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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, 14 Dec 2011 15:32:17 -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/2011/Dec/14/t13238948501k8g0sdqin6juy0.htm/, Retrieved Wed, 01 May 2024 22:22:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=155238, Retrieved Wed, 01 May 2024 22:22:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W83
Estimated Impact90

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] [] [2011-12-14 20:32:17] [ded1bbd321fb25f4a0a8bacc8426c40e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2.98
2.98
2.98
3.03
3.07
3.08
3.08
3.08
3.08
3.08
3.08
3.08
3.08
3.08
3.12
3.15
3.15
3.15
3.15
3.16
3.19
3.20
3.20
3.20
3.21
3.21
3.21
3.21
3.21
3.28
3.30
3.30
3.30
3.30
3.30
3.30
3.30
3.45
3.49
3.50
3.54
3.64
3.67
3.67
3.68
3.68
3.68
3.68
3.70
3.83
3.87
3.87
3.87
3.87
3.87
3.87
3.87
3.87
3.87
3.88
3.88
3.88
3.88
3.88
3.88
3.89
3.89
3.91
3.95
3.99
3.99
3.99
4.00
4.00
4.00
4.00
4.00
4.00
4.00
4.00
4.06
4.07
4.07
4.07
4.07
4.07
4.30
4.44
4.52
4.52
4.52
4.53
4.53
4.53
4.53
4.53
4.53
4.53
4.53
4.61
4.63
4.63
4.63
4.63
4.63
4.63
4.63
4.63
4.63
4.63
4.66
4.73
4.73
4.72
4.7
4.74
4.74
4.74
4.76
4.88
4.88
4.88
4.88
4.89
4.97
4.97
4.97
4.97
4.97
4.97
4.97
4.97

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=155238&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=155238&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=155238&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 time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
13.050.04451761653343750.1
23.15250.04245318276964320.12
33.260833333333330.04521832559590150.0899999999999999
43.581666666666670.1247421583130820.38
53.853333333333330.04978742691471290.18
63.91750.04807664335582970.11
74.02250.03333712099692540.0700000000000003
84.424166666666670.1783998743035290.46
94.603333333333330.04458563432181690.0999999999999996
104.721666666666670.06658328118479390.25
114.940833333333330.0431610795495060.0899999999999999

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 3.05 & 0.0445176165334375 & 0.1 \tabularnewline
2 & 3.1525 & 0.0424531827696432 & 0.12 \tabularnewline
3 & 3.26083333333333 & 0.0452183255959015 & 0.0899999999999999 \tabularnewline
4 & 3.58166666666667 & 0.124742158313082 & 0.38 \tabularnewline
5 & 3.85333333333333 & 0.0497874269147129 & 0.18 \tabularnewline
6 & 3.9175 & 0.0480766433558297 & 0.11 \tabularnewline
7 & 4.0225 & 0.0333371209969254 & 0.0700000000000003 \tabularnewline
8 & 4.42416666666667 & 0.178399874303529 & 0.46 \tabularnewline
9 & 4.60333333333333 & 0.0445856343218169 & 0.0999999999999996 \tabularnewline
10 & 4.72166666666667 & 0.0665832811847939 & 0.25 \tabularnewline
11 & 4.94083333333333 & 0.043161079549506 & 0.0899999999999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=155238&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]3.05[/C][C]0.0445176165334375[/C][C]0.1[/C][/ROW]
[ROW][C]2[/C][C]3.1525[/C][C]0.0424531827696432[/C][C]0.12[/C][/ROW]
[ROW][C]3[/C][C]3.26083333333333[/C][C]0.0452183255959015[/C][C]0.0899999999999999[/C][/ROW]
[ROW][C]4[/C][C]3.58166666666667[/C][C]0.124742158313082[/C][C]0.38[/C][/ROW]
[ROW][C]5[/C][C]3.85333333333333[/C][C]0.0497874269147129[/C][C]0.18[/C][/ROW]
[ROW][C]6[/C][C]3.9175[/C][C]0.0480766433558297[/C][C]0.11[/C][/ROW]
[ROW][C]7[/C][C]4.0225[/C][C]0.0333371209969254[/C][C]0.0700000000000003[/C][/ROW]
[ROW][C]8[/C][C]4.42416666666667[/C][C]0.178399874303529[/C][C]0.46[/C][/ROW]
[ROW][C]9[/C][C]4.60333333333333[/C][C]0.0445856343218169[/C][C]0.0999999999999996[/C][/ROW]
[ROW][C]10[/C][C]4.72166666666667[/C][C]0.0665832811847939[/C][C]0.25[/C][/ROW]
[ROW][C]11[/C][C]4.94083333333333[/C][C]0.043161079549506[/C][C]0.0899999999999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=155238&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=155238&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
13.050.04451761653343750.1
23.15250.04245318276964320.12
33.260833333333330.04521832559590150.0899999999999999
43.581666666666670.1247421583130820.38
53.853333333333330.04978742691471290.18
63.91750.04807664335582970.11
74.02250.03333712099692540.0700000000000003
84.424166666666670.1783998743035290.46
94.603333333333330.04458563432181690.0999999999999996
104.721666666666670.06658328118479390.25
114.940833333333330.0431610795495060.0899999999999999






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.0216038449041659
beta0.0111012761778157
S.D.0.022520983893526
T-STAT0.492930336893803
p-value0.633864546391268

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.0216038449041659 \tabularnewline
beta & 0.0111012761778157 \tabularnewline
S.D. & 0.022520983893526 \tabularnewline
T-STAT & 0.492930336893803 \tabularnewline
p-value & 0.633864546391268 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=155238&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.0216038449041659[/C][/ROW]
[ROW][C]beta[/C][C]0.0111012761778157[/C][/ROW]
[ROW][C]S.D.[/C][C]0.022520983893526[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.492930336893803[/C][/ROW]
[ROW][C]p-value[/C][C]0.633864546391268[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=155238&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=155238&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)
alpha0.0216038449041659
beta0.0111012761778157
S.D.0.022520983893526
T-STAT0.492930336893803
p-value0.633864546391268






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.59349270770075
beta0.530799200090022
S.D.0.999194014633924
T-STAT0.531227361569507
p-value0.608120140057668
Lambda0.469200799909978

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.59349270770075 \tabularnewline
beta & 0.530799200090022 \tabularnewline
S.D. & 0.999194014633924 \tabularnewline
T-STAT & 0.531227361569507 \tabularnewline
p-value & 0.608120140057668 \tabularnewline
Lambda & 0.469200799909978 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=155238&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.59349270770075[/C][/ROW]
[ROW][C]beta[/C][C]0.530799200090022[/C][/ROW]
[ROW][C]S.D.[/C][C]0.999194014633924[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.531227361569507[/C][/ROW]
[ROW][C]p-value[/C][C]0.608120140057668[/C][/ROW]
[ROW][C]Lambda[/C][C]0.469200799909978[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=155238&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=155238&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-3.59349270770075
beta0.530799200090022
S.D.0.999194014633924
T-STAT0.531227361569507
p-value0.608120140057668
Lambda0.469200799909978


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')