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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, 17 May 2008 03:56:30 -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/2008/May/17/t12110183646lj20v1b3cqzgyg.htm/, Retrieved Tue, 14 May 2024 11:33:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=12631, Retrieved Tue, 14 May 2024 11:33:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact222

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] [Verbetering eigen...] [2008-05-17 09:56:30] [dd867cfc9ddc7089fae26da93ef9f864] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
36409
33163
34122
35225
28249
30374
26311
22069
23651
28628
23187
14727
43080
32519
39657
33614
28671
34243
27336
22916
24537
26128
22602
15744
41086
39690
43129
37863
35953
29133
24693
22205
21725
27192
21790
13253
37702
30364
32609
30212
29965
28352
25814
22414
20506
28806
22228
13971
36845
35338
35022
34777
26887
23970
22780
17351
21382
24561
17409
11514
31514
27071
29462
26105
22397
23843
21705
18089
20764
25316
17704
15548
28029
29383
36438
32034
22679
24319
18004
17537
20366
22782
19169
13807
29743
25591
29096
26482
22405
27044
17970
18730
19684
19785
18479
10698
31956
29506
34506
27165
26736
23691
18157
17328
18205
20995
17382
9367

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12631&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12631&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12631&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
128009.58333333336391.8932955357721682
229253.91666666677727.8754984599127336
329809.33333333339534.1464349161529876
426911.91666666676314.1373766022923731
5256538306.2242051039425331
623293.16666666674863.9772508688515966
723712.256639.8206865848422631
822142.255608.3585043786519045
922916.16666666677303.0689045251725139

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 28009.5833333333 & 6391.89329553577 & 21682 \tabularnewline
2 & 29253.9166666667 & 7727.87549845991 & 27336 \tabularnewline
3 & 29809.3333333333 & 9534.14643491615 & 29876 \tabularnewline
4 & 26911.9166666667 & 6314.13737660229 & 23731 \tabularnewline
5 & 25653 & 8306.22420510394 & 25331 \tabularnewline
6 & 23293.1666666667 & 4863.97725086885 & 15966 \tabularnewline
7 & 23712.25 & 6639.82068658484 & 22631 \tabularnewline
8 & 22142.25 & 5608.35850437865 & 19045 \tabularnewline
9 & 22916.1666666667 & 7303.06890452517 & 25139 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12631&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]28009.5833333333[/C][C]6391.89329553577[/C][C]21682[/C][/ROW]
[ROW][C]2[/C][C]29253.9166666667[/C][C]7727.87549845991[/C][C]27336[/C][/ROW]
[ROW][C]3[/C][C]29809.3333333333[/C][C]9534.14643491615[/C][C]29876[/C][/ROW]
[ROW][C]4[/C][C]26911.9166666667[/C][C]6314.13737660229[/C][C]23731[/C][/ROW]
[ROW][C]5[/C][C]25653[/C][C]8306.22420510394[/C][C]25331[/C][/ROW]
[ROW][C]6[/C][C]23293.1666666667[/C][C]4863.97725086885[/C][C]15966[/C][/ROW]
[ROW][C]7[/C][C]23712.25[/C][C]6639.82068658484[/C][C]22631[/C][/ROW]
[ROW][C]8[/C][C]22142.25[/C][C]5608.35850437865[/C][C]19045[/C][/ROW]
[ROW][C]9[/C][C]22916.1666666667[/C][C]7303.06890452517[/C][C]25139[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12631&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12631&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
128009.58333333336391.8932955357721682
229253.91666666677727.8754984599127336
329809.33333333339534.1464349161529876
426911.91666666676314.1373766022923731
5256538306.2242051039425331
623293.16666666674863.9772508688515966
723712.256639.8206865848422631
822142.255608.3585043786519045
922916.16666666677303.0689045251725139






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-1046.50401955173
beta0.311210813908010
S.D.0.144935589778847
T-STAT2.14723529522926
p-value0.0688943077262728

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -1046.50401955173 \tabularnewline
beta & 0.311210813908010 \tabularnewline
S.D. & 0.144935589778847 \tabularnewline
T-STAT & 2.14723529522926 \tabularnewline
p-value & 0.0688943077262728 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12631&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1046.50401955173[/C][/ROW]
[ROW][C]beta[/C][C]0.311210813908010[/C][/ROW]
[ROW][C]S.D.[/C][C]0.144935589778847[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.14723529522926[/C][/ROW]
[ROW][C]p-value[/C][C]0.0688943077262728[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12631&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12631&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-1046.50401955173
beta0.311210813908010
S.D.0.144935589778847
T-STAT2.14723529522926
p-value0.0688943077262728






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.69448436012349
beta1.13538887424389
S.D.0.543656478133692
T-STAT2.08843069090531
p-value0.0751439394222767
Lambda-0.135388874243893

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.69448436012349 \tabularnewline
beta & 1.13538887424389 \tabularnewline
S.D. & 0.543656478133692 \tabularnewline
T-STAT & 2.08843069090531 \tabularnewline
p-value & 0.0751439394222767 \tabularnewline
Lambda & -0.135388874243893 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12631&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.69448436012349[/C][/ROW]
[ROW][C]beta[/C][C]1.13538887424389[/C][/ROW]
[ROW][C]S.D.[/C][C]0.543656478133692[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.08843069090531[/C][/ROW]
[ROW][C]p-value[/C][C]0.0751439394222767[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.135388874243893[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12631&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12631&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-2.69448436012349
beta1.13538887424389
S.D.0.543656478133692
T-STAT2.08843069090531
p-value0.0751439394222767
Lambda-0.135388874243893


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')