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Description of Statistical Computation

Author's title

sven van roy - tweede zittijd - oefening 8.2 - eigen reeks - spreidingsmate...

Author*Unverified author*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationTue, 12 Aug 2008 07:15:40 -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/Aug/12/t1218547126sejn1bj5jvp0h8b.htm/, Retrieved Fri, 01 Nov 2024 00:07:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=14005, Retrieved Fri, 01 Nov 2024 00:07:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact301

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] [sven van roy - tw...] [2008-08-12 13:15:40] [9ed44c8445a965e8d6beecda46dd06a5] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0,22
0,22
0,2
0,21
0,21
0,19
0,19
0,18
0,18
0,19
0,18
0,17
0,17
0,17
0,18
0,2
0,2
0,2
0,22
0,23
0,25
0,25
0,27
0,29
0,3
0,31
0,33
0,31
0,33
0,33
0,35
0,37
0,47
0,45
0,45
0,4
0,34
0,35
0,34
0,35
0,36
0,37
0,36
0,35
0,36
0,33
0,3
0,28
0,28
0,28
0,3
0,32
0,32
0,3
0,3
0,31
0,33
0,34
0,31
0,33
0,35
0,38
0,4
0,32
0,29
0,3
0,3
0,32
0,32
0,32
0,32
0,32
0,33
0,31
0,33
0,35
0,37
0,37
0,38
0,42
0,42
0,49
0,45
0,41
0,4
0,42
0,47
0,49
0,47
0,52
0,56
0,57
0,61
0,52
0,5
0,5

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'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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14005&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14005&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14005&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'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
10.1950.01678744119329040.05
20.2191666666666670.03941811612428830.12
30.3666666666666670.06095204274797950.17
40.3408333333333330.02644319239884670.09
50.310.01906925178491180.06
60.3283333333333330.03270622218625950.11
70.3858333333333330.05367551216393380.18
80.50250.06001893640571060.21

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 0.195 & 0.0167874411932904 & 0.05 \tabularnewline
2 & 0.219166666666667 & 0.0394181161242883 & 0.12 \tabularnewline
3 & 0.366666666666667 & 0.0609520427479795 & 0.17 \tabularnewline
4 & 0.340833333333333 & 0.0264431923988467 & 0.09 \tabularnewline
5 & 0.31 & 0.0190692517849118 & 0.06 \tabularnewline
6 & 0.328333333333333 & 0.0327062221862595 & 0.11 \tabularnewline
7 & 0.385833333333333 & 0.0536755121639338 & 0.18 \tabularnewline
8 & 0.5025 & 0.0600189364057106 & 0.21 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14005&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]0.195[/C][C]0.0167874411932904[/C][C]0.05[/C][/ROW]
[ROW][C]2[/C][C]0.219166666666667[/C][C]0.0394181161242883[/C][C]0.12[/C][/ROW]
[ROW][C]3[/C][C]0.366666666666667[/C][C]0.0609520427479795[/C][C]0.17[/C][/ROW]
[ROW][C]4[/C][C]0.340833333333333[/C][C]0.0264431923988467[/C][C]0.09[/C][/ROW]
[ROW][C]5[/C][C]0.31[/C][C]0.0190692517849118[/C][C]0.06[/C][/ROW]
[ROW][C]6[/C][C]0.328333333333333[/C][C]0.0327062221862595[/C][C]0.11[/C][/ROW]
[ROW][C]7[/C][C]0.385833333333333[/C][C]0.0536755121639338[/C][C]0.18[/C][/ROW]
[ROW][C]8[/C][C]0.5025[/C][C]0.0600189364057106[/C][C]0.21[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14005&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14005&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
10.1950.01678744119329040.05
20.2191666666666670.03941811612428830.12
30.3666666666666670.06095204274797950.17
40.3408333333333330.02644319239884670.09
50.310.01906925178491180.06
60.3283333333333330.03270622218625950.11
70.3858333333333330.05367551216393380.18
80.50250.06001893640571060.21






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.00438901932326101
beta0.129962065295648
S.D.0.0535910382748616
T-STAT2.42507086033843
p-value0.0515065618778822

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.00438901932326101 \tabularnewline
beta & 0.129962065295648 \tabularnewline
S.D. & 0.0535910382748616 \tabularnewline
T-STAT & 2.42507086033843 \tabularnewline
p-value & 0.0515065618778822 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14005&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.00438901932326101[/C][/ROW]
[ROW][C]beta[/C][C]0.129962065295648[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0535910382748616[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.42507086033843[/C][/ROW]
[ROW][C]p-value[/C][C]0.0515065618778822[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14005&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14005&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-0.00438901932326101
beta0.129962065295648
S.D.0.0535910382748616
T-STAT2.42507086033843
p-value0.0515065618778822






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.09749141860034
beta1.1016785718604
S.D.0.505062591509531
T-STAT2.18127137186641
p-value0.0719351217674321
Lambda-0.101678571860400

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.09749141860034 \tabularnewline
beta & 1.1016785718604 \tabularnewline
S.D. & 0.505062591509531 \tabularnewline
T-STAT & 2.18127137186641 \tabularnewline
p-value & 0.0719351217674321 \tabularnewline
Lambda & -0.101678571860400 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14005&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.09749141860034[/C][/ROW]
[ROW][C]beta[/C][C]1.1016785718604[/C][/ROW]
[ROW][C]S.D.[/C][C]0.505062591509531[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.18127137186641[/C][/ROW]
[ROW][C]p-value[/C][C]0.0719351217674321[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.101678571860400[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14005&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14005&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-2.09749141860034
beta1.1016785718604
S.D.0.505062591509531
T-STAT2.18127137186641
p-value0.0719351217674321
Lambda-0.101678571860400


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')