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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 computationSat, 30 Nov 2013 16:26:40 -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/Nov/30/t1385846827crig5v66547tf93.htm/, Retrieved Fri, 03 May 2024 06:52:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=229740, Retrieved Fri, 03 May 2024 06:52:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact60

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] [] [2013-11-30 21:26:40] [bcda2273799249ef8721f6589a0ab562] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
38.95
38.96
38.93
38.86
38.75
38.87
38.87
38.86
38.83
39.08
39.05
38.97
38.97
38.95
38.95
38.92
38.96
38.97
38.97
38.95
38.93
38.76
38.81
38.81
38.81
38.78
38.77
38.61
38.69
38.69
38.68
38.74
38.73
38.62
38.57
38.57
38.57
38.57
38.56
38.55
38.42
38.47
38.47
38.48
38.45
38.43
38.43
38.48
38.48
38.48
38.51
38.48
38.55
38.55
38.55
38.49
38.37
38.14
38.08
38.04
38.04
38.03
37.98
38.03
38.05
38.05
38.05
38.05
38.02
38.06
38.01
38
38
38
37.99
37.96
37.96
38.02
38.02
38.02
38
37.93
38
38
38
38
38
38.01
37.98
38
38
38
37.95
37.87
37.75
37.75

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 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 & 2 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=229740&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 Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=229740&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=229740&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 Maurice George Kendall' @ kendall.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
138.9150.09366283826965340.329999999999998
238.91250.07448306702014410.210000000000001
338.68833333333330.08155682161239050.240000000000002
438.490.05720775535473540.149999999999999
538.39333333333330.1923223304452150.509999999999998
638.03083333333330.02429303429280740.0800000000000054
737.99166666666670.02790677119961960.0900000000000034
837.94250.09780546554722330.259999999999998

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 38.915 & 0.0936628382696534 & 0.329999999999998 \tabularnewline
2 & 38.9125 & 0.0744830670201441 & 0.210000000000001 \tabularnewline
3 & 38.6883333333333 & 0.0815568216123905 & 0.240000000000002 \tabularnewline
4 & 38.49 & 0.0572077553547354 & 0.149999999999999 \tabularnewline
5 & 38.3933333333333 & 0.192322330445215 & 0.509999999999998 \tabularnewline
6 & 38.0308333333333 & 0.0242930342928074 & 0.0800000000000054 \tabularnewline
7 & 37.9916666666667 & 0.0279067711996196 & 0.0900000000000034 \tabularnewline
8 & 37.9425 & 0.0978054655472233 & 0.259999999999998 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=229740&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]38.915[/C][C]0.0936628382696534[/C][C]0.329999999999998[/C][/ROW]
[ROW][C]2[/C][C]38.9125[/C][C]0.0744830670201441[/C][C]0.210000000000001[/C][/ROW]
[ROW][C]3[/C][C]38.6883333333333[/C][C]0.0815568216123905[/C][C]0.240000000000002[/C][/ROW]
[ROW][C]4[/C][C]38.49[/C][C]0.0572077553547354[/C][C]0.149999999999999[/C][/ROW]
[ROW][C]5[/C][C]38.3933333333333[/C][C]0.192322330445215[/C][C]0.509999999999998[/C][/ROW]
[ROW][C]6[/C][C]38.0308333333333[/C][C]0.0242930342928074[/C][C]0.0800000000000054[/C][/ROW]
[ROW][C]7[/C][C]37.9916666666667[/C][C]0.0279067711996196[/C][C]0.0900000000000034[/C][/ROW]
[ROW][C]8[/C][C]37.9425[/C][C]0.0978054655472233[/C][C]0.259999999999998[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=229740&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=229740&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
138.9150.09366283826965340.329999999999998
238.91250.07448306702014410.210000000000001
338.68833333333330.08155682161239050.240000000000002
438.490.05720775535473540.149999999999999
538.39333333333330.1923223304452150.509999999999998
638.03083333333330.02429303429280740.0800000000000054
737.99166666666670.02790677119961960.0900000000000034
837.94250.09780546554722330.259999999999998






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-1.12306090035409
beta0.0313430332203368
S.D.0.0520962339726969
T-STAT0.601637216939009
p-value0.569434799029199

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -1.12306090035409 \tabularnewline
beta & 0.0313430332203368 \tabularnewline
S.D. & 0.0520962339726969 \tabularnewline
T-STAT & 0.601637216939009 \tabularnewline
p-value & 0.569434799029199 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=229740&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.12306090035409[/C][/ROW]
[ROW][C]beta[/C][C]0.0313430332203368[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0520962339726969[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.601637216939009[/C][/ROW]
[ROW][C]p-value[/C][C]0.569434799029199[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=229740&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=229740&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-1.12306090035409
beta0.0313430332203368
S.D.0.0520962339726969
T-STAT0.601637216939009
p-value0.569434799029199






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-104.900235244808
beta28.0111506453939
S.D.23.9911133115626
T-STAT1.16756360080605
p-value0.287277230357285
Lambda-27.0111506453939

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -104.900235244808 \tabularnewline
beta & 28.0111506453939 \tabularnewline
S.D. & 23.9911133115626 \tabularnewline
T-STAT & 1.16756360080605 \tabularnewline
p-value & 0.287277230357285 \tabularnewline
Lambda & -27.0111506453939 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=229740&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-104.900235244808[/C][/ROW]
[ROW][C]beta[/C][C]28.0111506453939[/C][/ROW]
[ROW][C]S.D.[/C][C]23.9911133115626[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.16756360080605[/C][/ROW]
[ROW][C]p-value[/C][C]0.287277230357285[/C][/ROW]
[ROW][C]Lambda[/C][C]-27.0111506453939[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=229740&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=229740&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-104.900235244808
beta28.0111506453939
S.D.23.9911133115626
T-STAT1.16756360080605
p-value0.287277230357285
Lambda-27.0111506453939


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')