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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 12:38:01 -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/t1228765159l4zekbk5rn5f6zb.htm/, Retrieved Thu, 16 May 2024 18:55:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30844, Retrieved Thu, 16 May 2024 18:55:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact204

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]
- RMPD  [(Partial) Autocorrelation Function] [Opdracht 1 - Blok...] [2008-12-02 21:26:11] [8094ad203a218aaca2d1cea2c78c2d6e]
- RMPD      [Standard Deviation-Mean Plot] [Verbetering Q8(2)] [2008-12-08 19:38:01] [1351baa662f198be3bff32f9007a9a6d] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
17
22
29
26
29
42
40
34
46
43
44
40
41
42
35
40
43
47
41
44
38
35
34
31
25
35
36
41
41
38
39
45
46
48
48
48
45
44
45
45
45
42
43
50
46
46
45
49
46
45
49
47
45
48
51
48
49
51
54
52
52
53
51
55
53
51
52
54
58
57
52
50
53
50
50
51
53
49
54
57
58
56
60
55
54
52
55
56
54
53
59
62
63
64
75
77
79
77
82
83
81
78
79
79
73
72

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=30844&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=30844&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30844&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
134.33333333333339.5663551844551329
239.254.712169930567616
340.83333333333336.860073327640623
445.41666666666672.234373344457968
548.752.832441927511899
653.16666666666672.443296332763798
753.83333333333333.4859023439441311
860.33333333333338.3593533170208725

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 34.3333333333333 & 9.56635518445513 & 29 \tabularnewline
2 & 39.25 & 4.7121699305676 & 16 \tabularnewline
3 & 40.8333333333333 & 6.8600733276406 & 23 \tabularnewline
4 & 45.4166666666667 & 2.23437334445796 & 8 \tabularnewline
5 & 48.75 & 2.83244192751189 & 9 \tabularnewline
6 & 53.1666666666667 & 2.44329633276379 & 8 \tabularnewline
7 & 53.8333333333333 & 3.48590234394413 & 11 \tabularnewline
8 & 60.3333333333333 & 8.35935331702087 & 25 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30844&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]34.3333333333333[/C][C]9.56635518445513[/C][C]29[/C][/ROW]
[ROW][C]2[/C][C]39.25[/C][C]4.7121699305676[/C][C]16[/C][/ROW]
[ROW][C]3[/C][C]40.8333333333333[/C][C]6.8600733276406[/C][C]23[/C][/ROW]
[ROW][C]4[/C][C]45.4166666666667[/C][C]2.23437334445796[/C][C]8[/C][/ROW]
[ROW][C]5[/C][C]48.75[/C][C]2.83244192751189[/C][C]9[/C][/ROW]
[ROW][C]6[/C][C]53.1666666666667[/C][C]2.44329633276379[/C][C]8[/C][/ROW]
[ROW][C]7[/C][C]53.8333333333333[/C][C]3.48590234394413[/C][C]11[/C][/ROW]
[ROW][C]8[/C][C]60.3333333333333[/C][C]8.35935331702087[/C][C]25[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30844&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30844&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
134.33333333333339.5663551844551329
239.254.712169930567616
340.83333333333336.860073327640623
445.41666666666672.234373344457968
548.752.832441927511899
653.16666666666672.443296332763798
753.83333333333333.4859023439441311
860.33333333333338.3593533170208725






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha9.32796769847824
beta-0.0907908026055347
S.D.0.128883763916145
T-STAT-0.704439409952407
p-value0.507565903330099

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 9.32796769847824 \tabularnewline
beta & -0.0907908026055347 \tabularnewline
S.D. & 0.128883763916145 \tabularnewline
T-STAT & -0.704439409952407 \tabularnewline
p-value & 0.507565903330099 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30844&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]9.32796769847824[/C][/ROW]
[ROW][C]beta[/C][C]-0.0907908026055347[/C][/ROW]
[ROW][C]S.D.[/C][C]0.128883763916145[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.704439409952407[/C][/ROW]
[ROW][C]p-value[/C][C]0.507565903330099[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30844&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30844&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)
alpha9.32796769847824
beta-0.0907908026055347
S.D.0.128883763916145
T-STAT-0.704439409952407
p-value0.507565903330099






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha5.44102293705954
beta-1.03279773767485
S.D.1.16250876537382
T-STAT-0.88842146264827
p-value0.408515473692838
Lambda2.03279773767485

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 5.44102293705954 \tabularnewline
beta & -1.03279773767485 \tabularnewline
S.D. & 1.16250876537382 \tabularnewline
T-STAT & -0.88842146264827 \tabularnewline
p-value & 0.408515473692838 \tabularnewline
Lambda & 2.03279773767485 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30844&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]5.44102293705954[/C][/ROW]
[ROW][C]beta[/C][C]-1.03279773767485[/C][/ROW]
[ROW][C]S.D.[/C][C]1.16250876537382[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.88842146264827[/C][/ROW]
[ROW][C]p-value[/C][C]0.408515473692838[/C][/ROW]
[ROW][C]Lambda[/C][C]2.03279773767485[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30844&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30844&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)
alpha5.44102293705954
beta-1.03279773767485
S.D.1.16250876537382
T-STAT-0.88842146264827
p-value0.408515473692838
Lambda2.03279773767485


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')