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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, 09 May 2011 20:06:24 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/May/09/t13049714959dg2guwl8yhgz5g.htm/, Retrieved Tue, 14 May 2024 21:58:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=121342, Retrieved Tue, 14 May 2024 21:58:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W83
Estimated Impact84

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] [] [2011-05-09 20:06:24] [95535446f37f05535215079c34b74784] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
71.42
71.47
71.55
71.6
71.62
71.64
71.65
71.65
71.65
71.7
71.73
71.83
71.83
71.87
71.91
71.99
72.1
72.12
72.12
72.12
72.25
72.59
72.72
72.76
72.76
72.91
73
73.11
73.11
73.16
73.16
73.33
73.51
73.65
73.65
73.65
73.65
73.66
73.71
73.73
73.77
73.77
73.78
73.85
73.88
74.3
74.53
74.53
74.53
74.53
74.65
74.65
74.65
74.71
74.71
74.78
74.85
74.9
74.96
74.96
74.96
74.98
75.19
75.22
75.33
75.33
75.37
75.44
75.54
75.58
75.59
75.61

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R Server'Herman Ole Andreas Wold' @ www.yougetit.org

\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 & 0 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ www.yougetit.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121342&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]0 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ www.yougetit.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121342&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121342&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 time0 seconds
R Server'Herman Ole Andreas Wold' @ www.yougetit.org






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
171.62583333333330.1099965564199290.409999999999997
272.19833333333330.3221753710279080.930000000000007
373.250.3056438807144410.89
473.930.3274141108748990.879999999999995
574.740.150876228623450.429999999999993
675.3450.2245601761828510.650000000000006

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 71.6258333333333 & 0.109996556419929 & 0.409999999999997 \tabularnewline
2 & 72.1983333333333 & 0.322175371027908 & 0.930000000000007 \tabularnewline
3 & 73.25 & 0.305643880714441 & 0.89 \tabularnewline
4 & 73.93 & 0.327414110874899 & 0.879999999999995 \tabularnewline
5 & 74.74 & 0.15087622862345 & 0.429999999999993 \tabularnewline
6 & 75.345 & 0.224560176182851 & 0.650000000000006 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121342&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]71.6258333333333[/C][C]0.109996556419929[/C][C]0.409999999999997[/C][/ROW]
[ROW][C]2[/C][C]72.1983333333333[/C][C]0.322175371027908[/C][C]0.930000000000007[/C][/ROW]
[ROW][C]3[/C][C]73.25[/C][C]0.305643880714441[/C][C]0.89[/C][/ROW]
[ROW][C]4[/C][C]73.93[/C][C]0.327414110874899[/C][C]0.879999999999995[/C][/ROW]
[ROW][C]5[/C][C]74.74[/C][C]0.15087622862345[/C][C]0.429999999999993[/C][/ROW]
[ROW][C]6[/C][C]75.345[/C][C]0.224560176182851[/C][C]0.650000000000006[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121342&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121342&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
171.62583333333330.1099965564199290.409999999999997
272.19833333333330.3221753710279080.930000000000007
373.250.3056438807144410.89
473.930.3274141108748990.879999999999995
574.740.150876228623450.429999999999993
675.3450.2245601761828510.650000000000006






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.106792343681735
beta0.00181349333015373
S.D.0.0324386269112872
T-STAT0.0559053666208884
p-value0.95809825377856

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.106792343681735 \tabularnewline
beta & 0.00181349333015373 \tabularnewline
S.D. & 0.0324386269112872 \tabularnewline
T-STAT & 0.0559053666208884 \tabularnewline
p-value & 0.95809825377856 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121342&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.106792343681735[/C][/ROW]
[ROW][C]beta[/C][C]0.00181349333015373[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0324386269112872[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.0559053666208884[/C][/ROW]
[ROW][C]p-value[/C][C]0.95809825377856[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121342&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121342&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)
alpha0.106792343681735
beta0.00181349333015373
S.D.0.0324386269112872
T-STAT0.0559053666208884
p-value0.95809825377856






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-15.965967657785
beta3.36523405187946
S.D.11.4622432537677
T-STAT0.293592971059422
p-value0.783672005885893
Lambda-2.36523405187946

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -15.965967657785 \tabularnewline
beta & 3.36523405187946 \tabularnewline
S.D. & 11.4622432537677 \tabularnewline
T-STAT & 0.293592971059422 \tabularnewline
p-value & 0.783672005885893 \tabularnewline
Lambda & -2.36523405187946 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121342&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-15.965967657785[/C][/ROW]
[ROW][C]beta[/C][C]3.36523405187946[/C][/ROW]
[ROW][C]S.D.[/C][C]11.4622432537677[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.293592971059422[/C][/ROW]
[ROW][C]p-value[/C][C]0.783672005885893[/C][/ROW]
[ROW][C]Lambda[/C][C]-2.36523405187946[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121342&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121342&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-15.965967657785
beta3.36523405187946
S.D.11.4622432537677
T-STAT0.293592971059422
p-value0.783672005885893
Lambda-2.36523405187946


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')