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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 computationSun, 17 Jan 2010 09:39:03 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Jan/17/t1263746427h19cesaatmjoi71.htm/, Retrieved Sat, 27 Apr 2024 14:46:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72263, Retrieved Sat, 27 Apr 2024 14:46:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W83
Estimated Impact203

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] [Opdracht 8c3] [2010-01-17 16:39:03] [dd4c09afc8b527b51f4c8ef6a655ef42] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
84.9
81.9
95.9
81
89.2
102.5
89.8
88.8
83.2
90.2
100.4
187.1
87.6
85.4
86.1
86.7
89.1
103.7
86.9
85.2
80.8
91.2
102.8
182.5
80.9
83.1
88.3
86.6
93
105.3
93.8
86.4
87
96.7
100.5
196.7
86.8
88.2
93.8
85
90.4
115.9
94.9
87.7
91.7
95.9
106.8
204.5
90.2
90.5
93.2
97.8
99.4
120
108.2
98.5
104.3
102.9
111.1
188.1
93.8
94.5
112.4
102.5
115.8
136.5
122.1
110.6
116.4
112.6
121.5
199.3
102.1
100.6
119
106.8
121.3
145.5
129.7
117.7
121.3
124.3
135.2
210.1
106.8
110.5
111.5
122.1
126.3
143.2
137.3
121.5
121.9
123.9
131.6
220.9

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' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72263&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72263&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72263&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' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
197.908333333333328.9170430505589106.1
297.333333333333327.6914930597609101.7
399.858333333333331.3312930509167115.8
4103.46666666666733.0387742820554119.5
5108.68333333333326.481789054275697.9
6119.83333333333327.7021276942382105.5
7127.829.0179881515524109.5
8131.45833333333330.1198955187532114.1

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 97.9083333333333 & 28.9170430505589 & 106.1 \tabularnewline
2 & 97.3333333333333 & 27.6914930597609 & 101.7 \tabularnewline
3 & 99.8583333333333 & 31.3312930509167 & 115.8 \tabularnewline
4 & 103.466666666667 & 33.0387742820554 & 119.5 \tabularnewline
5 & 108.683333333333 & 26.4817890542756 & 97.9 \tabularnewline
6 & 119.833333333333 & 27.7021276942382 & 105.5 \tabularnewline
7 & 127.8 & 29.0179881515524 & 109.5 \tabularnewline
8 & 131.458333333333 & 30.1198955187532 & 114.1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72263&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]97.9083333333333[/C][C]28.9170430505589[/C][C]106.1[/C][/ROW]
[ROW][C]2[/C][C]97.3333333333333[/C][C]27.6914930597609[/C][C]101.7[/C][/ROW]
[ROW][C]3[/C][C]99.8583333333333[/C][C]31.3312930509167[/C][C]115.8[/C][/ROW]
[ROW][C]4[/C][C]103.466666666667[/C][C]33.0387742820554[/C][C]119.5[/C][/ROW]
[ROW][C]5[/C][C]108.683333333333[/C][C]26.4817890542756[/C][C]97.9[/C][/ROW]
[ROW][C]6[/C][C]119.833333333333[/C][C]27.7021276942382[/C][C]105.5[/C][/ROW]
[ROW][C]7[/C][C]127.8[/C][C]29.0179881515524[/C][C]109.5[/C][/ROW]
[ROW][C]8[/C][C]131.458333333333[/C][C]30.1198955187532[/C][C]114.1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72263&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72263&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
197.908333333333328.9170430505589106.1
297.333333333333327.6914930597609101.7
399.858333333333331.3312930509167115.8
4103.46666666666733.0387742820554119.5
5108.68333333333326.481789054275697.9
6119.83333333333327.7021276942382105.5
7127.829.0179881515524109.5
8131.45833333333330.1198955187532114.1






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha30.9099114394054
beta-0.0146432105600345
S.D.0.0632968297785714
T-STAT-0.231341926779907
p-value0.824736616989911

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 30.9099114394054 \tabularnewline
beta & -0.0146432105600345 \tabularnewline
S.D. & 0.0632968297785714 \tabularnewline
T-STAT & -0.231341926779907 \tabularnewline
p-value & 0.824736616989911 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72263&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]30.9099114394054[/C][/ROW]
[ROW][C]beta[/C][C]-0.0146432105600345[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0632968297785714[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.231341926779907[/C][/ROW]
[ROW][C]p-value[/C][C]0.824736616989911[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72263&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72263&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)
alpha30.9099114394054
beta-0.0146432105600345
S.D.0.0632968297785714
T-STAT-0.231341926779907
p-value0.824736616989911






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha3.62501610820021
beta-0.0532109782306314
S.D.0.241443192284392
T-STAT-0.22038715495426
p-value0.832877233325517
Lambda1.05321097823063

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 3.62501610820021 \tabularnewline
beta & -0.0532109782306314 \tabularnewline
S.D. & 0.241443192284392 \tabularnewline
T-STAT & -0.22038715495426 \tabularnewline
p-value & 0.832877233325517 \tabularnewline
Lambda & 1.05321097823063 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72263&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.62501610820021[/C][/ROW]
[ROW][C]beta[/C][C]-0.0532109782306314[/C][/ROW]
[ROW][C]S.D.[/C][C]0.241443192284392[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.22038715495426[/C][/ROW]
[ROW][C]p-value[/C][C]0.832877233325517[/C][/ROW]
[ROW][C]Lambda[/C][C]1.05321097823063[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72263&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72263&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)
alpha3.62501610820021
beta-0.0532109782306314
S.D.0.241443192284392
T-STAT-0.22038715495426
p-value0.832877233325517
Lambda1.05321097823063


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')