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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 computationThu, 17 Nov 2016 18:55:59 +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/17/t1479408980je7qlygm4u291s7.htm/, Retrieved Sun, 05 May 2024 11:25:11 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sun, 05 May 2024 11:25:11 +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 
103.1
95.2
110.2
105.3
107.4
108.1
108
98.8
104.2
107.8
103.5
129.6
100.1
96
111.4
108.3
103.6
106.8
102.5
101
105.5
105.1
103.9
126.4
101
99.3
113.5
99.1
108.2
109.2
100.1
105.5
103
105.8
106.1
122.2
101.9
94.5
112.1
97.6
110
104.6
102.1
106
98.5
106.2
106
120.9
105.1
102.4
94.2
105.6
102.9
111.4
105.4
104.6
103.6
102.1
109.3
103.9
125.3
105.9
106.2
96.2
105.5
104.7
111
109.2
108.3
106.7
103.6
103.9
104.7
112.4
103.2
129.1
114.9
107.6
102.8
99.1
111.9
104.6
103.7
108.5
110.1
107.5
106.8

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'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.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]'George Udny Yule' @ yule.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'George Udny Yule' @ yule.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1106.7666666666678.3558725493275734.4
2105.8833333333337.5941165424693130.4
3106.0833333333336.7102138339228623.1
4105.0333333333337.1164768266497226.4
5104.2083333333334.1779634737367917.2
6107.2083333333336.7701830690077229.1
7108.5416666666677.9458918297254130

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 106.766666666667 & 8.35587254932757 & 34.4 \tabularnewline
2 & 105.883333333333 & 7.59411654246931 & 30.4 \tabularnewline
3 & 106.083333333333 & 6.71021383392286 & 23.1 \tabularnewline
4 & 105.033333333333 & 7.11647682664972 & 26.4 \tabularnewline
5 & 104.208333333333 & 4.17796347373679 & 17.2 \tabularnewline
6 & 107.208333333333 & 6.77018306900772 & 29.1 \tabularnewline
7 & 108.541666666667 & 7.94589182972541 & 30 \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]106.766666666667[/C][C]8.35587254932757[/C][C]34.4[/C][/ROW]
[ROW][C]2[/C][C]105.883333333333[/C][C]7.59411654246931[/C][C]30.4[/C][/ROW]
[ROW][C]3[/C][C]106.083333333333[/C][C]6.71021383392286[/C][C]23.1[/C][/ROW]
[ROW][C]4[/C][C]105.033333333333[/C][C]7.11647682664972[/C][C]26.4[/C][/ROW]
[ROW][C]5[/C][C]104.208333333333[/C][C]4.17796347373679[/C][C]17.2[/C][/ROW]
[ROW][C]6[/C][C]107.208333333333[/C][C]6.77018306900772[/C][C]29.1[/C][/ROW]
[ROW][C]7[/C][C]108.541666666667[/C][C]7.94589182972541[/C][C]30[/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
1106.7666666666678.3558725493275734.4
2105.8833333333337.5941165424693130.4
3106.0833333333336.7102138339228623.1
4105.0333333333337.1164768266497226.4
5104.2083333333334.1779634737367917.2
6107.2083333333336.7701830690077229.1
7108.5416666666677.9458918297254130






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-63.2874260083948
beta0.661108205564696
S.D.0.308590513503875
T-STAT2.14234779306135
p-value0.085064293307386

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -63.2874260083948 \tabularnewline
beta & 0.661108205564696 \tabularnewline
S.D. & 0.308590513503875 \tabularnewline
T-STAT & 2.14234779306135 \tabularnewline
p-value & 0.085064293307386 \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]-63.2874260083948[/C][/ROW]
[ROW][C]beta[/C][C]0.661108205564696[/C][/ROW]
[ROW][C]S.D.[/C][C]0.308590513503875[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.14234779306135[/C][/ROW]
[ROW][C]p-value[/C][C]0.085064293307386[/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)
alpha-63.2874260083948
beta0.661108205564696
S.D.0.308590513503875
T-STAT2.14234779306135
p-value0.085064293307386






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-53.4462265012507
beta11.8664270537696
S.D.5.53548502820243
T-STAT2.143701408876
p-value0.0849187586168888
Lambda-10.8664270537696

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -53.4462265012507 \tabularnewline
beta & 11.8664270537696 \tabularnewline
S.D. & 5.53548502820243 \tabularnewline
T-STAT & 2.143701408876 \tabularnewline
p-value & 0.0849187586168888 \tabularnewline
Lambda & -10.8664270537696 \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]-53.4462265012507[/C][/ROW]
[ROW][C]beta[/C][C]11.8664270537696[/C][/ROW]
[ROW][C]S.D.[/C][C]5.53548502820243[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.143701408876[/C][/ROW]
[ROW][C]p-value[/C][C]0.0849187586168888[/C][/ROW]
[ROW][C]Lambda[/C][C]-10.8664270537696[/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)
alpha-53.4462265012507
beta11.8664270537696
S.D.5.53548502820243
T-STAT2.143701408876
p-value0.0849187586168888
Lambda-10.8664270537696


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')