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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, 19 Nov 2016 19:34:39 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Nov/19/t147958410876u1hhlj8zoq7dv.htm/, Retrieved Sat, 04 May 2024 18:04:21 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sat, 04 May 2024 18:04:21 +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 
122.9
122.82
120.26
118.82
126.69
125.79
123.96
128.7
127.74
127.55
126.16
124.74
122.32
120.92
117.09
115.77
117.88
117.77
122.61
127.31
124.62
119.07
116.92
115.07
113.84
112.89
111.86
111.58
107.72
106.49
108.53
108.62
107.92
106.43
117.66
115.11
113.98
112.16
109.72
117.99
112.57
113.66
118.18
115.66
114.72
110.46
108.38
106.52
107.01
105.89
103.76
103.71
101.07
100.4
102.24
99.18
98.14
96.22
94.38
94.62
94.71
94.97
93.69
106.42
105.73
105.18
104.8
102.77
100.29
99.3
96.63
95.5

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'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 & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.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]1 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=&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 time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1124.67753.048836216120389.88
2119.7791666666673.7865874738304612.24
3110.7208333333333.6464340197796111.23
4112.8333333333333.6214570983447411.66
5100.5516666666674.1925644860511112.63
699.99916666666674.8324348433425912.73

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 124.6775 & 3.04883621612038 & 9.88 \tabularnewline
2 & 119.779166666667 & 3.78658747383046 & 12.24 \tabularnewline
3 & 110.720833333333 & 3.64643401977961 & 11.23 \tabularnewline
4 & 112.833333333333 & 3.62145709834474 & 11.66 \tabularnewline
5 & 100.551666666667 & 4.19256448605111 & 12.63 \tabularnewline
6 & 99.9991666666667 & 4.83243484334259 & 12.73 \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]124.6775[/C][C]3.04883621612038[/C][C]9.88[/C][/ROW]
[ROW][C]2[/C][C]119.779166666667[/C][C]3.78658747383046[/C][C]12.24[/C][/ROW]
[ROW][C]3[/C][C]110.720833333333[/C][C]3.64643401977961[/C][C]11.23[/C][/ROW]
[ROW][C]4[/C][C]112.833333333333[/C][C]3.62145709834474[/C][C]11.66[/C][/ROW]
[ROW][C]5[/C][C]100.551666666667[/C][C]4.19256448605111[/C][C]12.63[/C][/ROW]
[ROW][C]6[/C][C]99.9991666666667[/C][C]4.83243484334259[/C][C]12.73[/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
1124.67753.048836216120389.88
2119.7791666666673.7865874738304612.24
3110.7208333333333.6464340197796111.23
4112.8333333333333.6214570983447411.66
5100.5516666666674.1925644860511112.63
699.99916666666674.8324348433425912.73






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha9.74951523929264
beta-0.0529027897675162
S.D.0.0147441478895472
T-STAT-3.5880533865929
p-value0.023001723681628

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 9.74951523929264 \tabularnewline
beta & -0.0529027897675162 \tabularnewline
S.D. & 0.0147441478895472 \tabularnewline
T-STAT & -3.5880533865929 \tabularnewline
p-value & 0.023001723681628 \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]9.74951523929264[/C][/ROW]
[ROW][C]beta[/C][C]-0.0529027897675162[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0147441478895472[/C][/ROW]
[ROW][C]T-STAT[/C][C]-3.5880533865929[/C][/ROW]
[ROW][C]p-value[/C][C]0.023001723681628[/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)
alpha9.74951523929264
beta-0.0529027897675162
S.D.0.0147441478895472
T-STAT-3.5880533865929
p-value0.023001723681628






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha8.52234807466934
beta-1.52506597025105
S.D.0.404086384947609
T-STAT-3.77410877243185
p-value0.0195349578869448
Lambda2.52506597025105

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 8.52234807466934 \tabularnewline
beta & -1.52506597025105 \tabularnewline
S.D. & 0.404086384947609 \tabularnewline
T-STAT & -3.77410877243185 \tabularnewline
p-value & 0.0195349578869448 \tabularnewline
Lambda & 2.52506597025105 \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]8.52234807466934[/C][/ROW]
[ROW][C]beta[/C][C]-1.52506597025105[/C][/ROW]
[ROW][C]S.D.[/C][C]0.404086384947609[/C][/ROW]
[ROW][C]T-STAT[/C][C]-3.77410877243185[/C][/ROW]
[ROW][C]p-value[/C][C]0.0195349578869448[/C][/ROW]
[ROW][C]Lambda[/C][C]2.52506597025105[/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)
alpha8.52234807466934
beta-1.52506597025105
S.D.0.404086384947609
T-STAT-3.77410877243185
p-value0.0195349578869448
Lambda2.52506597025105


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')