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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationMon, 16 Aug 2010 16:32:56 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Aug/16/t1281976354e3ymnoh09en3mis.htm/, Retrieved Thu, 16 May 2024 15:58:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79028, Retrieved Thu, 16 May 2024 15:58:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact113

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Standard Deviation-Mean Plot] [Standard Deviatio...] [2010-08-16 16:32:56] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
257
256
255
253
251
250
251
253
254
254
255
257
260
251
255
252
245
239
240
247
251
255
259
260
259
266
261
243
232
225
229
238
240
241
239
246
242
251
246
219
203
192
197
203
208
207
208
212
208
215
200
170
162
150
148
152
155
150
146
147
142
146
130
102
98
90
86
104
108
94
88
92
93
95
81
50
49
34
27
45
47
42
32

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'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79028&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79028&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79028&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'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1253.8333333333332.329000305762637
2251.1666666666677.2341781380702421
3243.2512.835497652993441
4215.66666666666719.791335722910959
5166.91666666666725.685009187650669
6106.66666666666721.051164223185360

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 253.833333333333 & 2.32900030576263 & 7 \tabularnewline
2 & 251.166666666667 & 7.23417813807024 & 21 \tabularnewline
3 & 243.25 & 12.8354976529934 & 41 \tabularnewline
4 & 215.666666666667 & 19.7913357229109 & 59 \tabularnewline
5 & 166.916666666667 & 25.6850091876506 & 69 \tabularnewline
6 & 106.666666666667 & 21.0511642231853 & 60 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79028&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]253.833333333333[/C][C]2.32900030576263[/C][C]7[/C][/ROW]
[ROW][C]2[/C][C]251.166666666667[/C][C]7.23417813807024[/C][C]21[/C][/ROW]
[ROW][C]3[/C][C]243.25[/C][C]12.8354976529934[/C][C]41[/C][/ROW]
[ROW][C]4[/C][C]215.666666666667[/C][C]19.7913357229109[/C][C]59[/C][/ROW]
[ROW][C]5[/C][C]166.916666666667[/C][C]25.6850091876506[/C][C]69[/C][/ROW]
[ROW][C]6[/C][C]106.666666666667[/C][C]21.0511642231853[/C][C]60[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79028&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79028&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
1253.8333333333332.329000305762637
2251.1666666666677.2341781380702421
3243.2512.835497652993441
4215.66666666666719.791335722910959
5166.91666666666725.685009187650669
6106.66666666666721.051164223185360






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha38.9138776848269
beta-0.116813802730011
S.D.0.048870876695405
T-STAT-2.39025388183785
p-value0.075147048753332

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 38.9138776848269 \tabularnewline
beta & -0.116813802730011 \tabularnewline
S.D. & 0.048870876695405 \tabularnewline
T-STAT & -2.39025388183785 \tabularnewline
p-value & 0.075147048753332 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79028&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]38.9138776848269[/C][/ROW]
[ROW][C]beta[/C][C]-0.116813802730011[/C][/ROW]
[ROW][C]S.D.[/C][C]0.048870876695405[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.39025388183785[/C][/ROW]
[ROW][C]p-value[/C][C]0.075147048753332[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79028&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79028&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)
alpha38.9138776848269
beta-0.116813802730011
S.D.0.048870876695405
T-STAT-2.39025388183785
p-value0.075147048753332






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha11.0976095013278
beta-1.63728390108373
S.D.1.04434748967207
T-STAT-1.56775777916396
p-value0.192009420321788
Lambda2.63728390108373

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 11.0976095013278 \tabularnewline
beta & -1.63728390108373 \tabularnewline
S.D. & 1.04434748967207 \tabularnewline
T-STAT & -1.56775777916396 \tabularnewline
p-value & 0.192009420321788 \tabularnewline
Lambda & 2.63728390108373 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79028&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]11.0976095013278[/C][/ROW]
[ROW][C]beta[/C][C]-1.63728390108373[/C][/ROW]
[ROW][C]S.D.[/C][C]1.04434748967207[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.56775777916396[/C][/ROW]
[ROW][C]p-value[/C][C]0.192009420321788[/C][/ROW]
[ROW][C]Lambda[/C][C]2.63728390108373[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79028&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79028&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)
alpha11.0976095013278
beta-1.63728390108373
S.D.1.04434748967207
T-STAT-1.56775777916396
p-value0.192009420321788
Lambda2.63728390108373


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 0.1 ; par2 = 0.9 ; par3 = 0.1 ;
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')