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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 computationThu, 05 Dec 2013 13:40:17 -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/05/t1386269897iyfr5uigc17u521.htm/, Retrieved Tue, 23 Apr 2024 17:23:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=231214, Retrieved Tue, 23 Apr 2024 17:23:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact63

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] [] [2013-12-05 18:40:17] [98a545f74f3e64fcb7a2edd9d5a425e5] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
104.78
105.56
107.95
107.11
107.47
107.06
99.71
99.6
107.19
107.26
113.24
113.52
110.48
111.41
115.5
118.32
118.42
117.5
110.23
109.19
118.41
118.3
116.1
114.11
113.41
114.33
116.61
123.64
123.77
123.39
116.03
114.95
123.4
123.53
114.45
114.26
114.35
112.77
115.31
114.93
116.38
115.07
105
103.43
114.52
115.04
117.16
115
116.22
112.92
116.56
114.32
113.22
111.56
103.87
102.85
112.27
112.76
118.55
122.73
115.44
116.97
119.84
116.37
117.23
115.58
109.82
108.46
116.54
117.49
122.87
127.1

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 6 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=231214&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]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=231214&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=231214&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 time6 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1106.7041666666674.2270416440586513.92
2114.8308333333333.608362656469849.23
3118.4808333333334.5463640983924210.36
4113.2466666666674.3617976555405213.73
5113.15255.5520596096485619.88
6116.9758333333334.994195646099118.64

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 106.704166666667 & 4.22704164405865 & 13.92 \tabularnewline
2 & 114.830833333333 & 3.60836265646984 & 9.23 \tabularnewline
3 & 118.480833333333 & 4.54636409839242 & 10.36 \tabularnewline
4 & 113.246666666667 & 4.36179765554052 & 13.73 \tabularnewline
5 & 113.1525 & 5.55205960964856 & 19.88 \tabularnewline
6 & 116.975833333333 & 4.9941956460991 & 18.64 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=231214&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]106.704166666667[/C][C]4.22704164405865[/C][C]13.92[/C][/ROW]
[ROW][C]2[/C][C]114.830833333333[/C][C]3.60836265646984[/C][C]9.23[/C][/ROW]
[ROW][C]3[/C][C]118.480833333333[/C][C]4.54636409839242[/C][C]10.36[/C][/ROW]
[ROW][C]4[/C][C]113.246666666667[/C][C]4.36179765554052[/C][C]13.73[/C][/ROW]
[ROW][C]5[/C][C]113.1525[/C][C]5.55205960964856[/C][C]19.88[/C][/ROW]
[ROW][C]6[/C][C]116.975833333333[/C][C]4.9941956460991[/C][C]18.64[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=231214&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=231214&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
1106.7041666666674.2270416440586513.92
2114.8308333333333.608362656469849.23
3118.4808333333334.5463640983924210.36
4113.2466666666674.3617976555405213.73
5113.15255.5520596096485619.88
6116.9758333333334.994195646099118.64






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha1.60730525914338
beta0.0258212268801998
S.D.0.0803598756634119
T-STAT0.321319895868832
p-value0.764056988203668

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.60730525914338 \tabularnewline
beta & 0.0258212268801998 \tabularnewline
S.D. & 0.0803598756634119 \tabularnewline
T-STAT & 0.321319895868832 \tabularnewline
p-value & 0.764056988203668 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=231214&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.60730525914338[/C][/ROW]
[ROW][C]beta[/C][C]0.0258212268801998[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0803598756634119[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.321319895868832[/C][/ROW]
[ROW][C]p-value[/C][C]0.764056988203668[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=231214&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=231214&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)
alpha1.60730525914338
beta0.0258212268801998
S.D.0.0803598756634119
T-STAT0.321319895868832
p-value0.764056988203668






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.527001172724
beta0.640526357064582
S.D.1.99407669210733
T-STAT0.321214504737868
p-value0.764131154271433
Lambda0.359473642935418

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.527001172724 \tabularnewline
beta & 0.640526357064582 \tabularnewline
S.D. & 1.99407669210733 \tabularnewline
T-STAT & 0.321214504737868 \tabularnewline
p-value & 0.764131154271433 \tabularnewline
Lambda & 0.359473642935418 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=231214&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.527001172724[/C][/ROW]
[ROW][C]beta[/C][C]0.640526357064582[/C][/ROW]
[ROW][C]S.D.[/C][C]1.99407669210733[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.321214504737868[/C][/ROW]
[ROW][C]p-value[/C][C]0.764131154271433[/C][/ROW]
[ROW][C]Lambda[/C][C]0.359473642935418[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=231214&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=231214&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-1.527001172724
beta0.640526357064582
S.D.1.99407669210733
T-STAT0.321214504737868
p-value0.764131154271433
Lambda0.359473642935418


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')