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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, 18 Dec 2016 09:05:21 +0100

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/2016/Dec/18/t1482049596st9c9otp10r5q5z.htm/, Retrieved Wed, 08 May 2024 18:43:26 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300976, Retrieved Wed, 08 May 2024 18:43:26 +0000

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Estimated Impact

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

-       [Standard Deviation-Mean Plot] [N 2460- SMP] [2016-12-18 08:05:21] [86c7fb9c8a0af864c0a27e2f433e80d7] [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	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300976&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

1 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300976&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300976&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	Big Analytics Cloud Computing Center

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	3712.5	514.836690788271	1800
2	3779.16666666667	503.378735660488	1850
3	4000	543.975266817427	2000
4	4091.66666666667	550.550688498398	2050
5	4233.33333333333	713.293683406687	2250
6	4741.66666666667	638.475931536589	2350
7	5004.16666666667	680.727663250989	2450
8	5220.83333333333	730.024387305387	2700
9	5583.33333333333	728.427114134325	2700
10	6016.66666666667	728.115042525228	2700

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 3712.5 & 514.836690788271 & 1800 \tabularnewline
2 & 3779.16666666667 & 503.378735660488 & 1850 \tabularnewline
3 & 4000 & 543.975266817427 & 2000 \tabularnewline
4 & 4091.66666666667 & 550.550688498398 & 2050 \tabularnewline
5 & 4233.33333333333 & 713.293683406687 & 2250 \tabularnewline
6 & 4741.66666666667 & 638.475931536589 & 2350 \tabularnewline
7 & 5004.16666666667 & 680.727663250989 & 2450 \tabularnewline
8 & 5220.83333333333 & 730.024387305387 & 2700 \tabularnewline
9 & 5583.33333333333 & 728.427114134325 & 2700 \tabularnewline
10 & 6016.66666666667 & 728.115042525228 & 2700 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300976&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]3712.5[/C][C]514.836690788271[/C][C]1800[/C][/ROW]
[ROW][C]2[/C][C]3779.16666666667[/C][C]503.378735660488[/C][C]1850[/C][/ROW]
[ROW][C]3[/C][C]4000[/C][C]543.975266817427[/C][C]2000[/C][/ROW]
[ROW][C]4[/C][C]4091.66666666667[/C][C]550.550688498398[/C][C]2050[/C][/ROW]
[ROW][C]5[/C][C]4233.33333333333[/C][C]713.293683406687[/C][C]2250[/C][/ROW]
[ROW][C]6[/C][C]4741.66666666667[/C][C]638.475931536589[/C][C]2350[/C][/ROW]
[ROW][C]7[/C][C]5004.16666666667[/C][C]680.727663250989[/C][C]2450[/C][/ROW]
[ROW][C]8[/C][C]5220.83333333333[/C][C]730.024387305387[/C][C]2700[/C][/ROW]
[ROW][C]9[/C][C]5583.33333333333[/C][C]728.427114134325[/C][C]2700[/C][/ROW]
[ROW][C]10[/C][C]6016.66666666667[/C][C]728.115042525228[/C][C]2700[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300976&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300976&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	3712.5	514.836690788271	1800
2	3779.16666666667	503.378735660488	1850
3	4000	543.975266817427	2000
4	4091.66666666667	550.550688498398	2050
5	4233.33333333333	713.293683406687	2250
6	4741.66666666667	638.475931536589	2350
7	5004.16666666667	680.727663250989	2450
8	5220.83333333333	730.024387305387	2700
9	5583.33333333333	728.427114134325	2700
10	6016.66666666667	728.115042525228	2700

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	159.867131349958
beta	0.102043849595923
S.D.	0.0218910893242062
T-STAT	4.66143315595936
p-value	0.00162043145046135

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 159.867131349958 \tabularnewline
beta & 0.102043849595923 \tabularnewline
S.D. & 0.0218910893242062 \tabularnewline
T-STAT & 4.66143315595936 \tabularnewline
p-value & 0.00162043145046135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300976&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]159.867131349958[/C][/ROW]
[ROW][C]beta[/C][C]0.102043849595923[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0218910893242062[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.66143315595936[/C][/ROW]
[ROW][C]p-value[/C][C]0.00162043145046135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300976&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300976&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	159.867131349958
beta	0.102043849595923
S.D.	0.0218910893242062
T-STAT	4.66143315595936
p-value	0.00162043145046135

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-0.275115173914633
beta	0.796680815492611
S.D.	0.158674365147212
T-STAT	5.02085396562626
p-value	0.00102578447305288
Lambda	0.203319184507389

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -0.275115173914633 \tabularnewline
beta & 0.796680815492611 \tabularnewline
S.D. & 0.158674365147212 \tabularnewline
T-STAT & 5.02085396562626 \tabularnewline
p-value & 0.00102578447305288 \tabularnewline
Lambda & 0.203319184507389 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300976&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.275115173914633[/C][/ROW]
[ROW][C]beta[/C][C]0.796680815492611[/C][/ROW]
[ROW][C]S.D.[/C][C]0.158674365147212[/C][/ROW]
[ROW][C]T-STAT[/C][C]5.02085396562626[/C][/ROW]
[ROW][C]p-value[/C][C]0.00102578447305288[/C][/ROW]
[ROW][C]Lambda[/C][C]0.203319184507389[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300976&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300976&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	-0.275115173914633
beta	0.796680815492611
S.D.	0.158674365147212
T-STAT	5.02085396562626
p-value	0.00102578447305288
Lambda	0.203319184507389

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