8.6 & 0.182574185835055 & 0.4 \tabularnewline
8 & 8.625 & 0.0957427107756335 & 0.199999999999999 \tabularnewline
9 & 8.275 & 0.170782512765994 & 0.4 \tabularnewline
10 & 8 & 0.115470053837925 & 0.199999999999999 \tabularnewline
11 & 7.95 & 0.0577350269189624 & 0.0999999999999996 \tabularnewline
12 & 7.6 & 0.336650164612069 & 0.8 \tabularnewline
13 & 7.075 & 0.15 & 0.3 \tabularnewline
14 & 7.1 & 0.216024689946929 & 0.5 \tabularnewline
15 & 6.45 & 0.3 & 0.6 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35861&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]8.375[/C][C]0.0499999999999998[/C][C]0.0999999999999996[/C][/ROW]
[ROW][C]2[/C][C]8.65[/C][C]0.264575131106459[/C][C]0.6[/C][/ROW]
[ROW][C]3[/C][C]7.75[/C][C]0.714142842854285[/C][C]1.6[/C][/ROW]
[ROW][C]4[/C][C]8.875[/C][C]0.531507290636733[/C][C]1.10000000000000[/C][/ROW]
[ROW][C]5[/C][C]8.5[/C][C]0.141421356237309[/C][C]0.299999999999999[/C][/ROW]
[ROW][C]6[/C][C]8.225[/C][C]0.262995563967658[/C][C]0.6[/C][/ROW]
[ROW][C]7[/C][C]8.6[/C][C]0.182574185835055[/C][C]0.4[/C][/ROW]
[ROW][C]8[/C][C]8.625[/C][C]0.0957427107756335[/C][C]0.199999999999999[/C][/ROW]
[ROW][C]9[/C][C]8.275[/C][C]0.170782512765994[/C][C]0.4[/C][/ROW]
[ROW][C]10[/C][C]8[/C][C]0.115470053837925[/C][C]0.199999999999999[/C][/ROW]
[ROW][C]11[/C][C]7.95[/C][C]0.0577350269189624[/C][C]0.0999999999999996[/C][/ROW]
[ROW][C]12[/C][C]7.6[/C][C]0.336650164612069[/C][C]0.8[/C][/ROW]
[ROW][C]13[/C][C]7.075[/C][C]0.15[/C][C]0.3[/C][/ROW]
[ROW][C]14[/C][C]7.1[/C][C]0.216024689946929[/C][C]0.5[/C][/ROW]
[ROW][C]15[/C][C]6.45[/C][C]0.3[/C][C]0.6[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35861&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35861&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	8.375	0.0499999999999998	0.0999999999999996
2	8.65	0.264575131106459	0.6
3	7.75	0.714142842854285	1.6
4	8.875	0.531507290636733	1.10000000000000
5	8.5	0.141421356237309	0.299999999999999
6	8.225	0.262995563967658	0.6
7	8.6	0.182574185835055	0.4
8	8.625	0.0957427107756335	0.199999999999999
9	8.275	0.170782512765994	0.4
10	8	0.115470053837925	0.199999999999999
11	7.95	0.0577350269189624	0.0999999999999996
12	7.6	0.336650164612069	0.8
13	7.075	0.15	0.3
14	7.1	0.216024689946929	0.5
15	6.45	0.3	0.6

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	0.386593070057128
beta	-0.0184029531142183
S.D.	0.0719119586617445
T-STAT	-0.255909496232485
p-value	0.80202542056987

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.386593070057128 \tabularnewline
beta & -0.0184029531142183 \tabularnewline
S.D. & 0.0719119586617445 \tabularnewline
T-STAT & -0.255909496232485 \tabularnewline
p-value & 0.80202542056987 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35861&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.386593070057128[/C][/ROW]
[ROW][C]beta[/C][C]-0.0184029531142183[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0719119586617445[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.255909496232485[/C][/ROW]
[ROW][C]p-value[/C][C]0.80202542056987[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35861&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35861&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	0.386593070057128
beta	-0.0184029531142183
S.D.	0.0719119586617445
T-STAT	-0.255909496232485
p-value	0.80202542056987

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	0.944386790988822
beta	-1.26190234391819
S.D.	2.23805046794231
T-STAT	-0.563839985734724
p-value	0.582459672911399
Lambda	2.26190234391819

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.944386790988822 \tabularnewline
beta & -1.26190234391819 \tabularnewline
S.D. & 2.23805046794231 \tabularnewline
T-STAT & -0.563839985734724 \tabularnewline
p-value & 0.582459672911399 \tabularnewline
Lambda & 2.26190234391819 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35861&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.944386790988822[/C][/ROW]
[ROW][C]beta[/C][C]-1.26190234391819[/C][/ROW]
[ROW][C]S.D.[/C][C]2.23805046794231[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.563839985734724[/C][/ROW]
[ROW][C]p-value[/C][C]0.582459672911399[/C][/ROW]
[ROW][C]Lambda[/C][C]2.26190234391819[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35861&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35861&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	0.944386790988822
beta	-1.26190234391819
S.D.	2.23805046794231
T-STAT	-0.563839985734724
p-value	0.582459672911399
Lambda	2.26190234391819

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