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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 computationSun, 01 Jun 2008 15:12:02 -0600
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/Jun/01/t1212354767lowq1ul9qpsmiz3.htm/, Retrieved Fri, 24 May 2024 14:27:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13750, Retrieved Fri, 24 May 2024 14:27:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact201

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] [Standard deviatio...] [2008-06-01 21:12:02] [b3f4824a747975de0748bc1b396f9742] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
38
38
37,93
38
38,02
38,02
38,02
37,96
37,96
37,99
38
38
38
38,01
38,06
38,02
38,05
38,05
38,05
38,05
38,03
37,98
38,03
38,04
38,04
38,08
38,14
38,37
38,49
38,55
38,55
38,55
38,48
38,51
38,48
38,48
38,48
38,43
38,43
38,45
38,48
38,47
38,47
38,42
38,55
38,56
38,57
38,57
38,57
38,57
38,62
38,73
38,74
38,68
38,69
38,69
38,61
38,77
38,78
38,81
38,81
38,81
38,76
38,93
38,95
38,97
38,97
38,96
38,92
38,95
38,95
38,97
38,97
39,05
39,08
38,83
38,86
38,87
38,87
38,75
38,86
38,93
38,96
38,95

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 5 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13750&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13750&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13750&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 time5 seconds
R Server'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
137.99166666666670.02790677119961960.0900000000000034
238.03083333333330.02429303429280740.0800000000000054
338.39333333333330.1923223304452150.509999999999998
438.490.05720775535473540.149999999999999
538.68833333333330.08155682161239050.240000000000002
638.91250.0744830670201440.210000000000001
738.9150.09366283826965340.329999999999998

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 37.9916666666667 & 0.0279067711996196 & 0.0900000000000034 \tabularnewline
2 & 38.0308333333333 & 0.0242930342928074 & 0.0800000000000054 \tabularnewline
3 & 38.3933333333333 & 0.192322330445215 & 0.509999999999998 \tabularnewline
4 & 38.49 & 0.0572077553547354 & 0.149999999999999 \tabularnewline
5 & 38.6883333333333 & 0.0815568216123905 & 0.240000000000002 \tabularnewline
6 & 38.9125 & 0.074483067020144 & 0.210000000000001 \tabularnewline
7 & 38.915 & 0.0936628382696534 & 0.329999999999998 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13750&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]37.9916666666667[/C][C]0.0279067711996196[/C][C]0.0900000000000034[/C][/ROW]
[ROW][C]2[/C][C]38.0308333333333[/C][C]0.0242930342928074[/C][C]0.0800000000000054[/C][/ROW]
[ROW][C]3[/C][C]38.3933333333333[/C][C]0.192322330445215[/C][C]0.509999999999998[/C][/ROW]
[ROW][C]4[/C][C]38.49[/C][C]0.0572077553547354[/C][C]0.149999999999999[/C][/ROW]
[ROW][C]5[/C][C]38.6883333333333[/C][C]0.0815568216123905[/C][C]0.240000000000002[/C][/ROW]
[ROW][C]6[/C][C]38.9125[/C][C]0.074483067020144[/C][C]0.210000000000001[/C][/ROW]
[ROW][C]7[/C][C]38.915[/C][C]0.0936628382696534[/C][C]0.329999999999998[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13750&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13750&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
137.99166666666670.02790677119961960.0900000000000034
238.03083333333330.02429303429280740.0800000000000054
338.39333333333330.1923223304452150.509999999999998
438.490.05720775535473540.149999999999999
538.68833333333330.08155682161239050.240000000000002
638.91250.0744830670201440.210000000000001
738.9150.09366283826965340.329999999999998






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-1.89478781891465
beta0.0512763042464926
S.D.0.0624063052651857
T-STAT0.821652620333828
p-value0.448665945228404

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -1.89478781891465 \tabularnewline
beta & 0.0512763042464926 \tabularnewline
S.D. & 0.0624063052651857 \tabularnewline
T-STAT & 0.821652620333828 \tabularnewline
p-value & 0.448665945228404 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13750&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.89478781891465[/C][/ROW]
[ROW][C]beta[/C][C]0.0512763042464926[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0624063052651857[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.821652620333828[/C][/ROW]
[ROW][C]p-value[/C][C]0.448665945228404[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13750&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13750&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-1.89478781891465
beta0.0512763042464926
S.D.0.0624063052651857
T-STAT0.821652620333828
p-value0.448665945228404






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-169.332367202700
beta45.6338451246183
S.D.25.1622864391662
T-STAT1.81358102074489
p-value0.129474282990958
Lambda-44.6338451246183

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -169.332367202700 \tabularnewline
beta & 45.6338451246183 \tabularnewline
S.D. & 25.1622864391662 \tabularnewline
T-STAT & 1.81358102074489 \tabularnewline
p-value & 0.129474282990958 \tabularnewline
Lambda & -44.6338451246183 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13750&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-169.332367202700[/C][/ROW]
[ROW][C]beta[/C][C]45.6338451246183[/C][/ROW]
[ROW][C]S.D.[/C][C]25.1622864391662[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.81358102074489[/C][/ROW]
[ROW][C]p-value[/C][C]0.129474282990958[/C][/ROW]
[ROW][C]Lambda[/C][C]-44.6338451246183[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13750&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13750&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-169.332367202700
beta45.6338451246183
S.D.25.1622864391662
T-STAT1.81358102074489
p-value0.129474282990958
Lambda-44.6338451246183


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')