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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationTue, 24 Nov 2009 06:08:08 -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/2009/Nov/24/t1259068135iifm2qti0x8l4ta.htm/, Retrieved Fri, 26 Apr 2024 12:48:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=59046, Retrieved Fri, 26 Apr 2024 12:48:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact169

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Standard Deviation-Mean Plot] [Identifying Integ...] [2009-11-22 12:50:05] [b98453cac15ba1066b407e146608df68]
- R  D          [Standard Deviation-Mean Plot] [] [2009-11-24 13:08:08] [c60887983b0820a525cba943a935572d] [Current]
-    D            [Standard Deviation-Mean Plot] [SMP] [2009-12-16 12:46:02] [4f1a20f787b3465111b61213cdeef1a9]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
149
139
135
130
127
122
117
112
113
149
157
157
147
137
132
125
123
117
114
111
112
144
150
149
134
123
116
117
111
105
102
95
93
124
130
124
115
106
105
105
101
95
93
84
87
116
120
117
109
105
107
109
109
108
107
99
103
131
137
135

Tables (Output of Computation)





Summary of computational 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 computational 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=59046&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]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=59046&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59046&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1133.91666666666716.395444674073545
2130.08333333333315.023970745768139
3114.513.426567963285641
4103.66666666666712.040336248199136
5113.2513.101873564841438

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 133.916666666667 & 16.3954446740735 & 45 \tabularnewline
2 & 130.083333333333 & 15.0239707457681 & 39 \tabularnewline
3 & 114.5 & 13.4265679632856 & 41 \tabularnewline
4 & 103.666666666667 & 12.0403362481991 & 36 \tabularnewline
5 & 113.25 & 13.1018735648414 & 38 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59046&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]133.916666666667[/C][C]16.3954446740735[/C][C]45[/C][/ROW]
[ROW][C]2[/C][C]130.083333333333[/C][C]15.0239707457681[/C][C]39[/C][/ROW]
[ROW][C]3[/C][C]114.5[/C][C]13.4265679632856[/C][C]41[/C][/ROW]
[ROW][C]4[/C][C]103.666666666667[/C][C]12.0403362481991[/C][C]36[/C][/ROW]
[ROW][C]5[/C][C]113.25[/C][C]13.1018735648414[/C][C]38[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59046&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59046&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
1133.91666666666716.395444674073545
2130.08333333333315.023970745768139
3114.513.426567963285641
4103.66666666666712.040336248199136
5113.2513.101873564841438






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-1.95093176553941
beta0.133927813056176
S.D.0.0144189385476559
T-STAT9.28832678033358
p-value0.00264135396185874

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -1.95093176553941 \tabularnewline
beta & 0.133927813056176 \tabularnewline
S.D. & 0.0144189385476559 \tabularnewline
T-STAT & 9.28832678033358 \tabularnewline
p-value & 0.00264135396185874 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59046&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.95093176553941[/C][/ROW]
[ROW][C]beta[/C][C]0.133927813056176[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0144189385476559[/C][/ROW]
[ROW][C]T-STAT[/C][C]9.28832678033358[/C][/ROW]
[ROW][C]p-value[/C][C]0.00264135396185874[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59046&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59046&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-1.95093176553941
beta0.133927813056176
S.D.0.0144189385476559
T-STAT9.28832678033358
p-value0.00264135396185874






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.75551156966185
beta1.12839752821878
S.D.0.109882065029284
T-STAT10.2691692945346
p-value0.00196894830225498
Lambda-0.128397528218782

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.75551156966185 \tabularnewline
beta & 1.12839752821878 \tabularnewline
S.D. & 0.109882065029284 \tabularnewline
T-STAT & 10.2691692945346 \tabularnewline
p-value & 0.00196894830225498 \tabularnewline
Lambda & -0.128397528218782 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59046&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.75551156966185[/C][/ROW]
[ROW][C]beta[/C][C]1.12839752821878[/C][/ROW]
[ROW][C]S.D.[/C][C]0.109882065029284[/C][/ROW]
[ROW][C]T-STAT[/C][C]10.2691692945346[/C][/ROW]
[ROW][C]p-value[/C][C]0.00196894830225498[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.128397528218782[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59046&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59046&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-2.75551156966185
beta1.12839752821878
S.D.0.109882065029284
T-STAT10.2691692945346
p-value0.00196894830225498
Lambda-0.128397528218782


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')