Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*Unverified author*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Fri, 13 Aug 2010 09:10:22 +0000

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/2010/Aug/13/t12816906001t0u8amlrwkis8q.htm/, Retrieved Mon, 06 May 2024 10:04:42 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78710, Retrieved Mon, 06 May 2024 10:04:42 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

mattias debbaut

Estimated Impact

134

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

-       [Standard Deviation-Mean Plot] [SD mean plot - ma...] [2010-08-13 09:10:22] [59fa324537f53fb6459bc6951db20f7b] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	8 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 & 8 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78710&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]8 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=78710&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78710&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	8 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	898.25	1.70782512765993	4
2	905.25	12.5266382827424	26
3	892	1.41421356237310	3
4	886.5	7.76745346515403	18
5	886.25	16.0286202358989	35
6	866.5	3.69684550213647	9
7	856.75	7.5	18
8	859.25	15.2616076042685	33
9	825.75	2.98607881119482	7
10	815	5.29150262212918	12
11	811.5	13.5277492584687	30
12	769.75	5.85234995535981	12
13	742.75	7.27438428093173	17
14	729.75	16.5403546918841	35
15	694	4.39696865275764	10
16	654	13.4412301024373	31
17	636.5	21.4242852856285	45
18	595.5	4.79583152331272	10
19	539.75	19.8053023203384	45
20	516.75	19.3627649540727	43
21	470.25	10.1447851956888	19
22	413.25	16.4595463687997	37
23	388.25	17.3469497799085	41
24	337.75	10.0457287772798	22
25	279.75	17.8582380616529	38
26	251.75	20.4022057631032	48
27	194.5	14.247806848775	33
28	128	18.3484785926972	39
29	91.75	21.5154982899924	48
30	37.75	12.5532200384337	29

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 898.25 & 1.70782512765993 & 4 \tabularnewline
2 & 905.25 & 12.5266382827424 & 26 \tabularnewline
3 & 892 & 1.41421356237310 & 3 \tabularnewline
4 & 886.5 & 7.76745346515403 & 18 \tabularnewline
5 & 886.25 & 16.0286202358989 & 35 \tabularnewline
6 & 866.5 & 3.69684550213647 & 9 \tabularnewline
7 & 856.75 & 7.5 & 18 \tabularnewline
8 & 859.25 & 15.2616076042685 & 33 \tabularnewline
9 & 825.75 & 2.98607881119482 & 7 \tabularnewline
10 & 815 & 5.29150262212918 & 12 \tabularnewline
11 & 811.5 & 13.5277492584687 & 30 \tabularnewline
12 & 769.75 & 5.85234995535981 & 12 \tabularnewline
13 & 742.75 & 7.27438428093173 & 17 \tabularnewline
14 & 729.75 & 16.5403546918841 & 35 \tabularnewline
15 & 694 & 4.39696865275764 & 10 \tabularnewline
16 & 654 & 13.4412301024373 & 31 \tabularnewline
17 & 636.5 & 21.4242852856285 & 45 \tabularnewline
18 & 595.5 & 4.79583152331272 & 10 \tabularnewline
19 & 539.75 & 19.8053023203384 & 45 \tabularnewline
20 & 516.75 & 19.3627649540727 & 43 \tabularnewline
21 & 470.25 & 10.1447851956888 & 19 \tabularnewline
22 & 413.25 & 16.4595463687997 & 37 \tabularnewline
23 & 388.25 & 17.3469497799085 & 41 \tabularnewline
24 & 337.75 & 10.0457287772798 & 22 \tabularnewline
25 & 279.75 & 17.8582380616529 & 38 \tabularnewline
26 & 251.75 & 20.4022057631032 & 48 \tabularnewline
27 & 194.5 & 14.247806848775 & 33 \tabularnewline
28 & 128 & 18.3484785926972 & 39 \tabularnewline
29 & 91.75 & 21.5154982899924 & 48 \tabularnewline
30 & 37.75 & 12.5532200384337 & 29 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78710&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]898.25[/C][C]1.70782512765993[/C][C]4[/C][/ROW]
[ROW][C]2[/C][C]905.25[/C][C]12.5266382827424[/C][C]26[/C][/ROW]
[ROW][C]3[/C][C]892[/C][C]1.41421356237310[/C][C]3[/C][/ROW]
[ROW][C]4[/C][C]886.5[/C][C]7.76745346515403[/C][C]18[/C][/ROW]
[ROW][C]5[/C][C]886.25[/C][C]16.0286202358989[/C][C]35[/C][/ROW]
[ROW][C]6[/C][C]866.5[/C][C]3.69684550213647[/C][C]9[/C][/ROW]
[ROW][C]7[/C][C]856.75[/C][C]7.5[/C][C]18[/C][/ROW]
[ROW][C]8[/C][C]859.25[/C][C]15.2616076042685[/C][C]33[/C][/ROW]
[ROW][C]9[/C][C]825.75[/C][C]2.98607881119482[/C][C]7[/C][/ROW]
[ROW][C]10[/C][C]815[/C][C]5.29150262212918[/C][C]12[/C][/ROW]
[ROW][C]11[/C][C]811.5[/C][C]13.5277492584687[/C][C]30[/C][/ROW]
[ROW][C]12[/C][C]769.75[/C][C]5.85234995535981[/C][C]12[/C][/ROW]
[ROW][C]13[/C][C]742.75[/C][C]7.27438428093173[/C][C]17[/C][/ROW]
[ROW][C]14[/C][C]729.75[/C][C]16.5403546918841[/C][C]35[/C][/ROW]
[ROW][C]15[/C][C]694[/C][C]4.39696865275764[/C][C]10[/C][/ROW]
[ROW][C]16[/C][C]654[/C][C]13.4412301024373[/C][C]31[/C][/ROW]
[ROW][C]17[/C][C]636.5[/C][C]21.4242852856285[/C][C]45[/C][/ROW]
[ROW][C]18[/C][C]595.5[/C][C]4.79583152331272[/C][C]10[/C][/ROW]
[ROW][C]19[/C][C]539.75[/C][C]19.8053023203384[/C][C]45[/C][/ROW]
[ROW][C]20[/C][C]516.75[/C][C]19.3627649540727[/C][C]43[/C][/ROW]
[ROW][C]21[/C][C]470.25[/C][C]10.1447851956888[/C][C]19[/C][/ROW]
[ROW][C]22[/C][C]413.25[/C][C]16.4595463687997[/C][C]37[/C][/ROW]
[ROW][C]23[/C][C]388.25[/C][C]17.3469497799085[/C][C]41[/C][/ROW]
[ROW][C]24[/C][C]337.75[/C][C]10.0457287772798[/C][C]22[/C][/ROW]
[ROW][C]25[/C][C]279.75[/C][C]17.8582380616529[/C][C]38[/C][/ROW]
[ROW][C]26[/C][C]251.75[/C][C]20.4022057631032[/C][C]48[/C][/ROW]
[ROW][C]27[/C][C]194.5[/C][C]14.247806848775[/C][C]33[/C][/ROW]
[ROW][C]28[/C][C]128[/C][C]18.3484785926972[/C][C]39[/C][/ROW]
[ROW][C]29[/C][C]91.75[/C][C]21.5154982899924[/C][C]48[/C][/ROW]
[ROW][C]30[/C][C]37.75[/C][C]12.5532200384337[/C][C]29[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78710&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78710&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	898.25	1.70782512765993	4
2	905.25	12.5266382827424	26
3	892	1.41421356237310	3
4	886.5	7.76745346515403	18
5	886.25	16.0286202358989	35
6	866.5	3.69684550213647	9
7	856.75	7.5	18
8	859.25	15.2616076042685	33
9	825.75	2.98607881119482	7
10	815	5.29150262212918	12
11	811.5	13.5277492584687	30
12	769.75	5.85234995535981	12
13	742.75	7.27438428093173	17
14	729.75	16.5403546918841	35
15	694	4.39696865275764	10
16	654	13.4412301024373	31
17	636.5	21.4242852856285	45
18	595.5	4.79583152331272	10
19	539.75	19.8053023203384	45
20	516.75	19.3627649540727	43
21	470.25	10.1447851956888	19
22	413.25	16.4595463687997	37
23	388.25	17.3469497799085	41
24	337.75	10.0457287772798	22
25	279.75	17.8582380616529	38
26	251.75	20.4022057631032	48
27	194.5	14.247806848775	33
28	128	18.3484785926972	39
29	91.75	21.5154982899924	48
30	37.75	12.5532200384337	29

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	19.8933301090762
beta	-0.0132004861996526
S.D.	0.00356133775417746
T-STAT	-3.70660889553887
p-value	0.000917399785517359

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 19.8933301090762 \tabularnewline
beta & -0.0132004861996526 \tabularnewline
S.D. & 0.00356133775417746 \tabularnewline
T-STAT & -3.70660889553887 \tabularnewline
p-value & 0.000917399785517359 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78710&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]19.8933301090762[/C][/ROW]
[ROW][C]beta[/C][C]-0.0132004861996526[/C][/ROW]
[ROW][C]S.D.[/C][C]0.00356133775417746[/C][/ROW]
[ROW][C]T-STAT[/C][C]-3.70660889553887[/C][/ROW]
[ROW][C]p-value[/C][C]0.000917399785517359[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78710&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78710&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	19.8933301090762
beta	-0.0132004861996526
S.D.	0.00356133775417746
T-STAT	-3.70660889553887
p-value	0.000917399785517359

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	4.944861159188
beta	-0.430806614225836
S.D.	0.164496459373270
T-STAT	-2.61894156182573
p-value	0.0140781558162691
Lambda	1.43080661422584

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 4.944861159188 \tabularnewline
beta & -0.430806614225836 \tabularnewline
S.D. & 0.164496459373270 \tabularnewline
T-STAT & -2.61894156182573 \tabularnewline
p-value & 0.0140781558162691 \tabularnewline
Lambda & 1.43080661422584 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78710&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]4.944861159188[/C][/ROW]
[ROW][C]beta[/C][C]-0.430806614225836[/C][/ROW]
[ROW][C]S.D.[/C][C]0.164496459373270[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.61894156182573[/C][/ROW]
[ROW][C]p-value[/C][C]0.0140781558162691[/C][/ROW]
[ROW][C]Lambda[/C][C]1.43080661422584[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78710&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78710&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	4.944861159188
beta	-0.430806614225836
S.D.	0.164496459373270
T-STAT	-2.61894156182573
p-value	0.0140781558162691
Lambda	1.43080661422584

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