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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 computationFri, 19 Dec 2008 06:55:22 -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/19/t1229694970ug00gfq1x8lc6a9.htm/, Retrieved Wed, 15 May 2024 04:43:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35133, Retrieved Wed, 15 May 2024 04:43:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact166

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [Standard Deviation-Mean Plot] [SMP olie] [2008-12-19 13:55:22] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum
2009-01-01 21:55:39 [Kenny Simons] [reply] 
Hier heb je een lambda waarde gevonden van -0,23. We zien wel dat de brekende p-value groter is dan 5% nl. 9,3%. Bovendien zien we dat er een outlier rechts op het scatterplot ligt die het resultaat gaat beïnvloeden. Met andere woorden wordt er aan geen 1 van de 2 assumpties voldoen en mogen we niet de berekende lambda waarde nemen. Hierdoor gaan we lambda op 1 zetten bij ons ARIMA model.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
29.59
30.7
30.52
32.67
33.19
37.13
35.54
37.75
41.84
42.94
49.14
44.61
40.22
44.23
45.85
53.38
53.26
51.8
55.3
57.81
63.96
63.77
59.15
56.12
57.42
63.52
61.71
63.01
68.18
72.03
69.75
74.41
74.33
64.24
60.03
59.44
62.5
55.04
58.34
61.92
67.65
67.68
70.3
75.26
71.44
76.36
81.71
92.6
90.6
92.23
94.09
102.79
109.65
124.05
132.69
135.81
116.07
101.42
75.73
55.48

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'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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35133&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35133&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35133&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'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
137.1356.2982443441154219.55
253.73757.376784375815323.74
365.67255.8998368621513616.99
470.066666666666710.489432200018637.56
5102.55083333333323.291055426467680.33

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 37.135 & 6.29824434411542 & 19.55 \tabularnewline
2 & 53.7375 & 7.3767843758153 & 23.74 \tabularnewline
3 & 65.6725 & 5.89983686215136 & 16.99 \tabularnewline
4 & 70.0666666666667 & 10.4894322000186 & 37.56 \tabularnewline
5 & 102.550833333333 & 23.2910554264676 & 80.33 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35133&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]37.135[/C][C]6.29824434411542[/C][C]19.55[/C][/ROW]
[ROW][C]2[/C][C]53.7375[/C][C]7.3767843758153[/C][C]23.74[/C][/ROW]
[ROW][C]3[/C][C]65.6725[/C][C]5.89983686215136[/C][C]16.99[/C][/ROW]
[ROW][C]4[/C][C]70.0666666666667[/C][C]10.4894322000186[/C][C]37.56[/C][/ROW]
[ROW][C]5[/C][C]102.550833333333[/C][C]23.2910554264676[/C][C]80.33[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35133&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35133&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
137.1356.2982443441154219.55
253.73757.376784375815323.74
365.67255.8998368621513616.99
470.066666666666710.489432200018637.56
5102.55083333333323.291055426467680.33






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-7.04694308809057
beta0.269137792576679
S.D.0.0781718940522036
T-STAT3.4428971670681
p-value0.0411489805160606

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -7.04694308809057 \tabularnewline
beta & 0.269137792576679 \tabularnewline
S.D. & 0.0781718940522036 \tabularnewline
T-STAT & 3.4428971670681 \tabularnewline
p-value & 0.0411489805160606 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35133&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-7.04694308809057[/C][/ROW]
[ROW][C]beta[/C][C]0.269137792576679[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0781718940522036[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.4428971670681[/C][/ROW]
[ROW][C]p-value[/C][C]0.0411489805160606[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35133&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35133&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-7.04694308809057
beta0.269137792576679
S.D.0.0781718940522036
T-STAT3.4428971670681
p-value0.0411489805160606






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.87227977136409
beta1.23279177169722
S.D.0.506575160196654
T-STAT2.43358117128887
p-value0.093031824779335
Lambda-0.232791771697222

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.87227977136409 \tabularnewline
beta & 1.23279177169722 \tabularnewline
S.D. & 0.506575160196654 \tabularnewline
T-STAT & 2.43358117128887 \tabularnewline
p-value & 0.093031824779335 \tabularnewline
Lambda & -0.232791771697222 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35133&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.87227977136409[/C][/ROW]
[ROW][C]beta[/C][C]1.23279177169722[/C][/ROW]
[ROW][C]S.D.[/C][C]0.506575160196654[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.43358117128887[/C][/ROW]
[ROW][C]p-value[/C][C]0.093031824779335[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.232791771697222[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35133&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35133&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-2.87227977136409
beta1.23279177169722
S.D.0.506575160196654
T-STAT2.43358117128887
p-value0.093031824779335
Lambda-0.232791771697222


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')