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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 computationTue, 09 Dec 2008 09:53:45 -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/2008/Dec/09/t1228841697355uzjhaa7b0ozl.htm/, Retrieved Sun, 19 May 2024 09:25:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=31576, Retrieved Sun, 19 May 2024 09:25:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsSeverijns Britt
Estimated Impact143

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
F RMPD    [Standard Deviation-Mean Plot] [standard deviatio...] [2008-12-09 16:53:45] [78308c9f3efc33d1da821bcd963df161] [Current]
Feedback Forum
2008-12-15 17:47:38 [Steven Vercammen] [reply] 
Dit klopt. Het eerste wat we doen is kijken naar tabel 1: in deze tabel wordt een vergelijking weergegeven die het verband tussen het gemiddelde en de standaarddeviatie uitdrukt. Beta drukt hier de invloed van het gemiddelde op de standaarddeviatie uit, of nog: de helling van de regressielijn op de scatterplot op figuur 2. Alpha is een constante. De p-waarde is een getal dat uitdrukt of het gaat om een significant verband tussen het gemiddelde en de standaarddeviatie. Opdat dit het geval zou zijn moet deze waarde kleiner zijn dan 0.05. Dit is niet het geval dus kiezen we voor lambda = 1

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
492865
480961
461935
456608
441977
439148
488180
520564
501492
485025
464196
460170
467037
460070
447988
442867
436087
431328
484015
509673
512927
502831
470984
471067
476049
474605
470439
461251
454724
455626
516847
525192
522975
518585
509239
512238
519164
517009
509933
509127
500857
506971
569323
579714
577992
565464
547344
554788
562325
560854
555332
543599
536662
542722
593530
610763
612613
611324
594167
595454
590865
589379
584428
573100
567456
569028
620735
628884
628232
612117
595404
597141
593408
590072
579799
574205
572775
572942
619567
625809
619916
587625
565742
557274
560576
548854
531673
525919
511038
498662
555362
564591
541657
527070
509846
514258
516922
507561
492622
490243
469357
477580
528379
533590

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31576&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31576&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31576&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1474426.7524540.069612129981416
2469739.528068.080740487981599
3491480.83333333328234.064982291270468
4538140.530455.563407275078857
5576612.08333333329164.685309021375951
6596397.41666666721872.304573502661428
7588261.16666666722629.620286989668535
8532458.83333333321778.072975246365929

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 474426.75 & 24540.0696121299 & 81416 \tabularnewline
2 & 469739.5 & 28068.0807404879 & 81599 \tabularnewline
3 & 491480.833333333 & 28234.0649822912 & 70468 \tabularnewline
4 & 538140.5 & 30455.5634072750 & 78857 \tabularnewline
5 & 576612.083333333 & 29164.6853090213 & 75951 \tabularnewline
6 & 596397.416666667 & 21872.3045735026 & 61428 \tabularnewline
7 & 588261.166666667 & 22629.6202869896 & 68535 \tabularnewline
8 & 532458.833333333 & 21778.0729752463 & 65929 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31576&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]474426.75[/C][C]24540.0696121299[/C][C]81416[/C][/ROW]
[ROW][C]2[/C][C]469739.5[/C][C]28068.0807404879[/C][C]81599[/C][/ROW]
[ROW][C]3[/C][C]491480.833333333[/C][C]28234.0649822912[/C][C]70468[/C][/ROW]
[ROW][C]4[/C][C]538140.5[/C][C]30455.5634072750[/C][C]78857[/C][/ROW]
[ROW][C]5[/C][C]576612.083333333[/C][C]29164.6853090213[/C][C]75951[/C][/ROW]
[ROW][C]6[/C][C]596397.416666667[/C][C]21872.3045735026[/C][C]61428[/C][/ROW]
[ROW][C]7[/C][C]588261.166666667[/C][C]22629.6202869896[/C][C]68535[/C][/ROW]
[ROW][C]8[/C][C]532458.833333333[/C][C]21778.0729752463[/C][C]65929[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31576&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31576&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
1474426.7524540.069612129981416
2469739.528068.080740487981599
3491480.83333333328234.064982291270468
4538140.530455.563407275078857
5576612.08333333329164.685309021375951
6596397.41666666721872.304573502661428
7588261.16666666722629.620286989668535
8532458.83333333321778.072975246365929






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha38248.302410865
beta-0.0232556672795923
S.D.0.0266670887398313
T-STAT-0.872073720025405
p-value0.416695736342383

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 38248.302410865 \tabularnewline
beta & -0.0232556672795923 \tabularnewline
S.D. & 0.0266670887398313 \tabularnewline
T-STAT & -0.872073720025405 \tabularnewline
p-value & 0.416695736342383 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31576&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]38248.302410865[/C][/ROW]
[ROW][C]beta[/C][C]-0.0232556672795923[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0266670887398313[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.872073720025405[/C][/ROW]
[ROW][C]p-value[/C][C]0.416695736342383[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31576&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31576&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)
alpha38248.302410865
beta-0.0232556672795923
S.D.0.0266670887398313
T-STAT-0.872073720025405
p-value0.416695736342383






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha16.7556878069775
beta-0.500958301908446
S.D.0.548950482151325
T-STAT-0.91257466419412
p-value0.396651901882966
Lambda1.50095830190845

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 16.7556878069775 \tabularnewline
beta & -0.500958301908446 \tabularnewline
S.D. & 0.548950482151325 \tabularnewline
T-STAT & -0.91257466419412 \tabularnewline
p-value & 0.396651901882966 \tabularnewline
Lambda & 1.50095830190845 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31576&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]16.7556878069775[/C][/ROW]
[ROW][C]beta[/C][C]-0.500958301908446[/C][/ROW]
[ROW][C]S.D.[/C][C]0.548950482151325[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.91257466419412[/C][/ROW]
[ROW][C]p-value[/C][C]0.396651901882966[/C][/ROW]
[ROW][C]Lambda[/C][C]1.50095830190845[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31576&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31576&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)
alpha16.7556878069775
beta-0.500958301908446
S.D.0.548950482151325
T-STAT-0.91257466419412
p-value0.396651901882966
Lambda1.50095830190845


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')