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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, 26 May 2013 20:48:36 -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/2013/May/26/t1369615760grwbh8bks6j32vw.htm/, Retrieved Mon, 29 Apr 2024 13:21:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210720, Retrieved Mon, 29 Apr 2024 13:21:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact73

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] [] [2013-05-27 00:48:36] [5b48cba8ffed7710e2defc0d8d22bd89] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
13.29
13.34
13.41
13.45
13.52
13.52
13.53
13.55
13.52
13.51
13.55
13.56
13.62
13.69
13.67
13.66
13.69
13.69
13.7
13.73
13.79
13.8
13.84
13.84
13.88
13.97
14.06
14.11
14.13
14.15
14.2
14.28
14.3
14.33
14.4
14.4
14.42
14.51
14.64
14.68
14.72
14.73
14.76
14.78
14.83
14.84
14.85
14.87
14.87
14.96
15.08
15.08
15.12
15.12
15.1
15.16
15.22
15.28
15.29
15.32
15.4
15.44
15.48
15.52
15.6
15.61
15.66
15.69
15.75
15.82
15.81
15.82

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'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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210720&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210720&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210720&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'Gertrude Mary Cox' @ cox.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
113.47916666666670.0883647742787440.270000000000001
213.72666666666670.07315405082095710.220000000000001
314.18416666666670.1653348301496270.52
414.71916666666670.1392485242835680.449999999999999
515.13333333333330.133371206742230.450000000000001
615.63333333333330.1502321435968250.42

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 13.4791666666667 & 0.088364774278744 & 0.270000000000001 \tabularnewline
2 & 13.7266666666667 & 0.0731540508209571 & 0.220000000000001 \tabularnewline
3 & 14.1841666666667 & 0.165334830149627 & 0.52 \tabularnewline
4 & 14.7191666666667 & 0.139248524283568 & 0.449999999999999 \tabularnewline
5 & 15.1333333333333 & 0.13337120674223 & 0.450000000000001 \tabularnewline
6 & 15.6333333333333 & 0.150232143596825 & 0.42 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210720&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]13.4791666666667[/C][C]0.088364774278744[/C][C]0.270000000000001[/C][/ROW]
[ROW][C]2[/C][C]13.7266666666667[/C][C]0.0731540508209571[/C][C]0.220000000000001[/C][/ROW]
[ROW][C]3[/C][C]14.1841666666667[/C][C]0.165334830149627[/C][C]0.52[/C][/ROW]
[ROW][C]4[/C][C]14.7191666666667[/C][C]0.139248524283568[/C][C]0.449999999999999[/C][/ROW]
[ROW][C]5[/C][C]15.1333333333333[/C][C]0.13337120674223[/C][C]0.450000000000001[/C][/ROW]
[ROW][C]6[/C][C]15.6333333333333[/C][C]0.150232143596825[/C][C]0.42[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210720&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210720&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
113.47916666666670.0883647742787440.270000000000001
213.72666666666670.07315405082095710.220000000000001
314.18416666666670.1653348301496270.52
414.71916666666670.1392485242835680.449999999999999
515.13333333333330.133371206742230.450000000000001
615.63333333333330.1502321435968250.42






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.299587426954338
beta0.0293203528975029
S.D.0.0160644231900265
T-STAT1.82517308904725
p-value0.142021214246414

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.299587426954338 \tabularnewline
beta & 0.0293203528975029 \tabularnewline
S.D. & 0.0160644231900265 \tabularnewline
T-STAT & 1.82517308904725 \tabularnewline
p-value & 0.142021214246414 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210720&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.299587426954338[/C][/ROW]
[ROW][C]beta[/C][C]0.0293203528975029[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0160644231900265[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.82517308904725[/C][/ROW]
[ROW][C]p-value[/C][C]0.142021214246414[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210720&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210720&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-0.299587426954338
beta0.0293203528975029
S.D.0.0160644231900265
T-STAT1.82517308904725
p-value0.142021214246414






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-12.8240581623906
beta4.00680919902098
S.D.1.9870060809318
T-STAT2.01650575580624
p-value0.113950569691485
Lambda-3.00680919902098

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -12.8240581623906 \tabularnewline
beta & 4.00680919902098 \tabularnewline
S.D. & 1.9870060809318 \tabularnewline
T-STAT & 2.01650575580624 \tabularnewline
p-value & 0.113950569691485 \tabularnewline
Lambda & -3.00680919902098 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210720&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-12.8240581623906[/C][/ROW]
[ROW][C]beta[/C][C]4.00680919902098[/C][/ROW]
[ROW][C]S.D.[/C][C]1.9870060809318[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.01650575580624[/C][/ROW]
[ROW][C]p-value[/C][C]0.113950569691485[/C][/ROW]
[ROW][C]Lambda[/C][C]-3.00680919902098[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210720&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210720&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-12.8240581623906
beta4.00680919902098
S.D.1.9870060809318
T-STAT2.01650575580624
p-value0.113950569691485
Lambda-3.00680919902098


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')