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Description of Statistical Computation

Author's title

Standard deviation/Mean plot - Gem. prijs gebakken tong of forel - Niels Br...

Author*Unverified author*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationTue, 18 Aug 2009 16:17:57 -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/2009/Aug/19/t12506339561vd02qjzdut0qn7.htm/, Retrieved Wed, 08 May 2024 03:06:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=42903, Retrieved Wed, 08 May 2024 03:06:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact159

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] [Standard deviatio...] [2009-08-18 22:17:57] [b3f4824a747975de0748bc1b396f9742] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
15.22
15.27
15.31
15.33
15.42
15.49
15.65
15.67
15.69
15.83
15.92
15.99
15.94
15.96
16.03
16.09
16.04
16.23
16.2
16.2
16.26
16.28
16.27
16.29
16.3
16.37
16.39
16.42
16.43
16.37
16.37
16.39
16.48
16.51
16.5
16.54
16.52
16.56
16.61
16.75
16.75
16.79
16.82
16.84
17.14
17.25
17.28
17.3
17.34
17.44
17.48
17.55
17.59
17.66
17.67
17.64
17.68
17.72
17.78
17.83
17.88
18.11
18.16
18.27
18.29
18.35
18.35
18.38
18.41
18.41
18.42
18.43
18.48
18.54
18.65
18.66
18.69
18.72
18.72
18.73
18.84
18.83
18.91
18.91
18.94
18.97
19
19.08
19.18
19.24
19.23
19.25
19.3
19.33
19.35
19.35
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

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=42903&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=42903&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42903&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
115.56583333333330.263489117709850.77
216.14916666666670.1295768170436040.350000000000000
316.42250.07149380138420110.239999999999998
416.88416666666670.2848750390588620.780000000000001
517.6150.1426056227375470.489999999999998
618.28833333333330.1646943909920510.550000000000001
718.72333333333330.1341866632943100.43
819.1850.1506048411632850.41
920.04250.4300977690119901.29000000000000
1021.26666666666670.3285044162795251.06000000000000
1122.480.3697910958168881.17000000000000

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 15.5658333333333 & 0.26348911770985 & 0.77 \tabularnewline
2 & 16.1491666666667 & 0.129576817043604 & 0.350000000000000 \tabularnewline
3 & 16.4225 & 0.0714938013842011 & 0.239999999999998 \tabularnewline
4 & 16.8841666666667 & 0.284875039058862 & 0.780000000000001 \tabularnewline
5 & 17.615 & 0.142605622737547 & 0.489999999999998 \tabularnewline
6 & 18.2883333333333 & 0.164694390992051 & 0.550000000000001 \tabularnewline
7 & 18.7233333333333 & 0.134186663294310 & 0.43 \tabularnewline
8 & 19.185 & 0.150604841163285 & 0.41 \tabularnewline
9 & 20.0425 & 0.430097769011990 & 1.29000000000000 \tabularnewline
10 & 21.2666666666667 & 0.328504416279525 & 1.06000000000000 \tabularnewline
11 & 22.48 & 0.369791095816888 & 1.17000000000000 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42903&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]15.5658333333333[/C][C]0.26348911770985[/C][C]0.77[/C][/ROW]
[ROW][C]2[/C][C]16.1491666666667[/C][C]0.129576817043604[/C][C]0.350000000000000[/C][/ROW]
[ROW][C]3[/C][C]16.4225[/C][C]0.0714938013842011[/C][C]0.239999999999998[/C][/ROW]
[ROW][C]4[/C][C]16.8841666666667[/C][C]0.284875039058862[/C][C]0.780000000000001[/C][/ROW]
[ROW][C]5[/C][C]17.615[/C][C]0.142605622737547[/C][C]0.489999999999998[/C][/ROW]
[ROW][C]6[/C][C]18.2883333333333[/C][C]0.164694390992051[/C][C]0.550000000000001[/C][/ROW]
[ROW][C]7[/C][C]18.7233333333333[/C][C]0.134186663294310[/C][C]0.43[/C][/ROW]
[ROW][C]8[/C][C]19.185[/C][C]0.150604841163285[/C][C]0.41[/C][/ROW]
[ROW][C]9[/C][C]20.0425[/C][C]0.430097769011990[/C][C]1.29000000000000[/C][/ROW]
[ROW][C]10[/C][C]21.2666666666667[/C][C]0.328504416279525[/C][C]1.06000000000000[/C][/ROW]
[ROW][C]11[/C][C]22.48[/C][C]0.369791095816888[/C][C]1.17000000000000[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42903&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42903&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
115.56583333333330.263489117709850.77
216.14916666666670.1295768170436040.350000000000000
316.42250.07149380138420110.239999999999998
416.88416666666670.2848750390588620.780000000000001
517.6150.1426056227375470.489999999999998
618.28833333333330.1646943909920510.550000000000001
718.72333333333330.1341866632943100.43
819.1850.1506048411632850.41
920.04250.4300977690119901.29000000000000
1021.26666666666670.3285044162795251.06000000000000
1122.480.3697910958168881.17000000000000






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.358695120938954
beta0.0316626529868134
S.D.0.0141879413676123
T-STAT2.23165941882814
p-value0.052554206382819

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.358695120938954 \tabularnewline
beta & 0.0316626529868134 \tabularnewline
S.D. & 0.0141879413676123 \tabularnewline
T-STAT & 2.23165941882814 \tabularnewline
p-value & 0.052554206382819 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42903&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.358695120938954[/C][/ROW]
[ROW][C]beta[/C][C]0.0316626529868134[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0141879413676123[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.23165941882814[/C][/ROW]
[ROW][C]p-value[/C][C]0.052554206382819[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42903&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42903&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-0.358695120938954
beta0.0316626529868134
S.D.0.0141879413676123
T-STAT2.23165941882814
p-value0.052554206382819






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-9.10910990059749
beta2.57436675712676
S.D.1.31448252958674
T-STAT1.95846403370314
p-value0.0818461995525307
Lambda-1.57436675712676

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -9.10910990059749 \tabularnewline
beta & 2.57436675712676 \tabularnewline
S.D. & 1.31448252958674 \tabularnewline
T-STAT & 1.95846403370314 \tabularnewline
p-value & 0.0818461995525307 \tabularnewline
Lambda & -1.57436675712676 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42903&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-9.10910990059749[/C][/ROW]
[ROW][C]beta[/C][C]2.57436675712676[/C][/ROW]
[ROW][C]S.D.[/C][C]1.31448252958674[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.95846403370314[/C][/ROW]
[ROW][C]p-value[/C][C]0.0818461995525307[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.57436675712676[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42903&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42903&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-9.10910990059749
beta2.57436675712676
S.D.1.31448252958674
T-STAT1.95846403370314
p-value0.0818461995525307
Lambda-1.57436675712676


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')