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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 computationMon, 08 Dec 2008 13:34:45 -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/08/t12287687826xz4hlyed3kb4t5.htm/, Retrieved Thu, 16 May 2024 16:27:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30990, Retrieved Thu, 16 May 2024 16:27:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact235

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [Airline data] [2007-10-18 09:58:47] [42daae401fd3def69a25014f2252b4c2]
F RMPD  [Standard Deviation-Mean Plot] [] [2008-12-01 21:10:18] [cb714085b233acee8e8acd879ea442b6]
-   PD      [Standard Deviation-Mean Plot] [] [2008-12-08 20:34:45] [787873b6436f665b5b192a0bdb2e43c9] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
41
35
34
36
39
40
30
33
30
32
41
40
41
40
39
34
34
46
45
44
40
39
37
39
35
26
26
33
27
30
26
27
18
19
13
14
41
21
16
17
9
14
14
16
11
10
6
9
5
7
2
0
8
13
11
19
23
23
43
59

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=30990&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=30990&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30990&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
135.91666666666674.187825066532611
239.83333333333333.8336626999476212
324.57.0517567121443422
415.33333333333339.1087703324706235
517.7517.581627807562059

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 35.9166666666667 & 4.1878250665326 & 11 \tabularnewline
2 & 39.8333333333333 & 3.83366269994762 & 12 \tabularnewline
3 & 24.5 & 7.05175671214434 & 22 \tabularnewline
4 & 15.3333333333333 & 9.10877033247062 & 35 \tabularnewline
5 & 17.75 & 17.5816278075620 & 59 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30990&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]35.9166666666667[/C][C]4.1878250665326[/C][C]11[/C][/ROW]
[ROW][C]2[/C][C]39.8333333333333[/C][C]3.83366269994762[/C][C]12[/C][/ROW]
[ROW][C]3[/C][C]24.5[/C][C]7.05175671214434[/C][C]22[/C][/ROW]
[ROW][C]4[/C][C]15.3333333333333[/C][C]9.10877033247062[/C][C]35[/C][/ROW]
[ROW][C]5[/C][C]17.75[/C][C]17.5816278075620[/C][C]59[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30990&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30990&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
135.91666666666674.187825066532611
239.83333333333333.8336626999476212
324.57.0517567121443422
415.33333333333339.1087703324706235
517.7517.581627807562059






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha18.8745926354814
beta-0.394569904190624
S.D.0.191330252550155
T-STAT-2.06224524836809
p-value0.131213185592104

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 18.8745926354814 \tabularnewline
beta & -0.394569904190624 \tabularnewline
S.D. & 0.191330252550155 \tabularnewline
T-STAT & -2.06224524836809 \tabularnewline
p-value & 0.131213185592104 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30990&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]18.8745926354814[/C][/ROW]
[ROW][C]beta[/C][C]-0.394569904190624[/C][/ROW]
[ROW][C]S.D.[/C][C]0.191330252550155[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.06224524836809[/C][/ROW]
[ROW][C]p-value[/C][C]0.131213185592104[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30990&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30990&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)
alpha18.8745926354814
beta-0.394569904190624
S.D.0.191330252550155
T-STAT-2.06224524836809
p-value0.131213185592104






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha6.1132840914719
beta-1.29183361351408
S.D.0.416346718407664
T-STAT-3.10278322465169
p-value0.0531799025025303
Lambda2.29183361351408

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 6.1132840914719 \tabularnewline
beta & -1.29183361351408 \tabularnewline
S.D. & 0.416346718407664 \tabularnewline
T-STAT & -3.10278322465169 \tabularnewline
p-value & 0.0531799025025303 \tabularnewline
Lambda & 2.29183361351408 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30990&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]6.1132840914719[/C][/ROW]
[ROW][C]beta[/C][C]-1.29183361351408[/C][/ROW]
[ROW][C]S.D.[/C][C]0.416346718407664[/C][/ROW]
[ROW][C]T-STAT[/C][C]-3.10278322465169[/C][/ROW]
[ROW][C]p-value[/C][C]0.0531799025025303[/C][/ROW]
[ROW][C]Lambda[/C][C]2.29183361351408[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30990&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30990&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)
alpha6.1132840914719
beta-1.29183361351408
S.D.0.416346718407664
T-STAT-3.10278322465169
p-value0.0531799025025303
Lambda2.29183361351408


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')