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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 11:02:49 -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/t1228845796sfipdiwat3rpukr.htm/, Retrieved Fri, 17 May 2024 02:03:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=31642, Retrieved Fri, 17 May 2024 02:03:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact193

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] [Identification an...] [2008-12-09 12:57:00] [8ac58ef7b35dc5a117bc162cf16850e9]
F   PD      [Standard Deviation-Mean Plot] [step 1 ip] [2008-12-09 18:02:49] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum
2008-12-15 21:51:06 [Jonas Janssens] [reply] 
Goede uitleg.
2008-12-16 16:38:19 [c00776cbed2786c9c4960950021bd861] [reply] 
Dit is inderdaad een goede verklaring voor het niet moeten uitvoeren van een transformatie. de lambda waarde die gegeven is, moeten we dus niet gebruiken. De lambda-waarde moet op 1 gezet worden.
2008-12-16 19:34:31 [Kevin Vermeiren] [reply] 
Het klopt dat de p-waarde groter is dan 0.05. Hieruit kunnen we afleiden dat de helling van de regressierechte een grote kans heeft om door toeval bepaald te zijn (beta is niet significant verschillend van 0). De student vermeldt terecht dat er dus geen transformatie uitgevoerd moet worden en de lambda waarde op 1 mag blijven staan. Ook had nog iets vermeld kunnen worden omtrent de werking van de plot. De De Standard Deviation Mean plot verdeelt de tijdreeks in gelijke periodes en geeft het verband tussen het gemiddelde en de standaardfout weer.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
110.40
96.40
101.90
106.20
81.00
94.70
101.00
109.40
102.30
90.70
96.20
96.10
106.00
103.10
102.00
104.70
86.00
92.10
106.90
112.60
101.70
92.00
97.40
97.00
105.40
102.70
98.10
104.50
87.40
89.90
109.80
111.70
98.60
96.90
95.10
97.00
112.70
102.90
97.40
111.40
87.40
96.80
114.10
110.30
103.90
101.60
94.60
95.90
104.70
102.80
98.10
113.90
80.90
95.70
113.20
105.90
108.80
102.30
99.00
100.70
115.50

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=31642&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=31642&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31642&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
198.85833333333338.2429538321397829.4
2100.1257.5011665759400426.6
399.75833333333337.3724867314943724.3
4102.4166666666678.3881771053975226.7
5102.1666666666678.7748953201042733

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 98.8583333333333 & 8.24295383213978 & 29.4 \tabularnewline
2 & 100.125 & 7.50116657594004 & 26.6 \tabularnewline
3 & 99.7583333333333 & 7.37248673149437 & 24.3 \tabularnewline
4 & 102.416666666667 & 8.38817710539752 & 26.7 \tabularnewline
5 & 102.166666666667 & 8.77489532010427 & 33 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31642&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]98.8583333333333[/C][C]8.24295383213978[/C][C]29.4[/C][/ROW]
[ROW][C]2[/C][C]100.125[/C][C]7.50116657594004[/C][C]26.6[/C][/ROW]
[ROW][C]3[/C][C]99.7583333333333[/C][C]7.37248673149437[/C][C]24.3[/C][/ROW]
[ROW][C]4[/C][C]102.416666666667[/C][C]8.38817710539752[/C][C]26.7[/C][/ROW]
[ROW][C]5[/C][C]102.166666666667[/C][C]8.77489532010427[/C][C]33[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31642&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31642&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
198.85833333333338.2429538321397829.4
2100.1257.5011665759400426.6
399.75833333333337.3724867314943724.3
4102.4166666666678.3881771053975226.7
5102.1666666666678.7748953201042733






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-15.2187726488816
beta0.23120954216358
S.D.0.177655688113077
T-STAT1.30144744938544
p-value0.284032496741518

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -15.2187726488816 \tabularnewline
beta & 0.23120954216358 \tabularnewline
S.D. & 0.177655688113077 \tabularnewline
T-STAT & 1.30144744938544 \tabularnewline
p-value & 0.284032496741518 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31642&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-15.2187726488816[/C][/ROW]
[ROW][C]beta[/C][C]0.23120954216358[/C][/ROW]
[ROW][C]S.D.[/C][C]0.177655688113077[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.30144744938544[/C][/ROW]
[ROW][C]p-value[/C][C]0.284032496741518[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31642&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31642&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)
alpha-15.2187726488816
beta0.23120954216358
S.D.0.177655688113077
T-STAT1.30144744938544
p-value0.284032496741518






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-11.1014718424782
beta2.85917180740626
S.D.2.25530307950629
T-STAT1.26775502298883
p-value0.294341125821292
Lambda-1.85917180740626

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -11.1014718424782 \tabularnewline
beta & 2.85917180740626 \tabularnewline
S.D. & 2.25530307950629 \tabularnewline
T-STAT & 1.26775502298883 \tabularnewline
p-value & 0.294341125821292 \tabularnewline
Lambda & -1.85917180740626 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31642&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-11.1014718424782[/C][/ROW]
[ROW][C]beta[/C][C]2.85917180740626[/C][/ROW]
[ROW][C]S.D.[/C][C]2.25530307950629[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.26775502298883[/C][/ROW]
[ROW][C]p-value[/C][C]0.294341125821292[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.85917180740626[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31642&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31642&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-11.1014718424782
beta2.85917180740626
S.D.2.25530307950629
T-STAT1.26775502298883
p-value0.294341125821292
Lambda-1.85917180740626


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')