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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 12:31:21 -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/t1228764714iwj9lqatlxztw5m.htm/, Retrieved Thu, 16 May 2024 16:00:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30821, Retrieved Thu, 16 May 2024 16:00:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact161

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
F RMPD    [Standard Deviation-Mean Plot] [step 1] [2008-12-08 19:31:21] [e515c0250d6233b5d2604259ab52cebe] [Current]
F RM D      [Variance Reduction Matrix] [step 2] [2008-12-08 19:34:58] [5161246d1ccc1b670cc664d03050f084]
F RMP         [Spectral Analysis] [step 2] [2008-12-08 19:40:15] [5161246d1ccc1b670cc664d03050f084]
- RMP           [(Partial) Autocorrelation Function] [step 2] [2008-12-08 19:45:51] [5161246d1ccc1b670cc664d03050f084]
F   P             [(Partial) Autocorrelation Function] [step3] [2008-12-08 19:51:58] [5161246d1ccc1b670cc664d03050f084]
F RMPD              [ARIMA Backward Selection] [] [2008-12-08 20:09:39] [5161246d1ccc1b670cc664d03050f084]
-   PD                [ARIMA Backward Selection] [verbetering stap 5] [2008-12-15 16:48:15] [e43247bc0ab243a5af99ac7f55ba0b41]
-   P               [(Partial) Autocorrelation Function] [Assessment verbet...] [2008-12-10 15:30:12] [46c5a5fbda57fdfa1d4ef48658f82a0c]
-   P               [(Partial) Autocorrelation Function] [verbetering ] [2008-12-15 16:16:38] [e43247bc0ab243a5af99ac7f55ba0b41]
- RMP             [ARIMA Backward Selection] [Assessment verbet...] [2008-12-10 15:38:14] [46c5a5fbda57fdfa1d4ef48658f82a0c]
F RMP               [ARIMA Forecasting] [forecasting step 1] [2008-12-15 18:07:00] [5161246d1ccc1b670cc664d03050f084]
F   P           [Spectral Analysis] [step3] [2008-12-08 19:54:50] [5161246d1ccc1b670cc664d03050f084]
-   P             [Spectral Analysis] [verbetering] [2008-12-15 16:35:53] [e43247bc0ab243a5af99ac7f55ba0b41]
Feedback Forum
2008-12-10 15:27:28 [Ken Van den Heuvel] [reply] 
De p-waarde van 22,77% is te hoog. De verkregen beta waarde is dus met andere woorden niet betrouwbaar. Bijgevolg dien je dan ook niet met deze lambda -waarde te werken maar met lambda = 1.
2008-12-14 15:04:43 [Chi-Kwong Man] [reply] 
De p-waarde is inderdaad nogal groot, en wat betreft de lambda, is het denk ik niet mogelijk om die te gebruiken sinds één van de voorwaarde niet is voldaan, er bevinden zich namelijk nogal wat outliers op de grafiek.
2008-12-15 12:51:24 [Kristof Augustyns] [reply] 
De p-waarde is in ieder geval te groot en het is aan te raden een andere lambda-waarde te gebruiken.
2008-12-15 17:08:35 [Lindsay Heyndrickx] [reply] 
Hier is de correcte methode gebruikt. Hier heb je een veel te hoge p waarde om een accurate lamda te hebben. Je p waarde mag niet hoger zijn dan 5%. Hier heb je dus een foute lamda en moet je werken met lamda =1.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
83,1
89,6
105,7
110,7
110,4
109
106
100,9
114,3
101,2
109,2
111,6
91,7
93,7
105,7
109,5
105,3
102,8
100,6
97,6
110,3
107,2
107,2
108,1
97,1
92,2
112,2
111,6
115,7
111,3
104,2
103,2
112,7
106,4
102,6
110,6
95,2
89
112,5
116,8
107,2
113,6
101,8
102,6
122,7
110,3
110,5
121,6
100,3
100,7
123,4
127,1
124,1
131,2
111,6
114,2
130,1
125,9
119
133,8
107,5
113,5
134,4
126,8
135,6
139,9
129,8
131
153,1
134,1
144,1
155,9
123,3
128,1
144,3
153
149,9
150,9
141
138,9
157,4
142,9
151,7
161
138,5
135,9
151,5
164
159,1
157
142,1
144,8
152,1
154,6
148,7
157,7
146,7

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30821&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]3 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=30821&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30821&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1104.3083333333339.3862044157014531.2
2103.3083333333336.1600558340641618.6
3106.657.0415003566517923.5
4108.6510.133876580334633.7
5120.11666666666711.269817561912333.5
6133.80833333333314.092258244307148.4
7145.211.247626012145437.7
8150.58.7079900613798828.1

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 104.308333333333 & 9.38620441570145 & 31.2 \tabularnewline
2 & 103.308333333333 & 6.16005583406416 & 18.6 \tabularnewline
3 & 106.65 & 7.04150035665179 & 23.5 \tabularnewline
4 & 108.65 & 10.1338765803346 & 33.7 \tabularnewline
5 & 120.116666666667 & 11.2698175619123 & 33.5 \tabularnewline
6 & 133.808333333333 & 14.0922582443071 & 48.4 \tabularnewline
7 & 145.2 & 11.2476260121454 & 37.7 \tabularnewline
8 & 150.5 & 8.70799006137988 & 28.1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30821&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]104.308333333333[/C][C]9.38620441570145[/C][C]31.2[/C][/ROW]
[ROW][C]2[/C][C]103.308333333333[/C][C]6.16005583406416[/C][C]18.6[/C][/ROW]
[ROW][C]3[/C][C]106.65[/C][C]7.04150035665179[/C][C]23.5[/C][/ROW]
[ROW][C]4[/C][C]108.65[/C][C]10.1338765803346[/C][C]33.7[/C][/ROW]
[ROW][C]5[/C][C]120.116666666667[/C][C]11.2698175619123[/C][C]33.5[/C][/ROW]
[ROW][C]6[/C][C]133.808333333333[/C][C]14.0922582443071[/C][C]48.4[/C][/ROW]
[ROW][C]7[/C][C]145.2[/C][C]11.2476260121454[/C][C]37.7[/C][/ROW]
[ROW][C]8[/C][C]150.5[/C][C]8.70799006137988[/C][C]28.1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30821&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30821&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
1104.3083333333339.3862044157014531.2
2103.3083333333336.1600558340641618.6
3106.657.0415003566517923.5
4108.6510.133876580334633.7
5120.11666666666711.269817561912333.5
6133.80833333333314.092258244307148.4
7145.211.247626012145437.7
8150.58.7079900613798828.1






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha2.01711680381494
beta0.063650120871576
S.D.0.047380509916577
T-STAT1.34338193032631
p-value0.227726598922245

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 2.01711680381494 \tabularnewline
beta & 0.063650120871576 \tabularnewline
S.D. & 0.047380509916577 \tabularnewline
T-STAT & 1.34338193032631 \tabularnewline
p-value & 0.227726598922245 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30821&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.01711680381494[/C][/ROW]
[ROW][C]beta[/C][C]0.063650120871576[/C][/ROW]
[ROW][C]S.D.[/C][C]0.047380509916577[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.34338193032631[/C][/ROW]
[ROW][C]p-value[/C][C]0.227726598922245[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30821&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30821&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)
alpha2.01711680381494
beta0.063650120871576
S.D.0.047380509916577
T-STAT1.34338193032631
p-value0.227726598922245






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.13280663681589
beta0.914402681341961
S.D.0.605907294384562
T-STAT1.50914618427023
p-value0.181997354220434
Lambda0.0855973186580387

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.13280663681589 \tabularnewline
beta & 0.914402681341961 \tabularnewline
S.D. & 0.605907294384562 \tabularnewline
T-STAT & 1.50914618427023 \tabularnewline
p-value & 0.181997354220434 \tabularnewline
Lambda & 0.0855973186580387 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30821&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.13280663681589[/C][/ROW]
[ROW][C]beta[/C][C]0.914402681341961[/C][/ROW]
[ROW][C]S.D.[/C][C]0.605907294384562[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.50914618427023[/C][/ROW]
[ROW][C]p-value[/C][C]0.181997354220434[/C][/ROW]
[ROW][C]Lambda[/C][C]0.0855973186580387[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30821&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30821&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-2.13280663681589
beta0.914402681341961
S.D.0.605907294384562
T-STAT1.50914618427023
p-value0.181997354220434
Lambda0.0855973186580387


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')