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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 Dec 2011 05:10:16 -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/09/t1323425574m3r5c4vc3kg7pvn.htm/, Retrieved Thu, 02 May 2024 20:16:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=153226, Retrieved Thu, 02 May 2024 20:16:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W83
Estimated Impact122

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] [] [2011-12-09 10:10:16] [df3d6db53fdf346bf57a43ea3fa80561] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
14,66
14,71
14,87
14,94
15,01
15,03
15,04
15,05
15,06
15,11
15,23
15,23
15,25
15,33
15,38
15,52
15,59
15,66
15,67
15,72
15,75
15,77
15,79
15,79
16,49
16,67
16,64
16,66
16,73
16,76
16,76
16,76
16,76
16,79
16,8
16,81
16,91
17,03
17,12
17,2
17,25
17,25
17,3
17,27
17,31
17,33
17,35
17,36
17,39
17,42
17,54
17,59
17,64
17,63
17,67
17,7
17,78
17,87
17,9
17,91
17,93
17,97
18,08
18,08
18,09
18,09
18,12
18,13
18,15
18,17
18,19
18,2
18,21
18,39
18,48
18,48
18,5
18,52
18,48
18,53
18,62
18,65
18,7
18,72

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'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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=153226&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=153226&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=153226&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'Gwilym Jenkins' @ jenkins.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
114.9950.1774823934929880.57
215.60166666666670.1899202384415540.539999999999999
316.71916666666670.09110017795944470.32
417.22333333333330.1381259855305580.449999999999999
517.670.1732575591949220.52
618.10.08179797730328760.27
718.52333333333330.1406047544348940.509999999999998

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 14.995 & 0.177482393492988 & 0.57 \tabularnewline
2 & 15.6016666666667 & 0.189920238441554 & 0.539999999999999 \tabularnewline
3 & 16.7191666666667 & 0.0911001779594447 & 0.32 \tabularnewline
4 & 17.2233333333333 & 0.138125985530558 & 0.449999999999999 \tabularnewline
5 & 17.67 & 0.173257559194922 & 0.52 \tabularnewline
6 & 18.1 & 0.0817979773032876 & 0.27 \tabularnewline
7 & 18.5233333333333 & 0.140604754434894 & 0.509999999999998 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=153226&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]14.995[/C][C]0.177482393492988[/C][C]0.57[/C][/ROW]
[ROW][C]2[/C][C]15.6016666666667[/C][C]0.189920238441554[/C][C]0.539999999999999[/C][/ROW]
[ROW][C]3[/C][C]16.7191666666667[/C][C]0.0911001779594447[/C][C]0.32[/C][/ROW]
[ROW][C]4[/C][C]17.2233333333333[/C][C]0.138125985530558[/C][C]0.449999999999999[/C][/ROW]
[ROW][C]5[/C][C]17.67[/C][C]0.173257559194922[/C][C]0.52[/C][/ROW]
[ROW][C]6[/C][C]18.1[/C][C]0.0817979773032876[/C][C]0.27[/C][/ROW]
[ROW][C]7[/C][C]18.5233333333333[/C][C]0.140604754434894[/C][C]0.509999999999998[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=153226&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=153226&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
114.9950.1774823934929880.57
215.60166666666670.1899202384415540.539999999999999
316.71916666666670.09110017795944470.32
417.22333333333330.1381259855305580.449999999999999
517.670.1732575591949220.52
618.10.08179797730328760.27
718.52333333333330.1406047544348940.509999999999998






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.43172192557411
beta-0.0170808860594629
S.D.0.0124591217530131
T-STAT-1.37095426130915
p-value0.228724189081129

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.43172192557411 \tabularnewline
beta & -0.0170808860594629 \tabularnewline
S.D. & 0.0124591217530131 \tabularnewline
T-STAT & -1.37095426130915 \tabularnewline
p-value & 0.228724189081129 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=153226&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.43172192557411[/C][/ROW]
[ROW][C]beta[/C][C]-0.0170808860594629[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0124591217530131[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.37095426130915[/C][/ROW]
[ROW][C]p-value[/C][C]0.228724189081129[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=153226&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=153226&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)
alpha0.43172192557411
beta-0.0170808860594629
S.D.0.0124591217530131
T-STAT-1.37095426130915
p-value0.228724189081129






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha3.85112336371309
beta-2.06726226356486
S.D.1.6717159779279
T-STAT-1.23661093801786
p-value0.271146625336267
Lambda3.06726226356486

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 3.85112336371309 \tabularnewline
beta & -2.06726226356486 \tabularnewline
S.D. & 1.6717159779279 \tabularnewline
T-STAT & -1.23661093801786 \tabularnewline
p-value & 0.271146625336267 \tabularnewline
Lambda & 3.06726226356486 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=153226&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.85112336371309[/C][/ROW]
[ROW][C]beta[/C][C]-2.06726226356486[/C][/ROW]
[ROW][C]S.D.[/C][C]1.6717159779279[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.23661093801786[/C][/ROW]
[ROW][C]p-value[/C][C]0.271146625336267[/C][/ROW]
[ROW][C]Lambda[/C][C]3.06726226356486[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=153226&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=153226&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)
alpha3.85112336371309
beta-2.06726226356486
S.D.1.6717159779279
T-STAT-1.23661093801786
p-value0.271146625336267
Lambda3.06726226356486


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')