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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 computationSun, 05 Dec 2010 13:48:57 +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/Dec/05/t129155684572mottqf1sbxnuw.htm/, Retrieved Wed, 01 May 2024 20:09:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=105395, Retrieved Wed, 01 May 2024 20:09:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W83
Estimated Impact105

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] [opdracht 8: oefen...] [2010-12-05 13:48:57] [72a344459e5b13eacf7bf474aa92c893] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
132.1
125
127.1
101.5
85.7
79.3
70.9
77.1
83.9
96.2
111.7
127.2
143.6
134.9
135.6
105.3
86.4
74.6
67.6
73.4
78.5
98.2
118.6
136.9
137.9
115.6
119.3
98.5
84.3
73.5
60.7
69.5
77.9
113.9
126.3
135.1
130.5
113.1
110
90.8
85.4
72.5
64.7
67.2
77.9
105.2
107.2
120.7
121.3
107.9
105.6
81.3
71.7
64.8
57.3
61.9
70.1
88.8
106.8
110.7
114.1
108
111.5
86.8
78.4
68
57.3
65.3
73.3
88.6
101.3
122.9
126.6
114.1
124.7
93.3
77.2
66.5
57.9
63.7
65.8
85
101
105.3
121
117.9
106
86.6
79.9
65.2
61.2
67.6
78.9
95.5
113.1
124.4
122
110.3
114
93.3
75.5
65.4
59.2
63.8
74.2
91.7
107
120.7
127.4
119.7
112.7
84.4
75.6
66.5
59.9
64.8
74.3
100.4
105.9
131.1

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=105395&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=105395&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105395&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
1101.47522.402399425061661.2
2104.46666666666728.501206779341676
3101.04166666666727.086207772871377.2
495.433333333333321.998691421137465.8
587.3522.303464875542264
689.62521.667953924464865.6
790.091666666666724.381753920553568.7
893.108333333333322.981631334347863.2
991.42523.224443432023862.8
1093.558333333333325.713260050492371.2

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 101.475 & 22.4023994250616 & 61.2 \tabularnewline
2 & 104.466666666667 & 28.5012067793416 & 76 \tabularnewline
3 & 101.041666666667 & 27.0862077728713 & 77.2 \tabularnewline
4 & 95.4333333333333 & 21.9986914211374 & 65.8 \tabularnewline
5 & 87.35 & 22.3034648755422 & 64 \tabularnewline
6 & 89.625 & 21.6679539244648 & 65.6 \tabularnewline
7 & 90.0916666666667 & 24.3817539205535 & 68.7 \tabularnewline
8 & 93.1083333333333 & 22.9816313343478 & 63.2 \tabularnewline
9 & 91.425 & 23.2244434320238 & 62.8 \tabularnewline
10 & 93.5583333333333 & 25.7132600504923 & 71.2 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105395&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]101.475[/C][C]22.4023994250616[/C][C]61.2[/C][/ROW]
[ROW][C]2[/C][C]104.466666666667[/C][C]28.5012067793416[/C][C]76[/C][/ROW]
[ROW][C]3[/C][C]101.041666666667[/C][C]27.0862077728713[/C][C]77.2[/C][/ROW]
[ROW][C]4[/C][C]95.4333333333333[/C][C]21.9986914211374[/C][C]65.8[/C][/ROW]
[ROW][C]5[/C][C]87.35[/C][C]22.3034648755422[/C][C]64[/C][/ROW]
[ROW][C]6[/C][C]89.625[/C][C]21.6679539244648[/C][C]65.6[/C][/ROW]
[ROW][C]7[/C][C]90.0916666666667[/C][C]24.3817539205535[/C][C]68.7[/C][/ROW]
[ROW][C]8[/C][C]93.1083333333333[/C][C]22.9816313343478[/C][C]63.2[/C][/ROW]
[ROW][C]9[/C][C]91.425[/C][C]23.2244434320238[/C][C]62.8[/C][/ROW]
[ROW][C]10[/C][C]93.5583333333333[/C][C]25.7132600504923[/C][C]71.2[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105395&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105395&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
1101.47522.402399425061661.2
2104.46666666666728.501206779341676
3101.04166666666727.086207772871377.2
495.433333333333321.998691421137465.8
587.3522.303464875542264
689.62521.667953924464865.6
790.091666666666724.381753920553568.7
893.108333333333322.981631334347863.2
991.42523.224443432023862.8
1093.558333333333325.713260050492371.2






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.166573444588095
beta0.255311450156154
S.D.0.112208242405410
T-STAT2.27533597071871
p-value0.0524517756129725

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.166573444588095 \tabularnewline
beta & 0.255311450156154 \tabularnewline
S.D. & 0.112208242405410 \tabularnewline
T-STAT & 2.27533597071871 \tabularnewline
p-value & 0.0524517756129725 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105395&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.166573444588095[/C][/ROW]
[ROW][C]beta[/C][C]0.255311450156154[/C][/ROW]
[ROW][C]S.D.[/C][C]0.112208242405410[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.27533597071871[/C][/ROW]
[ROW][C]p-value[/C][C]0.0524517756129725[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105395&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105395&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-0.166573444588095
beta0.255311450156154
S.D.0.112208242405410
T-STAT2.27533597071871
p-value0.0524517756129725






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.19049610009359
beta0.959524881864812
S.D.0.441033791648697
T-STAT2.17562667540250
p-value0.0612787681592546
Lambda0.0404751181351883

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.19049610009359 \tabularnewline
beta & 0.959524881864812 \tabularnewline
S.D. & 0.441033791648697 \tabularnewline
T-STAT & 2.17562667540250 \tabularnewline
p-value & 0.0612787681592546 \tabularnewline
Lambda & 0.0404751181351883 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105395&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.19049610009359[/C][/ROW]
[ROW][C]beta[/C][C]0.959524881864812[/C][/ROW]
[ROW][C]S.D.[/C][C]0.441033791648697[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.17562667540250[/C][/ROW]
[ROW][C]p-value[/C][C]0.0612787681592546[/C][/ROW]
[ROW][C]Lambda[/C][C]0.0404751181351883[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105395&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105395&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-1.19049610009359
beta0.959524881864812
S.D.0.441033791648697
T-STAT2.17562667540250
p-value0.0612787681592546
Lambda0.0404751181351883


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')