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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 computationWed, 28 Jul 2010 13:51:50 +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/Jul/28/t12803251807um2r0iwv1efp2v.htm/, Retrieved Mon, 29 Apr 2024 09:21:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78146, Retrieved Mon, 29 Apr 2024 09:21:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsPatrick Fieremans
Estimated Impact210

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 1 - Sta...] [2010-07-28 13:51:50] [bffa0fb6afa860209dcefcd4361c2008] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
136
135
134
132
152
151
136
126
127
127
128
130
125
118
111
104
126
131
122
116
115
115
113
122
114
106
93
89
114
122
115
116
120
120
120
121
118
112
99
96
120
135
128
134
134
132
130
125
124
114
101
101
123
143
133
136
137
135
141
136
133
124
110
104
130
160
142
142
137
135
139
135
134
120
103
101
127
159
141
140
135
127
130
128
126
110
101
102
129
169
146
145
138
123
124
137
132
112
105
106
137
175
151
142
140
122
127
135
128
117
107
108
134
171
154
146
148
122
124
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'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 & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78146&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78146&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78146&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'RServer@AstonUniversity' @ vre.aston.ac.uk






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1134.58.7230103227560826
2118.1666666666677.4202834218516327
3112.510.991732430248733
4121.91666666666713.453342493314639
512714.647370226271142
6132.58333333333314.798392623606956
7128.7515.886672516180558
8129.16666666666719.618327856338568
913219.858590996433770
10132.83333333333319.229869442819464

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 134.5 & 8.72301032275608 & 26 \tabularnewline
2 & 118.166666666667 & 7.42028342185163 & 27 \tabularnewline
3 & 112.5 & 10.9917324302487 & 33 \tabularnewline
4 & 121.916666666667 & 13.4533424933146 & 39 \tabularnewline
5 & 127 & 14.6473702262711 & 42 \tabularnewline
6 & 132.583333333333 & 14.7983926236069 & 56 \tabularnewline
7 & 128.75 & 15.8866725161805 & 58 \tabularnewline
8 & 129.166666666667 & 19.6183278563385 & 68 \tabularnewline
9 & 132 & 19.8585909964337 & 70 \tabularnewline
10 & 132.833333333333 & 19.2298694428194 & 64 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78146&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]134.5[/C][C]8.72301032275608[/C][C]26[/C][/ROW]
[ROW][C]2[/C][C]118.166666666667[/C][C]7.42028342185163[/C][C]27[/C][/ROW]
[ROW][C]3[/C][C]112.5[/C][C]10.9917324302487[/C][C]33[/C][/ROW]
[ROW][C]4[/C][C]121.916666666667[/C][C]13.4533424933146[/C][C]39[/C][/ROW]
[ROW][C]5[/C][C]127[/C][C]14.6473702262711[/C][C]42[/C][/ROW]
[ROW][C]6[/C][C]132.583333333333[/C][C]14.7983926236069[/C][C]56[/C][/ROW]
[ROW][C]7[/C][C]128.75[/C][C]15.8866725161805[/C][C]58[/C][/ROW]
[ROW][C]8[/C][C]129.166666666667[/C][C]19.6183278563385[/C][C]68[/C][/ROW]
[ROW][C]9[/C][C]132[/C][C]19.8585909964337[/C][C]70[/C][/ROW]
[ROW][C]10[/C][C]132.833333333333[/C][C]19.2298694428194[/C][C]64[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78146&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78146&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
1134.58.7230103227560826
2118.1666666666677.4202834218516327
3112.510.991732430248733
4121.91666666666713.453342493314639
512714.647370226271142
6132.58333333333314.798392623606956
7128.7515.886672516180558
8129.16666666666719.618327856338568
913219.858590996433770
10132.83333333333319.229869442819464






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-24.8279977396725
beta0.30951820630989
S.D.0.18723806729415
T-STAT1.65307306779469
p-value0.136916325937971

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -24.8279977396725 \tabularnewline
beta & 0.30951820630989 \tabularnewline
S.D. & 0.18723806729415 \tabularnewline
T-STAT & 1.65307306779469 \tabularnewline
p-value & 0.136916325937971 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78146&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-24.8279977396725[/C][/ROW]
[ROW][C]beta[/C][C]0.30951820630989[/C][/ROW]
[ROW][C]S.D.[/C][C]0.18723806729415[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.65307306779469[/C][/ROW]
[ROW][C]p-value[/C][C]0.136916325937971[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78146&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78146&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-24.8279977396725
beta0.30951820630989
S.D.0.18723806729415
T-STAT1.65307306779469
p-value0.136916325937971






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-11.0969101664965
beta2.83344034294497
S.D.1.80209197560417
T-STAT1.57230617599028
p-value0.154523659807186
Lambda-1.83344034294497

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -11.0969101664965 \tabularnewline
beta & 2.83344034294497 \tabularnewline
S.D. & 1.80209197560417 \tabularnewline
T-STAT & 1.57230617599028 \tabularnewline
p-value & 0.154523659807186 \tabularnewline
Lambda & -1.83344034294497 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78146&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-11.0969101664965[/C][/ROW]
[ROW][C]beta[/C][C]2.83344034294497[/C][/ROW]
[ROW][C]S.D.[/C][C]1.80209197560417[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.57230617599028[/C][/ROW]
[ROW][C]p-value[/C][C]0.154523659807186[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.83344034294497[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78146&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78146&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-11.0969101664965
beta2.83344034294497
S.D.1.80209197560417
T-STAT1.57230617599028
p-value0.154523659807186
Lambda-1.83344034294497


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')