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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 computationMon, 16 Aug 2010 13:39:48 +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/16/t1281965982f4505k4rew577my.htm/, Retrieved Thu, 16 May 2024 14:54:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78993, Retrieved Thu, 16 May 2024 14:54:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsPhilippe De Vocht
Estimated Impact121

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] [Omzet product X] [2010-08-05 13:59:58] [44f4e89d2978fa9cb7cef84cf6986739]
-   P     [Standard Deviation-Mean Plot] [Omzet product X] [2010-08-16 13:39:48] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
73
72
71
69
89
88
73
63
64
64
65
67
69
71
70
72
88
83
76
70
75
71
75
81
87
90
80
85
105
104
98
94
107
112
121
118
120
122
109
112
132
127
116
113
123
125
137
127
123
128
114
120
143
135
119
117
132
139
158
141
139
150
142
149
166
150
139
140
158
169
186
177
175
187
176
185
204
188
171
171
182
185
200
192
185
195
190
195
213
194
171
171
186
182
193
185
172
185
179
182
193
173
155
164
188
186
200
185
173
190
190
193
195
178
163
165
188
182
200
177

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'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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78993&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78993&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78993&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'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
171.58.7230103227560826
275.08333333333336.0069404303133719
3100.08333333333313.255930633859641
4121.9166666666678.3932693092125728
5130.7513.060175412994344
6155.41666666666715.842740427161747
7184.66666666666710.568678711029633
8188.33333333333311.372481406154742
9180.16666666666712.496059985111945
10182.83333333333311.838560518556137

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 71.5 & 8.72301032275608 & 26 \tabularnewline
2 & 75.0833333333333 & 6.00694043031337 & 19 \tabularnewline
3 & 100.083333333333 & 13.2559306338596 & 41 \tabularnewline
4 & 121.916666666667 & 8.39326930921257 & 28 \tabularnewline
5 & 130.75 & 13.0601754129943 & 44 \tabularnewline
6 & 155.416666666667 & 15.8427404271617 & 47 \tabularnewline
7 & 184.666666666667 & 10.5686787110296 & 33 \tabularnewline
8 & 188.333333333333 & 11.3724814061547 & 42 \tabularnewline
9 & 180.166666666667 & 12.4960599851119 & 45 \tabularnewline
10 & 182.833333333333 & 11.8385605185561 & 37 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78993&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]71.5[/C][C]8.72301032275608[/C][C]26[/C][/ROW]
[ROW][C]2[/C][C]75.0833333333333[/C][C]6.00694043031337[/C][C]19[/C][/ROW]
[ROW][C]3[/C][C]100.083333333333[/C][C]13.2559306338596[/C][C]41[/C][/ROW]
[ROW][C]4[/C][C]121.916666666667[/C][C]8.39326930921257[/C][C]28[/C][/ROW]
[ROW][C]5[/C][C]130.75[/C][C]13.0601754129943[/C][C]44[/C][/ROW]
[ROW][C]6[/C][C]155.416666666667[/C][C]15.8427404271617[/C][C]47[/C][/ROW]
[ROW][C]7[/C][C]184.666666666667[/C][C]10.5686787110296[/C][C]33[/C][/ROW]
[ROW][C]8[/C][C]188.333333333333[/C][C]11.3724814061547[/C][C]42[/C][/ROW]
[ROW][C]9[/C][C]180.166666666667[/C][C]12.4960599851119[/C][C]45[/C][/ROW]
[ROW][C]10[/C][C]182.833333333333[/C][C]11.8385605185561[/C][C]37[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78993&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78993&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
171.58.7230103227560826
275.08333333333336.0069404303133719
3100.08333333333313.255930633859641
4121.9166666666678.3932693092125728
5130.7513.060175412994344
6155.41666666666715.842740427161747
7184.66666666666710.568678711029633
8188.33333333333311.372481406154742
9180.16666666666712.496059985111945
10182.83333333333311.838560518556137






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha6.82649450133512
beta0.0311291764470959
S.D.0.0189550551934071
T-STAT1.64226250620062
p-value0.139161393746462

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 6.82649450133512 \tabularnewline
beta & 0.0311291764470959 \tabularnewline
S.D. & 0.0189550551934071 \tabularnewline
T-STAT & 1.64226250620062 \tabularnewline
p-value & 0.139161393746462 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78993&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]6.82649450133512[/C][/ROW]
[ROW][C]beta[/C][C]0.0311291764470959[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0189550551934071[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.64226250620062[/C][/ROW]
[ROW][C]p-value[/C][C]0.139161393746462[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78993&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78993&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)
alpha6.82649450133512
beta0.0311291764470959
S.D.0.0189550551934071
T-STAT1.64226250620062
p-value0.139161393746462






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha0.137608652629888
beta0.45950254609265
S.D.0.212049642101978
T-STAT2.16695742344931
p-value0.0621123426241179
Lambda0.54049745390735

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.137608652629888 \tabularnewline
beta & 0.45950254609265 \tabularnewline
S.D. & 0.212049642101978 \tabularnewline
T-STAT & 2.16695742344931 \tabularnewline
p-value & 0.0621123426241179 \tabularnewline
Lambda & 0.54049745390735 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78993&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.137608652629888[/C][/ROW]
[ROW][C]beta[/C][C]0.45950254609265[/C][/ROW]
[ROW][C]S.D.[/C][C]0.212049642101978[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.16695742344931[/C][/ROW]
[ROW][C]p-value[/C][C]0.0621123426241179[/C][/ROW]
[ROW][C]Lambda[/C][C]0.54049745390735[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78993&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78993&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)
alpha0.137608652629888
beta0.45950254609265
S.D.0.212049642101978
T-STAT2.16695742344931
p-value0.0621123426241179
Lambda0.54049745390735


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')