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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, 01 Dec 2008 11:44:09 -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/01/t1228157590bcq02pffwbbe3ya.htm/, Retrieved Sun, 05 May 2024 13:41:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27147, Retrieved Sun, 05 May 2024 13:41:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact236

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  [(Partial) Autocorrelation Function] [NSTS_Q5] [2008-11-30 17:55:01] [9f5bfe3b95f9ec3d2ed4c0a560a9648a]
F RMPD      [Standard Deviation-Mean Plot] [NSTS_Q7 (bouw)] [2008-12-01 18:44:09] [a9e6d7cd6e144e8b311d9f96a24c5a25] [Current]
Feedback Forum
2008-12-08 17:05:15 [Sandra Hofmans] [reply] 
We gaan Lambda introduceren om zo de variantie gelijk te krijgen. Het Standard Deviation Plot gaat na of de spreiding afhankelijk is van het niveau van de tijdreeks. In de eerste tabel staat de vergelijking van de regressielijn die we door de punten van de grafiek kunnen tekenen geschreven. In de 2e tabel staat diezelfde regresievergelijking maar dan in de logaritmische vorm. Je ziet hier da de waarde voor Lambda 2,31 bedraagt. Dit kan echter niet omdat lambda gelegen is tussen -2 en 2.
2008-12-10 08:26:37 [Lana Van Wesemael] [reply] 
Hier had ik ook naar de eerste tabel moeten kijken, hieruit blijkt immers dan de bèta negatief is en de p-waarde is gelijk aan 0.248926256845782, wat dus te groot is. Bijgevolg is de lambda transformatie niet nodig. Dit is ook te zien in de eerste grafiek in de output. Daar is duidelijk geen verband te zien tussen de standaardafwijking en het gemiddelde.
2008-12-10 10:21:09 [Peter Van Doninck] [reply] 
In de eerste tabel is de p-waarde echter vrij groot. Daarom is het berekenen van een lambda waarde niet echt relevant.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
82,7
88,9
105,9
100,8
94
105
58,5
87,6
113,1
112,5
89,6
74,5
82,7
90,1
109,4
96
89,2
109,1
49,1
92,9
107,7
103,5
91,1
79,8
71,9
82,9
90,1
100,7
90,7
108,8
44,1
93,6
107,4
96,5
93,6
76,5
76,7
84
103,3
88,5
99
105,9
44,7
94
107,1
104,8
102,5
77,7
85,2
91,3
106,5
92,4
97,5
107
51,1
98,6
102,2
114,3
99,4
72,5

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=27147&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=27147&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27147&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
192.758333333333316.10174797588154.6
291.716666666666716.727105565699760.3
388.066666666666717.739495397831864.7
490.683333333333318.109055159998862.4
593.166666666666717.18552950136963.2

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 92.7583333333333 & 16.101747975881 & 54.6 \tabularnewline
2 & 91.7166666666667 & 16.7271055656997 & 60.3 \tabularnewline
3 & 88.0666666666667 & 17.7394953978318 & 64.7 \tabularnewline
4 & 90.6833333333333 & 18.1090551599988 & 62.4 \tabularnewline
5 & 93.1666666666667 & 17.185529501369 & 63.2 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27147&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]92.7583333333333[/C][C]16.101747975881[/C][C]54.6[/C][/ROW]
[ROW][C]2[/C][C]91.7166666666667[/C][C]16.7271055656997[/C][C]60.3[/C][/ROW]
[ROW][C]3[/C][C]88.0666666666667[/C][C]17.7394953978318[/C][C]64.7[/C][/ROW]
[ROW][C]4[/C][C]90.6833333333333[/C][C]18.1090551599988[/C][C]62.4[/C][/ROW]
[ROW][C]5[/C][C]93.1666666666667[/C][C]17.185529501369[/C][C]63.2[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27147&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27147&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
192.758333333333316.10174797588154.6
291.716666666666716.727105565699760.3
388.066666666666717.739495397831864.7
490.683333333333318.109055159998862.4
593.166666666666717.18552950136963.2






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha39.8784594614256
beta-0.248754243335617
S.D.0.174352583679078
T-STAT-1.42673104170046
p-value0.248926256845782

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 39.8784594614256 \tabularnewline
beta & -0.248754243335617 \tabularnewline
S.D. & 0.174352583679078 \tabularnewline
T-STAT & -1.42673104170046 \tabularnewline
p-value & 0.248926256845782 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27147&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]39.8784594614256[/C][/ROW]
[ROW][C]beta[/C][C]-0.248754243335617[/C][/ROW]
[ROW][C]S.D.[/C][C]0.174352583679078[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.42673104170046[/C][/ROW]
[ROW][C]p-value[/C][C]0.248926256845782[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27147&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27147&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)
alpha39.8784594614256
beta-0.248754243335617
S.D.0.174352583679078
T-STAT-1.42673104170046
p-value0.248926256845782






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha8.76174595071042
beta-1.31140395864577
S.D.0.926820594516995
T-STAT-1.41494909198603
p-value0.252020928335142
Lambda2.31140395864577

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 8.76174595071042 \tabularnewline
beta & -1.31140395864577 \tabularnewline
S.D. & 0.926820594516995 \tabularnewline
T-STAT & -1.41494909198603 \tabularnewline
p-value & 0.252020928335142 \tabularnewline
Lambda & 2.31140395864577 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27147&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]8.76174595071042[/C][/ROW]
[ROW][C]beta[/C][C]-1.31140395864577[/C][/ROW]
[ROW][C]S.D.[/C][C]0.926820594516995[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.41494909198603[/C][/ROW]
[ROW][C]p-value[/C][C]0.252020928335142[/C][/ROW]
[ROW][C]Lambda[/C][C]2.31140395864577[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27147&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27147&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)
alpha8.76174595071042
beta-1.31140395864577
S.D.0.926820594516995
T-STAT-1.41494909198603
p-value0.252020928335142
Lambda2.31140395864577


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')