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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, 27 May 2012 04:53:28 -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/27/t1338108838xs8j6y50778adw7.htm/, Retrieved Wed, 08 May 2024 08:20:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167656, Retrieved Wed, 08 May 2024 08:20:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W83
Estimated Impact137

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...] [2012-05-27 08:53:28] [a2709f7ab86902c8a6d752383a828f6c] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
67.66
68
68.02
68.11
68.41
68.4
68.4
68.55
68.54
68.99
68.97
68.98
68.98
68.94
69.21
69.21
69.67
69.66
69.66
69.66
69.77
70.32
70.34
70.38
70.38
70.29
70.42
70.29
70.59
70.64
70.64
70.68
70.78
70.9
71.04
71.15
71.15
71.15
71.07
71.17
71.24
71.23
71.23
71.23
71.24
71.28
71.52
71.52
71.52
71.6
71.61
71.78
71.66
71.86
71.86
71.82
71.8
72.22
72.51
72.56

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'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167656&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167656&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167656&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'Gertrude Mary Cox' @ cox.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
168.41916666666670.4246165828417951.33
269.650.5057128182530621.44
370.650.2814249455894070.859999999999999
471.25250.1371213795411650.450000000000003
571.90.3464364037138471.04000000000001

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 68.4191666666667 & 0.424616582841795 & 1.33 \tabularnewline
2 & 69.65 & 0.505712818253062 & 1.44 \tabularnewline
3 & 70.65 & 0.281424945589407 & 0.859999999999999 \tabularnewline
4 & 71.2525 & 0.137121379541165 & 0.450000000000003 \tabularnewline
5 & 71.9 & 0.346436403713847 & 1.04000000000001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167656&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]68.4191666666667[/C][C]0.424616582841795[/C][C]1.33[/C][/ROW]
[ROW][C]2[/C][C]69.65[/C][C]0.505712818253062[/C][C]1.44[/C][/ROW]
[ROW][C]3[/C][C]70.65[/C][C]0.281424945589407[/C][C]0.859999999999999[/C][/ROW]
[ROW][C]4[/C][C]71.2525[/C][C]0.137121379541165[/C][C]0.450000000000003[/C][/ROW]
[ROW][C]5[/C][C]71.9[/C][C]0.346436403713847[/C][C]1.04000000000001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167656&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167656&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
168.41916666666670.4246165828417951.33
269.650.5057128182530621.44
370.650.2814249455894070.859999999999999
471.25250.1371213795411650.450000000000003
571.90.3464364037138471.04000000000001






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha4.73581424251588
beta-0.0624766389715193
S.D.0.0470177435003396
T-STAT-1.32878854492598
p-value0.275945549257157

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 4.73581424251588 \tabularnewline
beta & -0.0624766389715193 \tabularnewline
S.D. & 0.0470177435003396 \tabularnewline
T-STAT & -1.32878854492598 \tabularnewline
p-value & 0.275945549257157 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167656&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]4.73581424251588[/C][/ROW]
[ROW][C]beta[/C][C]-0.0624766389715193[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0470177435003396[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.32878854492598[/C][/ROW]
[ROW][C]p-value[/C][C]0.275945549257157[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167656&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167656&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)
alpha4.73581424251588
beta-0.0624766389715193
S.D.0.0470177435003396
T-STAT-1.32878854492598
p-value0.275945549257157






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha60.1037262673228
beta-14.4050379432464
S.D.12.421210995595
T-STAT-1.15971284509658
p-value0.330080139014047
Lambda15.4050379432464

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 60.1037262673228 \tabularnewline
beta & -14.4050379432464 \tabularnewline
S.D. & 12.421210995595 \tabularnewline
T-STAT & -1.15971284509658 \tabularnewline
p-value & 0.330080139014047 \tabularnewline
Lambda & 15.4050379432464 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167656&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]60.1037262673228[/C][/ROW]
[ROW][C]beta[/C][C]-14.4050379432464[/C][/ROW]
[ROW][C]S.D.[/C][C]12.421210995595[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.15971284509658[/C][/ROW]
[ROW][C]p-value[/C][C]0.330080139014047[/C][/ROW]
[ROW][C]Lambda[/C][C]15.4050379432464[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167656&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167656&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)
alpha60.1037262673228
beta-14.4050379432464
S.D.12.421210995595
T-STAT-1.15971284509658
p-value0.330080139014047
Lambda15.4050379432464


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')