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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, 27 Nov 2007 02:42:38 -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/2007/Nov/27/t1196155973mqh1soyp84s5otl.htm/, Retrieved Sun, 05 May 2024 10:35:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6756, Retrieved Sun, 05 May 2024 10:35:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact227

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] [statistiek opdrac...] [2007-11-27 09:42:38] [0d8f90662bd29255b957138f6acc6b00] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
96
75
96
102
130
127
111
108
108
122
113
111
97
124
99
118
111
121
102
102
115
123
127
117
106
88
95
105
117
128
136
128
124
119
128
104
91
99
92
117
103
117
125
94
126
105
107
87
95
63
91
90
102
104
121
107
94
96
98
75
97
81
89
85
95
97
103
99
82
90
82
94

Tables (Output of Computation)





Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6756&T=0

[TABLE]
[ROW][C]Summary of compuational 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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6756&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6756&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1108.2515.064256310280239
211310.548588875898464
3114.83333333333315.014134754432047
4105.2513.424028659629241
594.666666666666714.846691295512426
691.16666666666677.432524755587726

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 108.25 & 15.0642563102802 & 39 \tabularnewline
2 & 113 & 10.5485888758984 & 64 \tabularnewline
3 & 114.833333333333 & 15.0141347544320 & 47 \tabularnewline
4 & 105.25 & 13.4240286596292 & 41 \tabularnewline
5 & 94.6666666666667 & 14.8466912955124 & 26 \tabularnewline
6 & 91.1666666666667 & 7.43252475558772 & 6 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6756&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]108.25[/C][C]15.0642563102802[/C][C]39[/C][/ROW]
[ROW][C]2[/C][C]113[/C][C]10.5485888758984[/C][C]64[/C][/ROW]
[ROW][C]3[/C][C]114.833333333333[/C][C]15.0141347544320[/C][C]47[/C][/ROW]
[ROW][C]4[/C][C]105.25[/C][C]13.4240286596292[/C][C]41[/C][/ROW]
[ROW][C]5[/C][C]94.6666666666667[/C][C]14.8466912955124[/C][C]26[/C][/ROW]
[ROW][C]6[/C][C]91.1666666666667[/C][C]7.43252475558772[/C][C]6[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6756&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6756&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
1108.2515.064256310280239
211310.548588875898464
3114.83333333333315.014134754432047
4105.2513.424028659629241
594.666666666666714.846691295512426
691.16666666666677.432524755587726






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-1.60362061480404
beta0.137048017550089
S.D.0.145529828685898
T-STAT0.941717713733343
p-value0.399657489478609

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -1.60362061480404 \tabularnewline
beta & 0.137048017550089 \tabularnewline
S.D. & 0.145529828685898 \tabularnewline
T-STAT & 0.941717713733343 \tabularnewline
p-value & 0.399657489478609 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6756&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.60362061480404[/C][/ROW]
[ROW][C]beta[/C][C]0.137048017550089[/C][/ROW]
[ROW][C]S.D.[/C][C]0.145529828685898[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.941717713733343[/C][/ROW]
[ROW][C]p-value[/C][C]0.399657489478609[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6756&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6756&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-1.60362061480404
beta0.137048017550089
S.D.0.145529828685898
T-STAT0.941717713733343
p-value0.399657489478609






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-4.23177957068919
beta1.45180652495473
S.D.1.31163191338702
T-STAT1.10687038805402
p-value0.33043196121484
Lambda-0.451806524954728

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -4.23177957068919 \tabularnewline
beta & 1.45180652495473 \tabularnewline
S.D. & 1.31163191338702 \tabularnewline
T-STAT & 1.10687038805402 \tabularnewline
p-value & 0.33043196121484 \tabularnewline
Lambda & -0.451806524954728 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6756&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.23177957068919[/C][/ROW]
[ROW][C]beta[/C][C]1.45180652495473[/C][/ROW]
[ROW][C]S.D.[/C][C]1.31163191338702[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.10687038805402[/C][/ROW]
[ROW][C]p-value[/C][C]0.33043196121484[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.451806524954728[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6756&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6756&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-4.23177957068919
beta1.45180652495473
S.D.1.31163191338702
T-STAT1.10687038805402
p-value0.33043196121484
Lambda-0.451806524954728


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')