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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 computationWed, 02 May 2012 17:37:37 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/May/02/t1335994671pjlsgbeon0l3pyf.htm/, Retrieved Tue, 07 May 2024 16:39:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=166029, Retrieved Tue, 07 May 2024 16:39:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact120

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Standard Deviation-Mean Plot] [] [2012-05-02 21:37:37] [41122821deba20d6652b4f9148627213] [Current]
- R  D    [Standard Deviation-Mean Plot] [] [2012-05-27 15:00:48] [74be16979710d4c4e7c6647856088456]
-    D      [Standard Deviation-Mean Plot] [] [2012-05-27 15:07:52] [74be16979710d4c4e7c6647856088456]
- R  D    [Standard Deviation-Mean Plot] [] [2012-05-27 16:07:44] [74be16979710d4c4e7c6647856088456]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
100.17
102.01
100.3
99.94
100.16
100.18
99.98
100.04
100.05
100.11
100.11
101.03
100.84
102.68
101.27
100.28
100.82
100.87
101.23
101.09
101.22
101.33
101.3
102.39
101.69
103.75
102.99
100.8
102.21
102.45
102.49
102.4
102.99
103.19
103.35
104.44
103.42
105.81
104.25
103.78
104.53
105.01
104.83
104.55
105.16
105.06
105.2
105.87
105.41
107.89
106.06
105.5
106.71
106.34
106.11
106.15
106.61
106.63
106.27
105.59
107.09
108.53
108.01
106.52
107.27
107.58
107.36
107.23
107.54
107.64
108.23
108.42

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'AstonUniversity' @ aston.wessa.net

\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 & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166029&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166029&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166029&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'AstonUniversity' @ aston.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1100.340.5971903914467862.07000000000001
2101.2766666666670.6612980806831012.40000000000001
3102.7291666666670.9542961074038083.64
4104.7891666666670.7353719940934462.45
5106.27250.6706187780360352.48
6107.6183333333330.5903594180024952.01000000000001

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 100.34 & 0.597190391446786 & 2.07000000000001 \tabularnewline
2 & 101.276666666667 & 0.661298080683101 & 2.40000000000001 \tabularnewline
3 & 102.729166666667 & 0.954296107403808 & 3.64 \tabularnewline
4 & 104.789166666667 & 0.735371994093446 & 2.45 \tabularnewline
5 & 106.2725 & 0.670618778036035 & 2.48 \tabularnewline
6 & 107.618333333333 & 0.590359418002495 & 2.01000000000001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166029&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]100.34[/C][C]0.597190391446786[/C][C]2.07000000000001[/C][/ROW]
[ROW][C]2[/C][C]101.276666666667[/C][C]0.661298080683101[/C][C]2.40000000000001[/C][/ROW]
[ROW][C]3[/C][C]102.729166666667[/C][C]0.954296107403808[/C][C]3.64[/C][/ROW]
[ROW][C]4[/C][C]104.789166666667[/C][C]0.735371994093446[/C][C]2.45[/C][/ROW]
[ROW][C]5[/C][C]106.2725[/C][C]0.670618778036035[/C][C]2.48[/C][/ROW]
[ROW][C]6[/C][C]107.618333333333[/C][C]0.590359418002495[/C][C]2.01000000000001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166029&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166029&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
1100.340.5971903914467862.07000000000001
2101.2766666666670.6612980806831012.40000000000001
3102.7291666666670.9542961074038083.64
4104.7891666666670.7353719940934462.45
5106.27250.6706187780360352.48
6107.6183333333330.5903594180024952.01000000000001






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha1.39693171329286
beta-0.00669708266793348
S.D.0.0232548521425451
T-STAT-0.287986465228091
p-value0.787662623183379

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.39693171329286 \tabularnewline
beta & -0.00669708266793348 \tabularnewline
S.D. & 0.0232548521425451 \tabularnewline
T-STAT & -0.287986465228091 \tabularnewline
p-value & 0.787662623183379 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166029&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.39693171329286[/C][/ROW]
[ROW][C]beta[/C][C]-0.00669708266793348[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0232548521425451[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.287986465228091[/C][/ROW]
[ROW][C]p-value[/C][C]0.787662623183379[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166029&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166029&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)
alpha1.39693171329286
beta-0.00669708266793348
S.D.0.0232548521425451
T-STAT-0.287986465228091
p-value0.787662623183379






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha3.43351442043668
beta-0.818913726149975
S.D.3.18249782636157
T-STAT-0.257317921591861
p-value0.809628230489793
Lambda1.81891372614998

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 3.43351442043668 \tabularnewline
beta & -0.818913726149975 \tabularnewline
S.D. & 3.18249782636157 \tabularnewline
T-STAT & -0.257317921591861 \tabularnewline
p-value & 0.809628230489793 \tabularnewline
Lambda & 1.81891372614998 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166029&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.43351442043668[/C][/ROW]
[ROW][C]beta[/C][C]-0.818913726149975[/C][/ROW]
[ROW][C]S.D.[/C][C]3.18249782636157[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.257317921591861[/C][/ROW]
[ROW][C]p-value[/C][C]0.809628230489793[/C][/ROW]
[ROW][C]Lambda[/C][C]1.81891372614998[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166029&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166029&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)
alpha3.43351442043668
beta-0.818913726149975
S.D.3.18249782636157
T-STAT-0.257317921591861
p-value0.809628230489793
Lambda1.81891372614998


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')