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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 computationSat, 23 May 2009 04:22:58 -0600
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/May/23/t124307421416zksd8y6pmq3d4.htm/, Retrieved Sat, 04 May 2024 03:45:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=40317, Retrieved Sat, 04 May 2024 03:45:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact207

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] [Goudprijs-Deviati...] [2009-05-23 10:22:58] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9721
9897
9828
9924
10371
10846
10413
10709
10662
10570
10297
10635
10872
10296
10383
10431
10574
10653
10805
10872
10625
10407
10463
10556
10646
10702
11353
11346
11451
11964
12574
13031
13812
14544
14931
14886
16005
17064
15168
16050
15839
15137
14954
15648
15305
15579
16348
15928
16171
15937
15713
15594
15683
16438
17032
17696
17745
19394
20148
20108
18584
18441
18391
19178
18079
18483
19644
19195
19650
20830
23595
22937

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=40317&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=40317&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40317&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
110322.75387.8828607148861125
210578.0833333333194.085013394240576
312603.33333333331605.855271036334285
415752.0833333333592.7253630988012110
517304.91666666671724.853799250214554
619750.58333333331811.109226078845516

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 10322.75 & 387.882860714886 & 1125 \tabularnewline
2 & 10578.0833333333 & 194.085013394240 & 576 \tabularnewline
3 & 12603.3333333333 & 1605.85527103633 & 4285 \tabularnewline
4 & 15752.0833333333 & 592.725363098801 & 2110 \tabularnewline
5 & 17304.9166666667 & 1724.85379925021 & 4554 \tabularnewline
6 & 19750.5833333333 & 1811.10922607884 & 5516 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40317&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]10322.75[/C][C]387.882860714886[/C][C]1125[/C][/ROW]
[ROW][C]2[/C][C]10578.0833333333[/C][C]194.085013394240[/C][C]576[/C][/ROW]
[ROW][C]3[/C][C]12603.3333333333[/C][C]1605.85527103633[/C][C]4285[/C][/ROW]
[ROW][C]4[/C][C]15752.0833333333[/C][C]592.725363098801[/C][C]2110[/C][/ROW]
[ROW][C]5[/C][C]17304.9166666667[/C][C]1724.85379925021[/C][C]4554[/C][/ROW]
[ROW][C]6[/C][C]19750.5833333333[/C][C]1811.10922607884[/C][C]5516[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40317&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40317&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
110322.75387.8828607148861125
210578.0833333333194.085013394240576
312603.33333333331605.855271036334285
415752.0833333333592.7253630988012110
517304.91666666671724.853799250214554
619750.58333333331811.109226078845516






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-984.22566506168
beta0.141601410282417
S.D.0.0653468474434982
T-STAT2.16692030024634
p-value0.0961409817965038

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -984.22566506168 \tabularnewline
beta & 0.141601410282417 \tabularnewline
S.D. & 0.0653468474434982 \tabularnewline
T-STAT & 2.16692030024634 \tabularnewline
p-value & 0.0961409817965038 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40317&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-984.22566506168[/C][/ROW]
[ROW][C]beta[/C][C]0.141601410282417[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0653468474434982[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.16692030024634[/C][/ROW]
[ROW][C]p-value[/C][C]0.0961409817965038[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40317&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40317&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)
alpha-984.22566506168
beta0.141601410282417
S.D.0.0653468474434982
T-STAT2.16692030024634
p-value0.0961409817965038






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-18.6195576482482
beta2.64852318171134
S.D.1.12984090721453
T-STAT2.34415585840391
p-value0.079018408047275
Lambda-1.64852318171134

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -18.6195576482482 \tabularnewline
beta & 2.64852318171134 \tabularnewline
S.D. & 1.12984090721453 \tabularnewline
T-STAT & 2.34415585840391 \tabularnewline
p-value & 0.079018408047275 \tabularnewline
Lambda & -1.64852318171134 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40317&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-18.6195576482482[/C][/ROW]
[ROW][C]beta[/C][C]2.64852318171134[/C][/ROW]
[ROW][C]S.D.[/C][C]1.12984090721453[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.34415585840391[/C][/ROW]
[ROW][C]p-value[/C][C]0.079018408047275[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.64852318171134[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40317&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40317&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)
alpha-18.6195576482482
beta2.64852318171134
S.D.1.12984090721453
T-STAT2.34415585840391
p-value0.079018408047275
Lambda-1.64852318171134


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')