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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, 21 Apr 2017 15:14:36 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Apr/21/t149278431795s9xj97t1f9ah9.htm/, Retrieved Mon, 13 May 2024 18:34:27 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Mon, 13 May 2024 18:34:27 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0

Tree of Dependent Computations

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
96,4
96,9
98,1
99,2
100
100,3
100,3
100,8
101,3
101,4
101,9
103,4
105,6
107,5
109
110,5
109,8
109,6
109,6
108,8
109,4
109,1
109
109,2
110,5
112,2
113,2
113,6
113,2
112,2
112,2
113,2
113,8
113,8
113,7
113,9
114
114,3
114,3
112,8
112,3
112,2
112,6
111,9
111,7
111
110,8
111,1
110,5
110,5
109,8
109
109
109,4
108,8
108,4
108,3
108,2
106,8
103,6
101,4
102,8
104,5
104,8
105,8
105,3
104,3
102,5
102,6
102,3
101,8
99,5

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

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






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
11002.055148744893277
2108.9251.265000898310864.90000000000001
3112.9583333333331.009462803433173.40000000000001
4112.4166666666671.242309676905613.5
5108.5251.861634179472926.90000000000001
6103.1333333333331.841112970378786.3

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 100 & 2.05514874489327 & 7 \tabularnewline
2 & 108.925 & 1.26500089831086 & 4.90000000000001 \tabularnewline
3 & 112.958333333333 & 1.00946280343317 & 3.40000000000001 \tabularnewline
4 & 112.416666666667 & 1.24230967690561 & 3.5 \tabularnewline
5 & 108.525 & 1.86163417947292 & 6.90000000000001 \tabularnewline
6 & 103.133333333333 & 1.84111297037878 & 6.3 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]100[/C][C]2.05514874489327[/C][C]7[/C][/ROW]
[ROW][C]2[/C][C]108.925[/C][C]1.26500089831086[/C][C]4.90000000000001[/C][/ROW]
[ROW][C]3[/C][C]112.958333333333[/C][C]1.00946280343317[/C][C]3.40000000000001[/C][/ROW]
[ROW][C]4[/C][C]112.416666666667[/C][C]1.24230967690561[/C][C]3.5[/C][/ROW]
[ROW][C]5[/C][C]108.525[/C][C]1.86163417947292[/C][C]6.90000000000001[/C][/ROW]
[ROW][C]6[/C][C]103.133333333333[/C][C]1.84111297037878[/C][C]6.3[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
11002.055148744893277
2108.9251.265000898310864.90000000000001
3112.9583333333331.009462803433173.40000000000001
4112.4166666666671.242309676905613.5
5108.5251.861634179472926.90000000000001
6103.1333333333331.841112970378786.3






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha9.36760884550268
beta-0.0726532678314465
S.D.0.0197900794142173
T-STAT-3.67119637626375
p-value0.0213686484684006

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 9.36760884550268 \tabularnewline
beta & -0.0726532678314465 \tabularnewline
S.D. & 0.0197900794142173 \tabularnewline
T-STAT & -3.67119637626375 \tabularnewline
p-value & 0.0213686484684006 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]9.36760884550268[/C][/ROW]
[ROW][C]beta[/C][C]-0.0726532678314465[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0197900794142173[/C][/ROW]
[ROW][C]T-STAT[/C][C]-3.67119637626375[/C][/ROW]
[ROW][C]p-value[/C][C]0.0213686484684006[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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)
alpha9.36760884550268
beta-0.0726532678314465
S.D.0.0197900794142173
T-STAT-3.67119637626375
p-value0.0213686484684006






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha24.2635672584678
beta-5.10073533900382
S.D.1.50479756890713
T-STAT-3.38964884340441
p-value0.0275389239060025
Lambda6.10073533900382

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 24.2635672584678 \tabularnewline
beta & -5.10073533900382 \tabularnewline
S.D. & 1.50479756890713 \tabularnewline
T-STAT & -3.38964884340441 \tabularnewline
p-value & 0.0275389239060025 \tabularnewline
Lambda & 6.10073533900382 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]24.2635672584678[/C][/ROW]
[ROW][C]beta[/C][C]-5.10073533900382[/C][/ROW]
[ROW][C]S.D.[/C][C]1.50479756890713[/C][/ROW]
[ROW][C]T-STAT[/C][C]-3.38964884340441[/C][/ROW]
[ROW][C]p-value[/C][C]0.0275389239060025[/C][/ROW]
[ROW][C]Lambda[/C][C]6.10073533900382[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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)
alpha24.2635672584678
beta-5.10073533900382
S.D.1.50479756890713
T-STAT-3.38964884340441
p-value0.0275389239060025
Lambda6.10073533900382


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')