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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 12:48:21 +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/t12820492738vn6mawojk75xv1.htm/, Retrieved Sat, 27 Apr 2024 06:35:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79104, Retrieved Sat, 27 Apr 2024 06:35:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsTrouillard Olivier
Estimated Impact176

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] [aantal bezoekers] [2010-08-17 12:48:21] [b58dfa1c2951471c561e0016df4afa08] [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 time1 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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79104&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79104&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79104&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'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
176.83333333333332.329000305762637
283.91666666666677.3293722084293825
3106.9166666666678.0392031868082522
4126.7510.532417489912733
513410.233634385069331
6140.0833333333339.1299540308843129
7160.5833333333337.178988702308928

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 76.8333333333333 & 2.32900030576263 & 7 \tabularnewline
2 & 83.9166666666667 & 7.32937220842938 & 25 \tabularnewline
3 & 106.916666666667 & 8.03920318680825 & 22 \tabularnewline
4 & 126.75 & 10.5324174899127 & 33 \tabularnewline
5 & 134 & 10.2336343850693 & 31 \tabularnewline
6 & 140.083333333333 & 9.12995403088431 & 29 \tabularnewline
7 & 160.583333333333 & 7.1789887023089 & 28 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79104&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]76.8333333333333[/C][C]2.32900030576263[/C][C]7[/C][/ROW]
[ROW][C]2[/C][C]83.9166666666667[/C][C]7.32937220842938[/C][C]25[/C][/ROW]
[ROW][C]3[/C][C]106.916666666667[/C][C]8.03920318680825[/C][C]22[/C][/ROW]
[ROW][C]4[/C][C]126.75[/C][C]10.5324174899127[/C][C]33[/C][/ROW]
[ROW][C]5[/C][C]134[/C][C]10.2336343850693[/C][C]31[/C][/ROW]
[ROW][C]6[/C][C]140.083333333333[/C][C]9.12995403088431[/C][C]29[/C][/ROW]
[ROW][C]7[/C][C]160.583333333333[/C][C]7.1789887023089[/C][C]28[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79104&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79104&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
176.83333333333332.329000305762637
283.91666666666677.3293722084293825
3106.9166666666678.0392031868082522
4126.7510.532417489912733
513410.233634385069331
6140.0833333333339.1299540308843129
7160.5833333333337.178988702308928






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha1.40161681555953
beta0.0542300765105141
S.D.0.0322862198856609
T-STAT1.67966633141215
p-value0.153857611236953

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.40161681555953 \tabularnewline
beta & 0.0542300765105141 \tabularnewline
S.D. & 0.0322862198856609 \tabularnewline
T-STAT & 1.67966633141215 \tabularnewline
p-value & 0.153857611236953 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79104&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.40161681555953[/C][/ROW]
[ROW][C]beta[/C][C]0.0542300765105141[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0322862198856609[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.67966633141215[/C][/ROW]
[ROW][C]p-value[/C][C]0.153857611236953[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79104&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79104&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)
alpha1.40161681555953
beta0.0542300765105141
S.D.0.0322862198856609
T-STAT1.67966633141215
p-value0.153857611236953






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-4.11830322944059
beta1.28333464098494
S.D.0.621104015276452
T-STAT2.06621533498497
p-value0.093689487593269
Lambda-0.283334640984941

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -4.11830322944059 \tabularnewline
beta & 1.28333464098494 \tabularnewline
S.D. & 0.621104015276452 \tabularnewline
T-STAT & 2.06621533498497 \tabularnewline
p-value & 0.093689487593269 \tabularnewline
Lambda & -0.283334640984941 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79104&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.11830322944059[/C][/ROW]
[ROW][C]beta[/C][C]1.28333464098494[/C][/ROW]
[ROW][C]S.D.[/C][C]0.621104015276452[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.06621533498497[/C][/ROW]
[ROW][C]p-value[/C][C]0.093689487593269[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.283334640984941[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79104&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79104&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-4.11830322944059
beta1.28333464098494
S.D.0.621104015276452
T-STAT2.06621533498497
p-value0.093689487593269
Lambda-0.283334640984941


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')