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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 computationThu, 12 Aug 2010 11:14:28 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Aug/12/t1281611657jv0osrinopc7j3h.htm/, Retrieved Sat, 04 May 2024 06:53:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78682, Retrieved Sat, 04 May 2024 06:53:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsVanhille Olivier
Estimated Impact166

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] [tijdreeks B - sta...] [2010-08-12 11:14:28] [ddb1c76c3acba5bf82e5ed3b5a08f68d] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
31
30
29
27
25
24
25
27
28
28
29
31
31
27
25
16
20
21
25
24
28
27
23
36
37
30
27
22
22
25
33
35
35
29
25
34
31
29
21
19
18
25
23
22
20
15
17
25
26
26
23
24
24
42
40
45
47
40
39
49
55
54
48
44
48
62
57
60
56
57
54
62
65
68
69
67
72
82
72
77
79
78
76
79

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=78682&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=78682&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78682&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
127.83333333333332.329000305762637
225.255.2245051962319420
329.55.3000857625994215
422.08333333333334.7950416309375516
535.416666666666710.004165798972626
654.755.6588627190211418
773.66666666666675.5650424050223517

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 27.8333333333333 & 2.32900030576263 & 7 \tabularnewline
2 & 25.25 & 5.22450519623194 & 20 \tabularnewline
3 & 29.5 & 5.30008576259942 & 15 \tabularnewline
4 & 22.0833333333333 & 4.79504163093755 & 16 \tabularnewline
5 & 35.4166666666667 & 10.0041657989726 & 26 \tabularnewline
6 & 54.75 & 5.65886271902114 & 18 \tabularnewline
7 & 73.6666666666667 & 5.56504240502235 & 17 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78682&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]27.8333333333333[/C][C]2.32900030576263[/C][C]7[/C][/ROW]
[ROW][C]2[/C][C]25.25[/C][C]5.22450519623194[/C][C]20[/C][/ROW]
[ROW][C]3[/C][C]29.5[/C][C]5.30008576259942[/C][C]15[/C][/ROW]
[ROW][C]4[/C][C]22.0833333333333[/C][C]4.79504163093755[/C][C]16[/C][/ROW]
[ROW][C]5[/C][C]35.4166666666667[/C][C]10.0041657989726[/C][C]26[/C][/ROW]
[ROW][C]6[/C][C]54.75[/C][C]5.65886271902114[/C][C]18[/C][/ROW]
[ROW][C]7[/C][C]73.6666666666667[/C][C]5.56504240502235[/C][C]17[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78682&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78682&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
127.83333333333332.329000305762637
225.255.2245051962319420
329.55.3000857625994215
422.08333333333334.7950416309375516
535.416666666666710.004165798972626
654.755.6588627190211418
773.66666666666675.5650424050223517






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha4.80661715239722
beta0.0194800139730618
S.D.0.0529584025544244
T-STAT0.367836132387916
p-value0.728053280987303

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 4.80661715239722 \tabularnewline
beta & 0.0194800139730618 \tabularnewline
S.D. & 0.0529584025544244 \tabularnewline
T-STAT & 0.367836132387916 \tabularnewline
p-value & 0.728053280987303 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78682&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]4.80661715239722[/C][/ROW]
[ROW][C]beta[/C][C]0.0194800139730618[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0529584025544244[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.367836132387916[/C][/ROW]
[ROW][C]p-value[/C][C]0.728053280987303[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78682&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78682&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)
alpha4.80661715239722
beta0.0194800139730618
S.D.0.0529584025544244
T-STAT0.367836132387916
p-value0.728053280987303






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha0.677196727681078
beta0.270900863098001
S.D.0.417638820048629
T-STAT0.64864866505096
p-value0.545174592150675
Lambda0.729099136901999

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.677196727681078 \tabularnewline
beta & 0.270900863098001 \tabularnewline
S.D. & 0.417638820048629 \tabularnewline
T-STAT & 0.64864866505096 \tabularnewline
p-value & 0.545174592150675 \tabularnewline
Lambda & 0.729099136901999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78682&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.677196727681078[/C][/ROW]
[ROW][C]beta[/C][C]0.270900863098001[/C][/ROW]
[ROW][C]S.D.[/C][C]0.417638820048629[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.64864866505096[/C][/ROW]
[ROW][C]p-value[/C][C]0.545174592150675[/C][/ROW]
[ROW][C]Lambda[/C][C]0.729099136901999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78682&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78682&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)
alpha0.677196727681078
beta0.270900863098001
S.D.0.417638820048629
T-STAT0.64864866505096
p-value0.545174592150675
Lambda0.729099136901999


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 0.01 ; par2 = 0.99 ; par3 = 0.01 ;
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')