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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 07:02:49 -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/t1228831525q2p4kbi03kt1xku.htm/, Retrieved Sat, 18 May 2024 05:49:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=31412, Retrieved Sat, 18 May 2024 05:49:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact214

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  [Variance Reduction Matrix] [] [2008-12-02 14:53:11] [3ba9e05a140f75dbe22af2042ab9e185]
- RMP       [Standard Deviation-Mean Plot] [] [2008-12-09 14:02:49] [84357e896eab491ec515599b43df427d] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
45
24
18
20
22
39
55
35
38
47
1
57
50
33
19
2
7
15
56
53
24
48
2
49
46
32
37
10
8
16
55
46
46
45
6
45
52
44
35
15
44
51
58
23
44
43
6
51
53
47
19
18
38
43
23
43
18
43
6
31
49

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31412&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31412&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31412&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 time1 seconds
R Server'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
133.416666666666716.741121572796556
229.833333333333320.840665376454154
332.666666666666717.752507291971949
438.833333333333316.084059490594152
531.833333333333314.720630750649647

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 33.4166666666667 & 16.7411215727965 & 56 \tabularnewline
2 & 29.8333333333333 & 20.8406653764541 & 54 \tabularnewline
3 & 32.6666666666667 & 17.7525072919719 & 49 \tabularnewline
4 & 38.8333333333333 & 16.0840594905941 & 52 \tabularnewline
5 & 31.8333333333333 & 14.7206307506496 & 47 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31412&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]33.4166666666667[/C][C]16.7411215727965[/C][C]56[/C][/ROW]
[ROW][C]2[/C][C]29.8333333333333[/C][C]20.8406653764541[/C][C]54[/C][/ROW]
[ROW][C]3[/C][C]32.6666666666667[/C][C]17.7525072919719[/C][C]49[/C][/ROW]
[ROW][C]4[/C][C]38.8333333333333[/C][C]16.0840594905941[/C][C]52[/C][/ROW]
[ROW][C]5[/C][C]31.8333333333333[/C][C]14.7206307506496[/C][C]47[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31412&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31412&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
133.416666666666716.741121572796556
229.833333333333320.840665376454154
332.666666666666717.752507291971949
438.833333333333316.084059490594152
531.833333333333314.720630750649647






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha28.7008255072132
beta-0.344363039841521
S.D.0.341337459588753
T-STAT-1.00886389749432
p-value0.387353246632501

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 28.7008255072132 \tabularnewline
beta & -0.344363039841521 \tabularnewline
S.D. & 0.341337459588753 \tabularnewline
T-STAT & -1.00886389749432 \tabularnewline
p-value & 0.387353246632501 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31412&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]28.7008255072132[/C][/ROW]
[ROW][C]beta[/C][C]-0.344363039841521[/C][/ROW]
[ROW][C]S.D.[/C][C]0.341337459588753[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.00886389749432[/C][/ROW]
[ROW][C]p-value[/C][C]0.387353246632501[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31412&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31412&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)
alpha28.7008255072132
beta-0.344363039841521
S.D.0.341337459588753
T-STAT-1.00886389749432
p-value0.387353246632501






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha5.15778497436756
beta-0.661907274044272
S.D.0.665032672053106
T-STAT-0.995300384266558
p-value0.392950064307168
Lambda1.66190727404427

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 5.15778497436756 \tabularnewline
beta & -0.661907274044272 \tabularnewline
S.D. & 0.665032672053106 \tabularnewline
T-STAT & -0.995300384266558 \tabularnewline
p-value & 0.392950064307168 \tabularnewline
Lambda & 1.66190727404427 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31412&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]5.15778497436756[/C][/ROW]
[ROW][C]beta[/C][C]-0.661907274044272[/C][/ROW]
[ROW][C]S.D.[/C][C]0.665032672053106[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.995300384266558[/C][/ROW]
[ROW][C]p-value[/C][C]0.392950064307168[/C][/ROW]
[ROW][C]Lambda[/C][C]1.66190727404427[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31412&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31412&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)
alpha5.15778497436756
beta-0.661907274044272
S.D.0.665032672053106
T-STAT-0.995300384266558
p-value0.392950064307168
Lambda1.66190727404427


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = FALSE ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;
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')