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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 computationFri, 09 May 2008 08:38:25 -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/May/09/t1210344044r9ip658wd2u8a3w.htm/, Retrieved Tue, 14 May 2024 02:06:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=12169, Retrieved Tue, 14 May 2024 02:06:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsopdracht 8 eigen cijfferreeks
Estimated Impact153

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [] [Variability - Ste...] [-0001-11-30 00:00:00] [cd00afdb012dd785c94e77d4cae74ef4]
- RMPD    [Standard Deviation-Mean Plot] [Stephanie De Coni...] [2008-05-09 14:38:25] [80d88a38ebee1e39f846defee1b12cef] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
68.64
68.61
68.61
68.61
68.58
68.75
68.54
68.5
68.47
68.47
68.47
68.59
68.32
67.86
67.91
67.91
68.05
68.15
68.25
68.25
68.31
68.31
69.65
69.65
70.18
70.08
70.08
70.09
70.04
70.14
70.26
70.23
70.54
70.54
70.57
70.61
70.63
70.45
70.4
70.4
70.33
70.51
70.45
70.39
70.59
70.59
70.32
70.94
70.44
70.57
70.61
70.61
70.68
69.96
70.11
70.22
70.49
70.49
70.58
70.85
70.69
70.7
70.7
70.7
70.67
70.64
70.98
70.75
70.88
70.88
70.92
70.89
71.02
71.01
71.02

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'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12169&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12169&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12169&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
168.570.0844231764817740.280000000000001
268.3850.6139810479752051.79000000000001
370.280.2204128357918790.569999999999993
470.50.1719407931924130.620000000000005
570.46750.2529148257633570.89
670.78333333333330.1173443520996940.340000000000003

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 68.57 & 0.084423176481774 & 0.280000000000001 \tabularnewline
2 & 68.385 & 0.613981047975205 & 1.79000000000001 \tabularnewline
3 & 70.28 & 0.220412835791879 & 0.569999999999993 \tabularnewline
4 & 70.5 & 0.171940793192413 & 0.620000000000005 \tabularnewline
5 & 70.4675 & 0.252914825763357 & 0.89 \tabularnewline
6 & 70.7833333333333 & 0.117344352099694 & 0.340000000000003 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12169&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]68.57[/C][C]0.084423176481774[/C][C]0.280000000000001[/C][/ROW]
[ROW][C]2[/C][C]68.385[/C][C]0.613981047975205[/C][C]1.79000000000001[/C][/ROW]
[ROW][C]3[/C][C]70.28[/C][C]0.220412835791879[/C][C]0.569999999999993[/C][/ROW]
[ROW][C]4[/C][C]70.5[/C][C]0.171940793192413[/C][C]0.620000000000005[/C][/ROW]
[ROW][C]5[/C][C]70.4675[/C][C]0.252914825763357[/C][C]0.89[/C][/ROW]
[ROW][C]6[/C][C]70.7833333333333[/C][C]0.117344352099694[/C][C]0.340000000000003[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12169&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12169&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
168.570.0844231764817740.280000000000001
268.3850.6139810479752051.79000000000001
370.280.2204128357918790.569999999999993
470.50.1719407931924130.620000000000005
570.46750.2529148257633570.89
670.78333333333330.1173443520996940.340000000000003






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha6.52463133765673
beta-0.0899476020342041
S.D.0.0783570007238744
T-STAT-1.14792043089008
p-value0.314986246588399

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 6.52463133765673 \tabularnewline
beta & -0.0899476020342041 \tabularnewline
S.D. & 0.0783570007238744 \tabularnewline
T-STAT & -1.14792043089008 \tabularnewline
p-value & 0.314986246588399 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12169&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]6.52463133765673[/C][/ROW]
[ROW][C]beta[/C][C]-0.0899476020342041[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0783570007238744[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.14792043089008[/C][/ROW]
[ROW][C]p-value[/C][C]0.314986246588399[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12169&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12169&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)
alpha6.52463133765673
beta-0.0899476020342041
S.D.0.0783570007238744
T-STAT-1.14792043089008
p-value0.314986246588399






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha48.095758619483
beta-11.7100730211531
S.D.21.7628032997146
T-STAT-0.538077418606573
p-value0.61906698149135
Lambda12.7100730211531

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 48.095758619483 \tabularnewline
beta & -11.7100730211531 \tabularnewline
S.D. & 21.7628032997146 \tabularnewline
T-STAT & -0.538077418606573 \tabularnewline
p-value & 0.61906698149135 \tabularnewline
Lambda & 12.7100730211531 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12169&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]48.095758619483[/C][/ROW]
[ROW][C]beta[/C][C]-11.7100730211531[/C][/ROW]
[ROW][C]S.D.[/C][C]21.7628032997146[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.538077418606573[/C][/ROW]
[ROW][C]p-value[/C][C]0.61906698149135[/C][/ROW]
[ROW][C]Lambda[/C][C]12.7100730211531[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12169&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12169&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)
alpha48.095758619483
beta-11.7100730211531
S.D.21.7628032997146
T-STAT-0.538077418606573
p-value0.61906698149135
Lambda12.7100730211531


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')