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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 computationSat, 06 Dec 2008 07:29:21 -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/06/t1228573863n5j77riopc9v4my.htm/, Retrieved Sat, 18 May 2024 07:49:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29646, Retrieved Sat, 18 May 2024 07:49:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact225

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 RMP   [Standard Deviation-Mean Plot] [Identification an...] [2008-12-04 19:58:38] [063e4b67ad7d3a8a83eccec794cd5aa7]
F    D    [Standard Deviation-Mean Plot] [Eigen tijdreeks SMP] [2008-12-06 14:17:16] [063e4b67ad7d3a8a83eccec794cd5aa7]
F    D        [Standard Deviation-Mean Plot] [Eigen tijdreeks t...] [2008-12-06 14:29:21] [6797a1f4a60918966297e9d9220cabc2] [Current]
Feedback Forum
2008-12-15 18:39:19 [Jeroen Michel] [reply] 
Ook hier stelt de student duidelijk hoe de data, grafieken, en tabellen moeten worden afgelezen. Op die manier kan de lezer van dit werk meteen de resultaten interpreteren. Ook hier hangt dus een zeer uitgebreide analyse aan vast.
2008-12-15 18:50:27 [Evelien Blockx] [reply] 
De p-value in de eerste kleine tabel bedraagt 0.199… . Dat is een p-waarde die groter is dan 5%. Beta verschilt niet significant van nul. De gegeven Lambda-waarde kan hier niet gebruikt worden. Hier moet Lambda 1 gebruikt worden.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
6,2
6,1
5,9
5,6
5,5
5,5
5,6
5,7
5,6
5,4
5,3
5,3
5,4
5,5
5,6
5,7
5,8
5,8
5,7
5,9
6,1
6,4
6,4
6,3
6,2
6,2
6,3
6,5
6,6
6,6
6,7
6,6
6,7
7
7,2
7,3
7,5
7,6
7,7
7,8
7,8
7,7
7,6
7,6
7,7
7,8
7,8
7,8
7,7
7,6
7,4
7,1
7,1
7,3
7,6
7,8
7,7
7,6
7,5
7,5
7,5
7,6
7,6
7,7
7,8
7,7
7,6
7,6
7,6
7,7
7,8
7,8
7,9
7,9
7,8
7,8
7,7
7,5
7,1
6,9
7,1
7,1
7,1
7
6,9
6,8
6,7
6,8
6,8
6,7
6,8
6,7
6,6
6,4
6,4
6,4
6,5
6,5
6,4
6,3
6,2
6,3

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'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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29646&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29646&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29646&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
15.641666666666670.2906367096044420.9
25.883333333333330.3433348043510711
36.658333333333330.3579190699111471.1
47.70.1044465935734190.3
57.491666666666670.2274696116900550.7
67.666666666666670.09847319278346630.3
77.408333333333330.3918680977836881
86.666666666666670.1775250729197190.5

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 5.64166666666667 & 0.290636709604442 & 0.9 \tabularnewline
2 & 5.88333333333333 & 0.343334804351071 & 1 \tabularnewline
3 & 6.65833333333333 & 0.357919069911147 & 1.1 \tabularnewline
4 & 7.7 & 0.104446593573419 & 0.3 \tabularnewline
5 & 7.49166666666667 & 0.227469611690055 & 0.7 \tabularnewline
6 & 7.66666666666667 & 0.0984731927834663 & 0.3 \tabularnewline
7 & 7.40833333333333 & 0.391868097783688 & 1 \tabularnewline
8 & 6.66666666666667 & 0.177525072919719 & 0.5 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29646&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]5.64166666666667[/C][C]0.290636709604442[/C][C]0.9[/C][/ROW]
[ROW][C]2[/C][C]5.88333333333333[/C][C]0.343334804351071[/C][C]1[/C][/ROW]
[ROW][C]3[/C][C]6.65833333333333[/C][C]0.357919069911147[/C][C]1.1[/C][/ROW]
[ROW][C]4[/C][C]7.7[/C][C]0.104446593573419[/C][C]0.3[/C][/ROW]
[ROW][C]5[/C][C]7.49166666666667[/C][C]0.227469611690055[/C][C]0.7[/C][/ROW]
[ROW][C]6[/C][C]7.66666666666667[/C][C]0.0984731927834663[/C][C]0.3[/C][/ROW]
[ROW][C]7[/C][C]7.40833333333333[/C][C]0.391868097783688[/C][C]1[/C][/ROW]
[ROW][C]8[/C][C]6.66666666666667[/C][C]0.177525072919719[/C][C]0.5[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29646&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29646&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
15.641666666666670.2906367096044420.9
25.883333333333330.3433348043510711
36.658333333333330.3579190699111471.1
47.70.1044465935734190.3
57.491666666666670.2274696116900550.7
67.666666666666670.09847319278346630.3
77.408333333333330.3918680977836881
86.666666666666670.1775250729197190.5






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.745629774649238
beta-0.072090082453769
S.D.0.0499376869719741
T-STAT-1.44360075175743
p-value0.19896078205773

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.745629774649238 \tabularnewline
beta & -0.072090082453769 \tabularnewline
S.D. & 0.0499376869719741 \tabularnewline
T-STAT & -1.44360075175743 \tabularnewline
p-value & 0.19896078205773 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29646&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.745629774649238[/C][/ROW]
[ROW][C]beta[/C][C]-0.072090082453769[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0499376869719741[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.44360075175743[/C][/ROW]
[ROW][C]p-value[/C][C]0.19896078205773[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29646&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29646&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)
alpha0.745629774649238
beta-0.072090082453769
S.D.0.0499376869719741
T-STAT-1.44360075175743
p-value0.19896078205773






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha3.3394879568109
beta-2.51928984396931
S.D.1.52779380428682
T-STAT-1.64897241820229
p-value0.150248258815839
Lambda3.51928984396931

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 3.3394879568109 \tabularnewline
beta & -2.51928984396931 \tabularnewline
S.D. & 1.52779380428682 \tabularnewline
T-STAT & -1.64897241820229 \tabularnewline
p-value & 0.150248258815839 \tabularnewline
Lambda & 3.51928984396931 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29646&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.3394879568109[/C][/ROW]
[ROW][C]beta[/C][C]-2.51928984396931[/C][/ROW]
[ROW][C]S.D.[/C][C]1.52779380428682[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.64897241820229[/C][/ROW]
[ROW][C]p-value[/C][C]0.150248258815839[/C][/ROW]
[ROW][C]Lambda[/C][C]3.51928984396931[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29646&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29646&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)
alpha3.3394879568109
beta-2.51928984396931
S.D.1.52779380428682
T-STAT-1.64897241820229
p-value0.150248258815839
Lambda3.51928984396931


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')