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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 computationTue, 02 Dec 2008 12:29:53 -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/02/t1228246245koi0m4zme7o361i.htm/, Retrieved Fri, 17 May 2024 02:39:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28231, Retrieved Fri, 17 May 2024 02:39:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsnon stationary time series , Q8
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] [loïqueverhasselt] [2008-12-02 19:29:53] [6440ec5a21e5d35520cb2ae6b4b70e45] [Current]
Feedback Forum
2008-12-09 20:48:18 [Gert-Jan Geudens] [reply] 
Correcte conclusie. De transformatie is hier nuttig aangezien de p-waarde kleiner is dan 0.05. Als deze groter zou zijn, is de transformatie niet meer nuttig en is de (in de tweede tabel) gevonden lambda nutteloos.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
93
98,4
92,6
94,6
99,5
97,6
91,3
93,6
93,1
78,4
70,2
69,3
71,1
73,5
85,9
91,5
91,8
88,3
91,3
94
99,3
96,7
88
96,7
106,8
114,3
105,7
90,1
91,6
97,7
100,8
104,6
95,9
102,7
104
107,9
113,8
113,8
123,1
125,1
137,6
134
140,3
152,1
150,6
167,3
153,2
142
154,4
158,5
180,9
181,3
172,4
192
199,3
215,4
214,3
201,5
190,5
196

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'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28231&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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28231&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28231&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'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
189.310.569940225168630.2
289.00833333333338.742836894835528.2
3101.8416666666677.0109600345502324.2
4137.74166666666716.633616472965153.5
5188.04166666666719.485400517652561

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 89.3 & 10.5699402251686 & 30.2 \tabularnewline
2 & 89.0083333333333 & 8.7428368948355 & 28.2 \tabularnewline
3 & 101.841666666667 & 7.01096003455023 & 24.2 \tabularnewline
4 & 137.741666666667 & 16.6336164729651 & 53.5 \tabularnewline
5 & 188.041666666667 & 19.4854005176525 & 61 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28231&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]89.3[/C][C]10.5699402251686[/C][C]30.2[/C][/ROW]
[ROW][C]2[/C][C]89.0083333333333[/C][C]8.7428368948355[/C][C]28.2[/C][/ROW]
[ROW][C]3[/C][C]101.841666666667[/C][C]7.01096003455023[/C][C]24.2[/C][/ROW]
[ROW][C]4[/C][C]137.741666666667[/C][C]16.6336164729651[/C][C]53.5[/C][/ROW]
[ROW][C]5[/C][C]188.041666666667[/C][C]19.4854005176525[/C][C]61[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28231&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28231&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
189.310.569940225168630.2
289.00833333333338.742836894835528.2
3101.8416666666677.0109600345502324.2
4137.74166666666716.633616472965153.5
5188.04166666666719.485400517652561






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-1.43960370376031
beta0.114931410491760
S.D.0.0298308185586595
T-STAT3.85277427991987
p-value0.0308825663471922

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -1.43960370376031 \tabularnewline
beta & 0.114931410491760 \tabularnewline
S.D. & 0.0298308185586595 \tabularnewline
T-STAT & 3.85277427991987 \tabularnewline
p-value & 0.0308825663471922 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28231&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.43960370376031[/C][/ROW]
[ROW][C]beta[/C][C]0.114931410491760[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0298308185586595[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.85277427991987[/C][/ROW]
[ROW][C]p-value[/C][C]0.0308825663471922[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28231&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28231&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-1.43960370376031
beta0.114931410491760
S.D.0.0298308185586595
T-STAT3.85277427991987
p-value0.0308825663471922






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.97070816153848
beta1.14062668930672
S.D.0.395882989380292
T-STAT2.88122177487907
p-value0.063465697475684
Lambda-0.140626689306718

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.97070816153848 \tabularnewline
beta & 1.14062668930672 \tabularnewline
S.D. & 0.395882989380292 \tabularnewline
T-STAT & 2.88122177487907 \tabularnewline
p-value & 0.063465697475684 \tabularnewline
Lambda & -0.140626689306718 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28231&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.97070816153848[/C][/ROW]
[ROW][C]beta[/C][C]1.14062668930672[/C][/ROW]
[ROW][C]S.D.[/C][C]0.395882989380292[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.88122177487907[/C][/ROW]
[ROW][C]p-value[/C][C]0.063465697475684[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.140626689306718[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28231&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28231&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-2.97070816153848
beta1.14062668930672
S.D.0.395882989380292
T-STAT2.88122177487907
p-value0.063465697475684
Lambda-0.140626689306718


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')