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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 computationTue, 25 Apr 2017 19:04:00 +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/25/t1493143561dckoryyracov4n8.htm/, Retrieved Sat, 11 May 2024 14:33:14 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sat, 11 May 2024 14:33:14 +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 
99.49
99.84
100.9
101.31
100.09
99.28
99.57
101.04
101.87
101.39
100.3
99.95
99.87
100.51
100.27
100.04
99.23
99.32
99.95
100.23
101.02
99.83
99.61
100.12
99.83
100.03
100.07
100.46
100.43
100.68
101.8
101.21
100.63
100.55
99.76
98.8
96.59
97.59
98.79
98.79
99.65
99.78
100.05
99.22
97.72
97.55
98.14
97.95
97.24
97.02
97.57
98.07
98.86
99.57
100.14
99.88
99.79
100.59
100.55
101.42

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 4 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.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 time4 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1100.4191666666670.8537559618674682.59
21000.4952501663530541.78999999999999
3100.3541666666670.7561560485091483
498.4851.064574178635843.45999999999999
599.2251.450702024413144.40000000000001

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 100.419166666667 & 0.853755961867468 & 2.59 \tabularnewline
2 & 100 & 0.495250166353054 & 1.78999999999999 \tabularnewline
3 & 100.354166666667 & 0.756156048509148 & 3 \tabularnewline
4 & 98.485 & 1.06457417863584 & 3.45999999999999 \tabularnewline
5 & 99.225 & 1.45070202441314 & 4.40000000000001 \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]100.419166666667[/C][C]0.853755961867468[/C][C]2.59[/C][/ROW]
[ROW][C]2[/C][C]100[/C][C]0.495250166353054[/C][C]1.78999999999999[/C][/ROW]
[ROW][C]3[/C][C]100.354166666667[/C][C]0.756156048509148[/C][C]3[/C][/ROW]
[ROW][C]4[/C][C]98.485[/C][C]1.06457417863584[/C][C]3.45999999999999[/C][/ROW]
[ROW][C]5[/C][C]99.225[/C][C]1.45070202441314[/C][C]4.40000000000001[/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
1100.4191666666670.8537559618674682.59
21000.4952501663530541.78999999999999
3100.3541666666670.7561560485091483
498.4851.064574178635843.45999999999999
599.2251.450702024413144.40000000000001






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha26.7839547168149
beta-0.259385473010055
S.D.0.200466515884915
T-STAT-1.2939092190287
p-value0.286305679672405

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 26.7839547168149 \tabularnewline
beta & -0.259385473010055 \tabularnewline
S.D. & 0.200466515884915 \tabularnewline
T-STAT & -1.2939092190287 \tabularnewline
p-value & 0.286305679672405 \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]26.7839547168149[/C][/ROW]
[ROW][C]beta[/C][C]-0.259385473010055[/C][/ROW]
[ROW][C]S.D.[/C][C]0.200466515884915[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.2939092190287[/C][/ROW]
[ROW][C]p-value[/C][C]0.286305679672405[/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)
alpha26.7839547168149
beta-0.259385473010055
S.D.0.200466515884915
T-STAT-1.2939092190287
p-value0.286305679672405






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha127.357932892172
beta-27.7045136338646
S.D.22.6940350452144
T-STAT-1.2207839451498
p-value0.309364890138014
Lambda28.7045136338646

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 127.357932892172 \tabularnewline
beta & -27.7045136338646 \tabularnewline
S.D. & 22.6940350452144 \tabularnewline
T-STAT & -1.2207839451498 \tabularnewline
p-value & 0.309364890138014 \tabularnewline
Lambda & 28.7045136338646 \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]127.357932892172[/C][/ROW]
[ROW][C]beta[/C][C]-27.7045136338646[/C][/ROW]
[ROW][C]S.D.[/C][C]22.6940350452144[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.2207839451498[/C][/ROW]
[ROW][C]p-value[/C][C]0.309364890138014[/C][/ROW]
[ROW][C]Lambda[/C][C]28.7045136338646[/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)
alpha127.357932892172
beta-27.7045136338646
S.D.22.6940350452144
T-STAT-1.2207839451498
p-value0.309364890138014
Lambda28.7045136338646


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')