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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

Mon, 05 Dec 2011 12:07:43 -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/05/t1323105479ivimcxwi8yjc714.htm/, Retrieved Fri, 03 May 2024 12:34:29 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=151083, Retrieved Fri, 03 May 2024 12:34:29 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

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

-     [Univariate Data Series] [] [2008-12-14 11:54:22] [d2d412c7f4d35ffbf5ee5ee89db327d4]
- RMP     [Standard Deviation-Mean Plot] [] [2011-12-05 17:07:43] [ef12b3094dcc95645ac503919f1fca4e] [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	2 seconds
R Server	'George Udny Yule' @ yule.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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151083&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151083&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151083&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	'George Udny Yule' @ yule.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	58.6666666666667	6.80196050169851	20
2	50.6666666666667	15.1877143331927	43
3	51.1666666666667	12.5286338707246	36
4	49.8333333333333	8.58875233469138	26
5	58.1666666666667	10.6848802832164	29
6	44	12.8218563398597	34
7	54.3333333333333	9.83192080250175	24
8	45.1666666666667	16.3268694692726	42
9	54.6666666666667	3.98329846567724	10
10	50.6666666666667	17.7951304200522	48
11	49.5	8.96102672688794	23
12	56.6666666666667	14.6924016643525	33

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 58.6666666666667 & 6.80196050169851 & 20 \tabularnewline
2 & 50.6666666666667 & 15.1877143331927 & 43 \tabularnewline
3 & 51.1666666666667 & 12.5286338707246 & 36 \tabularnewline
4 & 49.8333333333333 & 8.58875233469138 & 26 \tabularnewline
5 & 58.1666666666667 & 10.6848802832164 & 29 \tabularnewline
6 & 44 & 12.8218563398597 & 34 \tabularnewline
7 & 54.3333333333333 & 9.83192080250175 & 24 \tabularnewline
8 & 45.1666666666667 & 16.3268694692726 & 42 \tabularnewline
9 & 54.6666666666667 & 3.98329846567724 & 10 \tabularnewline
10 & 50.6666666666667 & 17.7951304200522 & 48 \tabularnewline
11 & 49.5 & 8.96102672688794 & 23 \tabularnewline
12 & 56.6666666666667 & 14.6924016643525 & 33 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151083&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]58.6666666666667[/C][C]6.80196050169851[/C][C]20[/C][/ROW]
[ROW][C]2[/C][C]50.6666666666667[/C][C]15.1877143331927[/C][C]43[/C][/ROW]
[ROW][C]3[/C][C]51.1666666666667[/C][C]12.5286338707246[/C][C]36[/C][/ROW]
[ROW][C]4[/C][C]49.8333333333333[/C][C]8.58875233469138[/C][C]26[/C][/ROW]
[ROW][C]5[/C][C]58.1666666666667[/C][C]10.6848802832164[/C][C]29[/C][/ROW]
[ROW][C]6[/C][C]44[/C][C]12.8218563398597[/C][C]34[/C][/ROW]
[ROW][C]7[/C][C]54.3333333333333[/C][C]9.83192080250175[/C][C]24[/C][/ROW]
[ROW][C]8[/C][C]45.1666666666667[/C][C]16.3268694692726[/C][C]42[/C][/ROW]
[ROW][C]9[/C][C]54.6666666666667[/C][C]3.98329846567724[/C][C]10[/C][/ROW]
[ROW][C]10[/C][C]50.6666666666667[/C][C]17.7951304200522[/C][C]48[/C][/ROW]
[ROW][C]11[/C][C]49.5[/C][C]8.96102672688794[/C][C]23[/C][/ROW]
[ROW][C]12[/C][C]56.6666666666667[/C][C]14.6924016643525[/C][C]33[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151083&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151083&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	58.6666666666667	6.80196050169851	20
2	50.6666666666667	15.1877143331927	43
3	51.1666666666667	12.5286338707246	36
4	49.8333333333333	8.58875233469138	26
5	58.1666666666667	10.6848802832164	29
6	44	12.8218563398597	34
7	54.3333333333333	9.83192080250175	24
8	45.1666666666667	16.3268694692726	42
9	54.6666666666667	3.98329846567724	10
10	50.6666666666667	17.7951304200522	48
11	49.5	8.96102672688794	23
12	56.6666666666667	14.6924016643525	33

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	30.8826971675117
beta	-0.372715189732178
S.D.	0.2508873070664
T-STAT	-1.48558806776755
p-value	0.168216590724727

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 30.8826971675117 \tabularnewline
beta & -0.372715189732178 \tabularnewline
S.D. & 0.2508873070664 \tabularnewline
T-STAT & -1.48558806776755 \tabularnewline
p-value & 0.168216590724727 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151083&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]30.8826971675117[/C][/ROW]
[ROW][C]beta[/C][C]-0.372715189732178[/C][/ROW]
[ROW][C]S.D.[/C][C]0.2508873070664[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.48558806776755[/C][/ROW]
[ROW][C]p-value[/C][C]0.168216590724727[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151083&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151083&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	30.8826971675117
beta	-0.372715189732178
S.D.	0.2508873070664
T-STAT	-1.48558806776755
p-value	0.168216590724727

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	9.94809970340105
beta	-1.91980853788816
S.D.	1.33584742561157
T-STAT	-1.43714656410648
p-value	0.181219243245857
Lambda	2.91980853788816

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 9.94809970340105 \tabularnewline
beta & -1.91980853788816 \tabularnewline
S.D. & 1.33584742561157 \tabularnewline
T-STAT & -1.43714656410648 \tabularnewline
p-value & 0.181219243245857 \tabularnewline
Lambda & 2.91980853788816 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151083&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]9.94809970340105[/C][/ROW]
[ROW][C]beta[/C][C]-1.91980853788816[/C][/ROW]
[ROW][C]S.D.[/C][C]1.33584742561157[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.43714656410648[/C][/ROW]
[ROW][C]p-value[/C][C]0.181219243245857[/C][/ROW]
[ROW][C]Lambda[/C][C]2.91980853788816[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151083&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151083&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	9.94809970340105
beta	-1.91980853788816
S.D.	1.33584742561157
T-STAT	-1.43714656410648
p-value	0.181219243245857
Lambda	2.91980853788816

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 6 ;

Parameters (R input):

par1 = 6 ;

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