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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 computationWed, 04 Dec 2013 11:40:50 -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/2013/Dec/04/t1386175259kabw3x2olyl5lau.htm/, Retrieved Fri, 19 Apr 2024 00:34:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=230674, Retrieved Fri, 19 Apr 2024 00:34:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact61

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] [] [2013-12-04 16:40:50] [ae504791db7208fc7796929702667c6a] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
19.31
19.47
19.7
19.76
19.9
19.97
20.1
20.26
20.44
20.43
20.57
20.6
20.69
20.93
20.98
21.11
21.14
21.16
21.32
21.32
21.48
21.58
21.74
21.75
21.81
21.89
22.21
22.37
22.47
22.51
22.55
22.61
22.58
22.85
22.93
22.98
23.01
23.11
23.18
23.18
23.21
23.22
23.12
23.15
23.16
23.21
23.21
23.22
23.25
23.39
23.41
23.45
23.46
23.44
23.54
23.62
23.86
24.07
24.13
24.12
24.17
24.23
24.28
24.12
24.14
24.17
24.2
24.36
24.34
24.38
24.46
24.6
24.63
24.75
24.64
24.69
24.7
24.74
24.87
24.92
24.94
24.98
25.13
25.15

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230674&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]4 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=230674&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230674&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 time4 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
120.04250.430097769011991.29
221.26666666666670.3285044162795251.06
322.480.3697910958168881.17
423.1650.06171783299088570.209999999999997
523.6450.31477264522480.879999999999999
624.28750.1453600545354380.48
724.8450.181182981340060.52

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 20.0425 & 0.43009776901199 & 1.29 \tabularnewline
2 & 21.2666666666667 & 0.328504416279525 & 1.06 \tabularnewline
3 & 22.48 & 0.369791095816888 & 1.17 \tabularnewline
4 & 23.165 & 0.0617178329908857 & 0.209999999999997 \tabularnewline
5 & 23.645 & 0.3147726452248 & 0.879999999999999 \tabularnewline
6 & 24.2875 & 0.145360054535438 & 0.48 \tabularnewline
7 & 24.845 & 0.18118298134006 & 0.52 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230674&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]20.0425[/C][C]0.43009776901199[/C][C]1.29[/C][/ROW]
[ROW][C]2[/C][C]21.2666666666667[/C][C]0.328504416279525[/C][C]1.06[/C][/ROW]
[ROW][C]3[/C][C]22.48[/C][C]0.369791095816888[/C][C]1.17[/C][/ROW]
[ROW][C]4[/C][C]23.165[/C][C]0.0617178329908857[/C][C]0.209999999999997[/C][/ROW]
[ROW][C]5[/C][C]23.645[/C][C]0.3147726452248[/C][C]0.879999999999999[/C][/ROW]
[ROW][C]6[/C][C]24.2875[/C][C]0.145360054535438[/C][C]0.48[/C][/ROW]
[ROW][C]7[/C][C]24.845[/C][C]0.18118298134006[/C][C]0.52[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230674&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230674&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
120.04250.430097769011991.29
221.26666666666670.3285044162795251.06
322.480.3697910958168881.17
423.1650.06171783299088570.209999999999997
523.6450.31477264522480.879999999999999
624.28750.1453600545354380.48
724.8450.181182981340060.52






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha1.53765379317932
beta-0.0559197180086747
S.D.0.0248124784764236
T-STAT-2.25369336085505
p-value0.0739337618500975

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.53765379317932 \tabularnewline
beta & -0.0559197180086747 \tabularnewline
S.D. & 0.0248124784764236 \tabularnewline
T-STAT & -2.25369336085505 \tabularnewline
p-value & 0.0739337618500975 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230674&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.53765379317932[/C][/ROW]
[ROW][C]beta[/C][C]-0.0559197180086747[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0248124784764236[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.25369336085505[/C][/ROW]
[ROW][C]p-value[/C][C]0.0739337618500975[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230674&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230674&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)
alpha1.53765379317932
beta-0.0559197180086747
S.D.0.0248124784764236
T-STAT-2.25369336085505
p-value0.0739337618500975






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha13.9952470780982
beta-4.95959954361548
S.D.3.38466218312373
T-STAT-1.46531596811775
p-value0.202729283042654
Lambda5.95959954361548

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 13.9952470780982 \tabularnewline
beta & -4.95959954361548 \tabularnewline
S.D. & 3.38466218312373 \tabularnewline
T-STAT & -1.46531596811775 \tabularnewline
p-value & 0.202729283042654 \tabularnewline
Lambda & 5.95959954361548 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230674&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]13.9952470780982[/C][/ROW]
[ROW][C]beta[/C][C]-4.95959954361548[/C][/ROW]
[ROW][C]S.D.[/C][C]3.38466218312373[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.46531596811775[/C][/ROW]
[ROW][C]p-value[/C][C]0.202729283042654[/C][/ROW]
[ROW][C]Lambda[/C][C]5.95959954361548[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230674&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230674&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)
alpha13.9952470780982
beta-4.95959954361548
S.D.3.38466218312373
T-STAT-1.46531596811775
p-value0.202729283042654
Lambda5.95959954361548


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')