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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 computationMon, 26 Nov 2012 05:05:50 -0500
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/Nov/26/t1353924372lp8zdt9a2tj86tp.htm/, Retrieved Tue, 30 Apr 2024 00:12:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=192927, Retrieved Tue, 30 Apr 2024 00:12:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact92

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] [] [2012-11-26 10:05:50] [606ba890a58836132a627f58687546e9] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
46,83
45,93
45,93
45,93
45,9
45,91
45,85
45,58
45,56
45,5
45,5
45,5
45,51
45,49
45,4
45,38
45,38
45,38
45,49
45,41
44,99
44,98
44,93
44,93
44,91
44,86
44,76
44,89
44,89
45
45,01
45,11
45,05
44,67
44,48
44,48
44,48
44,58
44,79
44,79
44,41
44,41
44,44
44,43
44,36
44,39
44,39
44,41
44,32
44,43
44,82
44,97
44,91
44,79
44,76
44,8
44,65
44,49
44,56
44,4
44,45
44,46
44,39
44,5
44,44
44,41
44,4
44,42
44,49
44,46
44,49
44,5

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'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=192927&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=192927&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=192927&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'Gwilym Jenkins' @ jenkins.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
145.82666666666670.3697255329253981.33
245.27250.2375681720341270.579999999999998
344.84250.2080701367764770.630000000000003
444.490.1508762286234530.43
544.65833333333330.2144266491805240.649999999999999
644.45083333333330.03941811612428910.109999999999999

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 45.8266666666667 & 0.369725532925398 & 1.33 \tabularnewline
2 & 45.2725 & 0.237568172034127 & 0.579999999999998 \tabularnewline
3 & 44.8425 & 0.208070136776477 & 0.630000000000003 \tabularnewline
4 & 44.49 & 0.150876228623453 & 0.43 \tabularnewline
5 & 44.6583333333333 & 0.214426649180524 & 0.649999999999999 \tabularnewline
6 & 44.4508333333333 & 0.0394181161242891 & 0.109999999999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=192927&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]45.8266666666667[/C][C]0.369725532925398[/C][C]1.33[/C][/ROW]
[ROW][C]2[/C][C]45.2725[/C][C]0.237568172034127[/C][C]0.579999999999998[/C][/ROW]
[ROW][C]3[/C][C]44.8425[/C][C]0.208070136776477[/C][C]0.630000000000003[/C][/ROW]
[ROW][C]4[/C][C]44.49[/C][C]0.150876228623453[/C][C]0.43[/C][/ROW]
[ROW][C]5[/C][C]44.6583333333333[/C][C]0.214426649180524[/C][C]0.649999999999999[/C][/ROW]
[ROW][C]6[/C][C]44.4508333333333[/C][C]0.0394181161242891[/C][C]0.109999999999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=192927&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=192927&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
145.82666666666670.3697255329253981.33
245.27250.2375681720341270.579999999999998
344.84250.2080701367764770.630000000000003
444.490.1508762286234530.43
544.65833333333330.2144266491805240.649999999999999
644.45083333333330.03941811612428910.109999999999999






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-7.96134041353445
beta0.181746589973211
S.D.0.0449635740160782
T-STAT4.04208504217707
p-value0.0155771519227401

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -7.96134041353445 \tabularnewline
beta & 0.181746589973211 \tabularnewline
S.D. & 0.0449635740160782 \tabularnewline
T-STAT & 4.04208504217707 \tabularnewline
p-value & 0.0155771519227401 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=192927&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-7.96134041353445[/C][/ROW]
[ROW][C]beta[/C][C]0.181746589973211[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0449635740160782[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.04208504217707[/C][/ROW]
[ROW][C]p-value[/C][C]0.0155771519227401[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=192927&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=192927&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-7.96134041353445
beta0.181746589973211
S.D.0.0449635740160782
T-STAT4.04208504217707
p-value0.0155771519227401






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-180.701809559386
beta47.0246057459377
S.D.22.452262965891
T-STAT2.09442610828925
p-value0.104307759514152
Lambda-46.0246057459377

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -180.701809559386 \tabularnewline
beta & 47.0246057459377 \tabularnewline
S.D. & 22.452262965891 \tabularnewline
T-STAT & 2.09442610828925 \tabularnewline
p-value & 0.104307759514152 \tabularnewline
Lambda & -46.0246057459377 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=192927&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-180.701809559386[/C][/ROW]
[ROW][C]beta[/C][C]47.0246057459377[/C][/ROW]
[ROW][C]S.D.[/C][C]22.452262965891[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.09442610828925[/C][/ROW]
[ROW][C]p-value[/C][C]0.104307759514152[/C][/ROW]
[ROW][C]Lambda[/C][C]-46.0246057459377[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=192927&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=192927&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-180.701809559386
beta47.0246057459377
S.D.22.452262965891
T-STAT2.09442610828925
p-value0.104307759514152
Lambda-46.0246057459377


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')