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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, 17 Aug 2010 14:34:43 +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/2010/Aug/17/t1282055655kw04rvjfnp5ak5o.htm/, Retrieved Sat, 27 Apr 2024 05:56:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79133, Retrieved Sat, 27 Apr 2024 05:56:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsQuaglia Laura
Estimated Impact129

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] [Tijdreeks B - Sta...] [2010-08-17 14:34:43] [f9e29edf9cfe01f572cce0cb5a360ea2] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
93
92
91
89
87
86
87
89
90
90
91
93
93
87
89
92
98
92
92
87
92
98
101
102
102
90
87
92
105
90
88
83
98
109
118
118
115
107
101
111
128
115
111
105
120
132
135
142
139
127
113
130
143
139
137
134
139
157
152
153
147
132
117
123
139
134
134
128
118
144
140
151
144
135
122
124
146
146
147
148
132
161
159
173

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'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79133&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79133&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79133&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'RServer@AstonUniversity' @ vre.aston.ac.uk






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
189.83333333333332.329000305762637
293.58333333333335.0714590572829215
398.333333333333312.040336248199135
4118.512.993005111142841
5138.58333333333312.183881552976944
6133.91666666666710.974833470124734
7144.7515.046141154341351

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 89.8333333333333 & 2.32900030576263 & 7 \tabularnewline
2 & 93.5833333333333 & 5.07145905728292 & 15 \tabularnewline
3 & 98.3333333333333 & 12.0403362481991 & 35 \tabularnewline
4 & 118.5 & 12.9930051111428 & 41 \tabularnewline
5 & 138.583333333333 & 12.1838815529769 & 44 \tabularnewline
6 & 133.916666666667 & 10.9748334701247 & 34 \tabularnewline
7 & 144.75 & 15.0461411543413 & 51 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79133&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]89.8333333333333[/C][C]2.32900030576263[/C][C]7[/C][/ROW]
[ROW][C]2[/C][C]93.5833333333333[/C][C]5.07145905728292[/C][C]15[/C][/ROW]
[ROW][C]3[/C][C]98.3333333333333[/C][C]12.0403362481991[/C][C]35[/C][/ROW]
[ROW][C]4[/C][C]118.5[/C][C]12.9930051111428[/C][C]41[/C][/ROW]
[ROW][C]5[/C][C]138.583333333333[/C][C]12.1838815529769[/C][C]44[/C][/ROW]
[ROW][C]6[/C][C]133.916666666667[/C][C]10.9748334701247[/C][C]34[/C][/ROW]
[ROW][C]7[/C][C]144.75[/C][C]15.0461411543413[/C][C]51[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79133&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79133&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
189.83333333333332.329000305762637
293.58333333333335.0714590572829215
398.333333333333312.040336248199135
4118.512.993005111142841
5138.58333333333312.183881552976944
6133.91666666666710.974833470124734
7144.7515.046141154341351






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-8.17269293561872
beta0.156388388317017
S.D.0.0563349185860803
T-STAT2.77604711681715
p-value0.03908447111614

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -8.17269293561872 \tabularnewline
beta & 0.156388388317017 \tabularnewline
S.D. & 0.0563349185860803 \tabularnewline
T-STAT & 2.77604711681715 \tabularnewline
p-value & 0.03908447111614 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79133&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-8.17269293561872[/C][/ROW]
[ROW][C]beta[/C][C]0.156388388317017[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0563349185860803[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.77604711681715[/C][/ROW]
[ROW][C]p-value[/C][C]0.03908447111614[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79133&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79133&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-8.17269293561872
beta0.156388388317017
S.D.0.0563349185860803
T-STAT2.77604711681715
p-value0.03908447111614






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-10.1444001394551
beta2.59426417609671
S.D.0.97860667703063
T-STAT2.65097739162014
p-value0.0453730974474255
Lambda-1.59426417609671

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -10.1444001394551 \tabularnewline
beta & 2.59426417609671 \tabularnewline
S.D. & 0.97860667703063 \tabularnewline
T-STAT & 2.65097739162014 \tabularnewline
p-value & 0.0453730974474255 \tabularnewline
Lambda & -1.59426417609671 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79133&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-10.1444001394551[/C][/ROW]
[ROW][C]beta[/C][C]2.59426417609671[/C][/ROW]
[ROW][C]S.D.[/C][C]0.97860667703063[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.65097739162014[/C][/ROW]
[ROW][C]p-value[/C][C]0.0453730974474255[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.59426417609671[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79133&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79133&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-10.1444001394551
beta2.59426417609671
S.D.0.97860667703063
T-STAT2.65097739162014
p-value0.0453730974474255
Lambda-1.59426417609671


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')