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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, 05 Aug 2010 14:21:52 +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/05/t1281018120nx90twqw1n75462.htm/, Retrieved Sun, 05 May 2024 10:11:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78414, Retrieved Sun, 05 May 2024 10:11:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsGhielens Nick
Estimated Impact112

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 2 - sta...] [2010-08-05 14:21:52] [fa169e33c07134f82fd2ac8a5210a945] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
80
79
78
76
74
73
74
76
77
77
78
80
90
90
89
82
78
76
74
78
81
82
88
99
117
113
106
100
97
96
100
104
104
111
117
118
140
147
134
126
116
114
120
122
117
119
132
134
154
152
132
130
123
129
124
128
128
129
141
138
155
160
142
133
131
140
134
134
134
136
145
137
152
168
160
157
147
161
159
164
163
158
175
163

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 4 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78414&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78414&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78414&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 time4 seconds
R Server'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
178.251.707825127659934
274.251.258305739211793
3781.414213562373103
487.753.862210075418828
576.51.914854215512684
687.58.266397845091518
71097.5277265270908117
899.253.593976442141308
9112.56.4549722436790314
10136.758.9209491273817621
111183.651483716701118
12125.58.736894948054117
1314212.754084313139324
141262.943920288775956
151346.4807406984078613
16147.512.288205727444527
17134.753.774917217635379
181384.8304589153964811
19159.256.7019897542943716
20157.757.4554230821150117
21164.757.2284161474004817

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 78.25 & 1.70782512765993 & 4 \tabularnewline
2 & 74.25 & 1.25830573921179 & 3 \tabularnewline
3 & 78 & 1.41421356237310 & 3 \tabularnewline
4 & 87.75 & 3.86221007541882 & 8 \tabularnewline
5 & 76.5 & 1.91485421551268 & 4 \tabularnewline
6 & 87.5 & 8.2663978450915 & 18 \tabularnewline
7 & 109 & 7.52772652709081 & 17 \tabularnewline
8 & 99.25 & 3.59397644214130 & 8 \tabularnewline
9 & 112.5 & 6.45497224367903 & 14 \tabularnewline
10 & 136.75 & 8.92094912738176 & 21 \tabularnewline
11 & 118 & 3.65148371670111 & 8 \tabularnewline
12 & 125.5 & 8.7368949480541 & 17 \tabularnewline
13 & 142 & 12.7540843131393 & 24 \tabularnewline
14 & 126 & 2.94392028877595 & 6 \tabularnewline
15 & 134 & 6.48074069840786 & 13 \tabularnewline
16 & 147.5 & 12.2882057274445 & 27 \tabularnewline
17 & 134.75 & 3.77491721763537 & 9 \tabularnewline
18 & 138 & 4.83045891539648 & 11 \tabularnewline
19 & 159.25 & 6.70198975429437 & 16 \tabularnewline
20 & 157.75 & 7.45542308211501 & 17 \tabularnewline
21 & 164.75 & 7.22841614740048 & 17 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78414&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]78.25[/C][C]1.70782512765993[/C][C]4[/C][/ROW]
[ROW][C]2[/C][C]74.25[/C][C]1.25830573921179[/C][C]3[/C][/ROW]
[ROW][C]3[/C][C]78[/C][C]1.41421356237310[/C][C]3[/C][/ROW]
[ROW][C]4[/C][C]87.75[/C][C]3.86221007541882[/C][C]8[/C][/ROW]
[ROW][C]5[/C][C]76.5[/C][C]1.91485421551268[/C][C]4[/C][/ROW]
[ROW][C]6[/C][C]87.5[/C][C]8.2663978450915[/C][C]18[/C][/ROW]
[ROW][C]7[/C][C]109[/C][C]7.52772652709081[/C][C]17[/C][/ROW]
[ROW][C]8[/C][C]99.25[/C][C]3.59397644214130[/C][C]8[/C][/ROW]
[ROW][C]9[/C][C]112.5[/C][C]6.45497224367903[/C][C]14[/C][/ROW]
[ROW][C]10[/C][C]136.75[/C][C]8.92094912738176[/C][C]21[/C][/ROW]
[ROW][C]11[/C][C]118[/C][C]3.65148371670111[/C][C]8[/C][/ROW]
[ROW][C]12[/C][C]125.5[/C][C]8.7368949480541[/C][C]17[/C][/ROW]
[ROW][C]13[/C][C]142[/C][C]12.7540843131393[/C][C]24[/C][/ROW]
[ROW][C]14[/C][C]126[/C][C]2.94392028877595[/C][C]6[/C][/ROW]
[ROW][C]15[/C][C]134[/C][C]6.48074069840786[/C][C]13[/C][/ROW]
[ROW][C]16[/C][C]147.5[/C][C]12.2882057274445[/C][C]27[/C][/ROW]
[ROW][C]17[/C][C]134.75[/C][C]3.77491721763537[/C][C]9[/C][/ROW]
[ROW][C]18[/C][C]138[/C][C]4.83045891539648[/C][C]11[/C][/ROW]
[ROW][C]19[/C][C]159.25[/C][C]6.70198975429437[/C][C]16[/C][/ROW]
[ROW][C]20[/C][C]157.75[/C][C]7.45542308211501[/C][C]17[/C][/ROW]
[ROW][C]21[/C][C]164.75[/C][C]7.22841614740048[/C][C]17[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78414&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78414&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
178.251.707825127659934
274.251.258305739211793
3781.414213562373103
487.753.862210075418828
576.51.914854215512684
687.58.266397845091518
71097.5277265270908117
899.253.593976442141308
9112.56.4549722436790314
10136.758.9209491273817621
111183.651483716701118
12125.58.736894948054117
1314212.754084313139324
141262.943920288775956
151346.4807406984078613
16147.512.288205727444527
17134.753.774917217635379
181384.8304589153964811
19159.256.7019897542943716
20157.757.4554230821150117
21164.757.2284161474004817






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-2.66928402686994
beta0.0714937904429366
S.D.0.0200602797311470
T-STAT3.56394783129221
p-value0.00207151619180409

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -2.66928402686994 \tabularnewline
beta & 0.0714937904429366 \tabularnewline
S.D. & 0.0200602797311470 \tabularnewline
T-STAT & 3.56394783129221 \tabularnewline
p-value & 0.00207151619180409 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78414&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.66928402686994[/C][/ROW]
[ROW][C]beta[/C][C]0.0714937904429366[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0200602797311470[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.56394783129221[/C][/ROW]
[ROW][C]p-value[/C][C]0.00207151619180409[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78414&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78414&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-2.66928402686994
beta0.0714937904429366
S.D.0.0200602797311470
T-STAT3.56394783129221
p-value0.00207151619180409






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-7.6103288687736
beta1.9344240492632
S.D.0.397220902770957
T-STAT4.86989490172579
p-value0.000106377949001327
Lambda-0.934424049263199

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -7.6103288687736 \tabularnewline
beta & 1.9344240492632 \tabularnewline
S.D. & 0.397220902770957 \tabularnewline
T-STAT & 4.86989490172579 \tabularnewline
p-value & 0.000106377949001327 \tabularnewline
Lambda & -0.934424049263199 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78414&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-7.6103288687736[/C][/ROW]
[ROW][C]beta[/C][C]1.9344240492632[/C][/ROW]
[ROW][C]S.D.[/C][C]0.397220902770957[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.86989490172579[/C][/ROW]
[ROW][C]p-value[/C][C]0.000106377949001327[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.934424049263199[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78414&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78414&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-7.6103288687736
beta1.9344240492632
S.D.0.397220902770957
T-STAT4.86989490172579
p-value0.000106377949001327
Lambda-0.934424049263199


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
par1 = 4 ;
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')