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

Wed, 25 Jul 2012 09:23:20 -0400

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/2012/Jul/25/t1343222654fdh3ti4kobabxcq.htm/, Retrieved Sat, 26 Apr 2025 05:09:40 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=168869, Retrieved Sat, 26 Apr 2025 05:09:40 +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

Van Maele Karen

Estimated Impact

185

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

-       [Standard Deviation-Mean Plot] [Deviation mean pl...] [2012-07-25 13:23:20] [459538fe31c621d37110fb87514358a8] [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	1 seconds
R Server	'Gertrude Mary Cox' @ cox.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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168869&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168869&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168869&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	'Gertrude Mary Cox' @ cox.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	14232.0833333333	2851.63823595979	8484
2	16169.1666666667	3530.11137690206	11431
3	20203.0833333333	4723.66341765936	15707
4	26961.9166666667	4324.99796023774	16373
5	32854.5	4515.68689026477	16369
6	32989.3333333333	4614.70588707909	15386
7	32825.6666666667	4354.03756891407	15356
8	36398.1666666667	4880.27623721395	18969
9	38363.5833333333	5830.77619124798	21591
10	40567.0833333333	5259.5759673248	17666

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 14232.0833333333 & 2851.63823595979 & 8484 \tabularnewline
2 & 16169.1666666667 & 3530.11137690206 & 11431 \tabularnewline
3 & 20203.0833333333 & 4723.66341765936 & 15707 \tabularnewline
4 & 26961.9166666667 & 4324.99796023774 & 16373 \tabularnewline
5 & 32854.5 & 4515.68689026477 & 16369 \tabularnewline
6 & 32989.3333333333 & 4614.70588707909 & 15386 \tabularnewline
7 & 32825.6666666667 & 4354.03756891407 & 15356 \tabularnewline
8 & 36398.1666666667 & 4880.27623721395 & 18969 \tabularnewline
9 & 38363.5833333333 & 5830.77619124798 & 21591 \tabularnewline
10 & 40567.0833333333 & 5259.5759673248 & 17666 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168869&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]14232.0833333333[/C][C]2851.63823595979[/C][C]8484[/C][/ROW]
[ROW][C]2[/C][C]16169.1666666667[/C][C]3530.11137690206[/C][C]11431[/C][/ROW]
[ROW][C]3[/C][C]20203.0833333333[/C][C]4723.66341765936[/C][C]15707[/C][/ROW]
[ROW][C]4[/C][C]26961.9166666667[/C][C]4324.99796023774[/C][C]16373[/C][/ROW]
[ROW][C]5[/C][C]32854.5[/C][C]4515.68689026477[/C][C]16369[/C][/ROW]
[ROW][C]6[/C][C]32989.3333333333[/C][C]4614.70588707909[/C][C]15386[/C][/ROW]
[ROW][C]7[/C][C]32825.6666666667[/C][C]4354.03756891407[/C][C]15356[/C][/ROW]
[ROW][C]8[/C][C]36398.1666666667[/C][C]4880.27623721395[/C][C]18969[/C][/ROW]
[ROW][C]9[/C][C]38363.5833333333[/C][C]5830.77619124798[/C][C]21591[/C][/ROW]
[ROW][C]10[/C][C]40567.0833333333[/C][C]5259.5759673248[/C][C]17666[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168869&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168869&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	14232.0833333333	2851.63823595979	8484
2	16169.1666666667	3530.11137690206	11431
3	20203.0833333333	4723.66341765936	15707
4	26961.9166666667	4324.99796023774	16373
5	32854.5	4515.68689026477	16369
6	32989.3333333333	4614.70588707909	15386
7	32825.6666666667	4354.03756891407	15356
8	36398.1666666667	4880.27623721395	18969
9	38363.5833333333	5830.77619124798	21591
10	40567.0833333333	5259.5759673248	17666

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	2290.97655623932
beta	0.0753716515194388
S.D.	0.0169291902138178
T-STAT	4.45217110608866
p-value	0.00213313507645315

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 2290.97655623932 \tabularnewline
beta & 0.0753716515194388 \tabularnewline
S.D. & 0.0169291902138178 \tabularnewline
T-STAT & 4.45217110608866 \tabularnewline
p-value & 0.00213313507645315 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168869&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2290.97655623932[/C][/ROW]
[ROW][C]beta[/C][C]0.0753716515194388[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0169291902138178[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.45217110608866[/C][/ROW]
[ROW][C]p-value[/C][C]0.00213313507645315[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168869&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168869&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	2290.97655623932
beta	0.0753716515194388
S.D.	0.0169291902138178
T-STAT	4.45217110608866
p-value	0.00213313507645315

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	3.60251228253677
beta	0.468453961525005
S.D.	0.0964665506847869
T-STAT	4.85612845281179
p-value	0.00126199092221761
Lambda	0.531546038474995

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 3.60251228253677 \tabularnewline
beta & 0.468453961525005 \tabularnewline
S.D. & 0.0964665506847869 \tabularnewline
T-STAT & 4.85612845281179 \tabularnewline
p-value & 0.00126199092221761 \tabularnewline
Lambda & 0.531546038474995 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168869&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.60251228253677[/C][/ROW]
[ROW][C]beta[/C][C]0.468453961525005[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0964665506847869[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.85612845281179[/C][/ROW]
[ROW][C]p-value[/C][C]0.00126199092221761[/C][/ROW]
[ROW][C]Lambda[/C][C]0.531546038474995[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168869&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168869&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	3.60251228253677
beta	0.468453961525005
S.D.	0.0964665506847869
T-STAT	4.85612845281179
p-value	0.00126199092221761
Lambda	0.531546038474995

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