FreeStatistics.org

Free Statistics

of Irreproducible Research!

Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationTue, 24 Nov 2009 12:20:35 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/24/t125909053355llvdr7k05ovzc.htm/, Retrieved Mon, 10 Nov 2025 00:43:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=59247, Retrieved Mon, 10 Nov 2025 00:43:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact788

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Standard Deviation-Mean Plot] [Identifying Integ...] [2009-11-22 12:50:05] [b98453cac15ba1066b407e146608df68]
- R  D          [Standard Deviation-Mean Plot] [Heteroskedasticit...] [2009-11-24 19:20:35] [a931a0a30926b49d162330b43e89b999] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
325412
326011
328282
317480
317539
313737
312276
309391
302950
300316
304035
333476
337698
335932
323931
313927
314485
313218
309664
302963
298989
298423
310631
329765
335083
327616
309119
295916
291413
291542
284678
276475
272566
264981
263290
296806
303598
286994
276427
266424
267153
268381
262522
255542
253158
243803
250741
280445
285257
270976
261076
255603
260376
263903
264291
263276
262572
256167
264221
293860
300713
287224

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59247&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59247&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59247&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1315908.7510751.924877350233160
2315802.16666666713387.870058264339275
3292457.08333333322725.221380893271793
4267932.33333333316911.632620146059795
5266798.16666666711498.783831608538257

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 315908.75 & 10751.9248773502 & 33160 \tabularnewline
2 & 315802.166666667 & 13387.8700582643 & 39275 \tabularnewline
3 & 292457.083333333 & 22725.2213808932 & 71793 \tabularnewline
4 & 267932.333333333 & 16911.6326201460 & 59795 \tabularnewline
5 & 266798.166666667 & 11498.7838316085 & 38257 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59247&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]315908.75[/C][C]10751.9248773502[/C][C]33160[/C][/ROW]
[ROW][C]2[/C][C]315802.166666667[/C][C]13387.8700582643[/C][C]39275[/C][/ROW]
[ROW][C]3[/C][C]292457.083333333[/C][C]22725.2213808932[/C][C]71793[/C][/ROW]
[ROW][C]4[/C][C]267932.333333333[/C][C]16911.6326201460[/C][C]59795[/C][/ROW]
[ROW][C]5[/C][C]266798.166666667[/C][C]11498.7838316085[/C][C]38257[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59247&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59247&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1315908.7510751.924877350233160
2315802.16666666713387.870058264339275
3292457.08333333322725.221380893271793
4267932.33333333316911.632620146059795
5266798.16666666711498.783831608538257






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha26728.4035965120
beta-0.0400072967477159
S.D.0.114456642440636
T-STAT-0.349541065460366
p-value0.749780780575886

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 26728.4035965120 \tabularnewline
beta & -0.0400072967477159 \tabularnewline
S.D. & 0.114456642440636 \tabularnewline
T-STAT & -0.349541065460366 \tabularnewline
p-value & 0.749780780575886 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59247&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]26728.4035965120[/C][/ROW]
[ROW][C]beta[/C][C]-0.0400072967477159[/C][/ROW]
[ROW][C]S.D.[/C][C]0.114456642440636[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.349541065460366[/C][/ROW]
[ROW][C]p-value[/C][C]0.749780780575886[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59247&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59247&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha26728.4035965120
beta-0.0400072967477159
S.D.0.114456642440636
T-STAT-0.349541065460366
p-value0.749780780575886






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha19.2648068488478
beta-0.769766947369532
S.D.2.07297550823369
T-STAT-0.37133431838055
p-value0.735063057292018
Lambda1.76976694736953

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 19.2648068488478 \tabularnewline
beta & -0.769766947369532 \tabularnewline
S.D. & 2.07297550823369 \tabularnewline
T-STAT & -0.37133431838055 \tabularnewline
p-value & 0.735063057292018 \tabularnewline
Lambda & 1.76976694736953 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59247&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]19.2648068488478[/C][/ROW]
[ROW][C]beta[/C][C]-0.769766947369532[/C][/ROW]
[ROW][C]S.D.[/C][C]2.07297550823369[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.37133431838055[/C][/ROW]
[ROW][C]p-value[/C][C]0.735063057292018[/C][/ROW]
[ROW][C]Lambda[/C][C]1.76976694736953[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59247&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59247&T=3

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha19.2648068488478
beta-0.769766947369532
S.D.2.07297550823369
T-STAT-0.37133431838055
p-value0.735063057292018
Lambda1.76976694736953


Figures (Output of Computation)

Input Parameters & R Code

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')