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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 16:18:51 -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/t1386192003fxii10zfk1ooibk.htm/, Retrieved Thu, 25 Apr 2024 08:06:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=230825, Retrieved Thu, 25 Apr 2024 08:06:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact70

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 21:18:51] [5084d5e36b1f8e83675c5d3d354927b3] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1.94
1.82
1.8
1.79
1.79
1.78
1.81
1.84
1.87
1.87
1.87
1.84
1.82
1.83
1.83
1.82
1.83
1.87
1.88
1.9
1.98
2.03
2.14
2.42
2.73
2.84
2.85
2.94
3.06
3.24
3.18
3.01
2.87
2.73
2.63
2.39
2.26
2.11
2.01
1.99
1.96
1.93
1.98
2.07
2.24
2.31
2.23
2.26
2.28
2.3
2.33
2.26
2.24
2.47
2.55
2.89
3.21
3.21
2.92
2.68
2.4
2.28
2.24
2.2
2.18
2.23
2.24
2.25
2.23
2.25
2.23
2.21
2.17
2.17
2.13
2.12
2.13
2.17
2.33
2.5
2.57
2.59
2.58
2.31

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 Ronald Aylmer Fisher' @ fisher.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 Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230825&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 Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230825&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230825&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 Ronald Aylmer Fisher' @ fisher.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
11.8350.04661252270288830.16
21.945833333333330.1796187038921020.6
32.87250.2377976603600790.85
42.11250.1394876990340660.38
52.611666666666670.3649865086755280.97
62.2450.05518563713009520.22
72.314166666666670.1942097429132330.47

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 1.835 & 0.0466125227028883 & 0.16 \tabularnewline
2 & 1.94583333333333 & 0.179618703892102 & 0.6 \tabularnewline
3 & 2.8725 & 0.237797660360079 & 0.85 \tabularnewline
4 & 2.1125 & 0.139487699034066 & 0.38 \tabularnewline
5 & 2.61166666666667 & 0.364986508675528 & 0.97 \tabularnewline
6 & 2.245 & 0.0551856371300952 & 0.22 \tabularnewline
7 & 2.31416666666667 & 0.194209742913233 & 0.47 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230825&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]1.835[/C][C]0.0466125227028883[/C][C]0.16[/C][/ROW]
[ROW][C]2[/C][C]1.94583333333333[/C][C]0.179618703892102[/C][C]0.6[/C][/ROW]
[ROW][C]3[/C][C]2.8725[/C][C]0.237797660360079[/C][C]0.85[/C][/ROW]
[ROW][C]4[/C][C]2.1125[/C][C]0.139487699034066[/C][C]0.38[/C][/ROW]
[ROW][C]5[/C][C]2.61166666666667[/C][C]0.364986508675528[/C][C]0.97[/C][/ROW]
[ROW][C]6[/C][C]2.245[/C][C]0.0551856371300952[/C][C]0.22[/C][/ROW]
[ROW][C]7[/C][C]2.31416666666667[/C][C]0.194209742913233[/C][C]0.47[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230825&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230825&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
11.8350.04661252270288830.16
21.945833333333330.1796187038921020.6
32.87250.2377976603600790.85
42.11250.1394876990340660.38
52.611666666666670.3649865086755280.97
62.2450.05518563713009520.22
72.314166666666670.1942097429132330.47






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.299418703786903
beta0.207937423209557
S.D.0.0972490932002919
T-STAT2.13819395499446
p-value0.0855125473105164

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.299418703786903 \tabularnewline
beta & 0.207937423209557 \tabularnewline
S.D. & 0.0972490932002919 \tabularnewline
T-STAT & 2.13819395499446 \tabularnewline
p-value & 0.0855125473105164 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230825&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.299418703786903[/C][/ROW]
[ROW][C]beta[/C][C]0.207937423209557[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0972490932002919[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.13819395499446[/C][/ROW]
[ROW][C]p-value[/C][C]0.0855125473105164[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230825&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230825&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-0.299418703786903
beta0.207937423209557
S.D.0.0972490932002919
T-STAT2.13819395499446
p-value0.0855125473105164






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-4.52714900811826
beta3.15954157528787
S.D.1.6176892026572
T-STAT1.9531202718656
p-value0.108236896932661
Lambda-2.15954157528787

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -4.52714900811826 \tabularnewline
beta & 3.15954157528787 \tabularnewline
S.D. & 1.6176892026572 \tabularnewline
T-STAT & 1.9531202718656 \tabularnewline
p-value & 0.108236896932661 \tabularnewline
Lambda & -2.15954157528787 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230825&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.52714900811826[/C][/ROW]
[ROW][C]beta[/C][C]3.15954157528787[/C][/ROW]
[ROW][C]S.D.[/C][C]1.6176892026572[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.9531202718656[/C][/ROW]
[ROW][C]p-value[/C][C]0.108236896932661[/C][/ROW]
[ROW][C]Lambda[/C][C]-2.15954157528787[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230825&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230825&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-4.52714900811826
beta3.15954157528787
S.D.1.6176892026572
T-STAT1.9531202718656
p-value0.108236896932661
Lambda-2.15954157528787


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')