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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, 18 Aug 2008 03:58:29 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Aug/18/t12190549348v12xs9076p2i2i.htm/, Retrieved Tue, 14 May 2024 20:15:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=14215, Retrieved Tue, 14 May 2024 20:15:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact249

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] [Toon Raeman - Opg...] [2008-08-18 09:58:29] [b46ff5180a79ecd706507099e9497e04] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
12,11
11,42
11,71
12,04
12,21
12
12,36
12,32
12,96
12,79
13,19
12,34
13,25
12,54
12,77
12,96
13
13,61
13,8
14,16
14,27
14,69
15,01
15,09
15,14
14,2
13,83
14,31
14,04
14,9
14,92
15,36
15,5
15,65
16,18
15,44
15,58
15,24
15,33
16,07
15,82
15,87
15,72
17,07
16,83
17,52
17,76
17,36
17,95
16,71
17,14
16,72
17,26
17,24
17,69
18,13
18,08
18,18
18,18
17,64
17,89
16,82
16,61
16,66
17,02
16,91
17,18
18,06
17,58
17,48
17,54
17,44
17,79
16,79
16,19
16,62
16,39
16,54
17,26
18
17,29
18,16
17,82
17,48
18,31
17,04
17,03
16,97
17,11
17,12
17,69
18,5
18,27
18,45
18,35
18,03

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time8 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 & 8 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14215&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]8 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=14215&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14215&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 time8 seconds
R Server'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
111.820.318642955882180.69
212.22250.1613226580490170.359999999999999
312.820.3595367389665020.85
412.880.3005550421026630.710000000000001
513.64250.4852748362182681.16
614.7650.3725139818405030.82
714.370.5528712930390461.31
814.8050.5524189231612791.32
915.69250.3367862823809780.74
1015.5550.3722454387452810.83
1116.120.6363961030678931.35
1217.36750.394239774756430.930000000000003
1317.130.5822370651203851.24000000000000
1417.580.421347046190350.89
1518.020.2576819745345020.539999999999999
1616.9950.6033517492585351.28
1717.29250.5235376458925051.15000000000000
1817.510.06218252702059080.139999999999997
1916.84750.6771693535101341.60000000000000
2017.04750.7398817473083121.61
2117.68750.3837859646556490.870000000000001
2217.33750.6490698472943151.34
2317.6050.6553624951124381.39
2418.2750.1791647286716890.419999999999998

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 11.82 & 0.31864295588218 & 0.69 \tabularnewline
2 & 12.2225 & 0.161322658049017 & 0.359999999999999 \tabularnewline
3 & 12.82 & 0.359536738966502 & 0.85 \tabularnewline
4 & 12.88 & 0.300555042102663 & 0.710000000000001 \tabularnewline
5 & 13.6425 & 0.485274836218268 & 1.16 \tabularnewline
6 & 14.765 & 0.372513981840503 & 0.82 \tabularnewline
7 & 14.37 & 0.552871293039046 & 1.31 \tabularnewline
8 & 14.805 & 0.552418923161279 & 1.32 \tabularnewline
9 & 15.6925 & 0.336786282380978 & 0.74 \tabularnewline
10 & 15.555 & 0.372245438745281 & 0.83 \tabularnewline
11 & 16.12 & 0.636396103067893 & 1.35 \tabularnewline
12 & 17.3675 & 0.39423977475643 & 0.930000000000003 \tabularnewline
13 & 17.13 & 0.582237065120385 & 1.24000000000000 \tabularnewline
14 & 17.58 & 0.42134704619035 & 0.89 \tabularnewline
15 & 18.02 & 0.257681974534502 & 0.539999999999999 \tabularnewline
16 & 16.995 & 0.603351749258535 & 1.28 \tabularnewline
17 & 17.2925 & 0.523537645892505 & 1.15000000000000 \tabularnewline
18 & 17.51 & 0.0621825270205908 & 0.139999999999997 \tabularnewline
19 & 16.8475 & 0.677169353510134 & 1.60000000000000 \tabularnewline
20 & 17.0475 & 0.739881747308312 & 1.61 \tabularnewline
21 & 17.6875 & 0.383785964655649 & 0.870000000000001 \tabularnewline
22 & 17.3375 & 0.649069847294315 & 1.34 \tabularnewline
23 & 17.605 & 0.655362495112438 & 1.39 \tabularnewline
24 & 18.275 & 0.179164728671689 & 0.419999999999998 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14215&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]11.82[/C][C]0.31864295588218[/C][C]0.69[/C][/ROW]
[ROW][C]2[/C][C]12.2225[/C][C]0.161322658049017[/C][C]0.359999999999999[/C][/ROW]
[ROW][C]3[/C][C]12.82[/C][C]0.359536738966502[/C][C]0.85[/C][/ROW]
[ROW][C]4[/C][C]12.88[/C][C]0.300555042102663[/C][C]0.710000000000001[/C][/ROW]
[ROW][C]5[/C][C]13.6425[/C][C]0.485274836218268[/C][C]1.16[/C][/ROW]
[ROW][C]6[/C][C]14.765[/C][C]0.372513981840503[/C][C]0.82[/C][/ROW]
[ROW][C]7[/C][C]14.37[/C][C]0.552871293039046[/C][C]1.31[/C][/ROW]
[ROW][C]8[/C][C]14.805[/C][C]0.552418923161279[/C][C]1.32[/C][/ROW]
[ROW][C]9[/C][C]15.6925[/C][C]0.336786282380978[/C][C]0.74[/C][/ROW]
[ROW][C]10[/C][C]15.555[/C][C]0.372245438745281[/C][C]0.83[/C][/ROW]
[ROW][C]11[/C][C]16.12[/C][C]0.636396103067893[/C][C]1.35[/C][/ROW]
[ROW][C]12[/C][C]17.3675[/C][C]0.39423977475643[/C][C]0.930000000000003[/C][/ROW]
[ROW][C]13[/C][C]17.13[/C][C]0.582237065120385[/C][C]1.24000000000000[/C][/ROW]
[ROW][C]14[/C][C]17.58[/C][C]0.42134704619035[/C][C]0.89[/C][/ROW]
[ROW][C]15[/C][C]18.02[/C][C]0.257681974534502[/C][C]0.539999999999999[/C][/ROW]
[ROW][C]16[/C][C]16.995[/C][C]0.603351749258535[/C][C]1.28[/C][/ROW]
[ROW][C]17[/C][C]17.2925[/C][C]0.523537645892505[/C][C]1.15000000000000[/C][/ROW]
[ROW][C]18[/C][C]17.51[/C][C]0.0621825270205908[/C][C]0.139999999999997[/C][/ROW]
[ROW][C]19[/C][C]16.8475[/C][C]0.677169353510134[/C][C]1.60000000000000[/C][/ROW]
[ROW][C]20[/C][C]17.0475[/C][C]0.739881747308312[/C][C]1.61[/C][/ROW]
[ROW][C]21[/C][C]17.6875[/C][C]0.383785964655649[/C][C]0.870000000000001[/C][/ROW]
[ROW][C]22[/C][C]17.3375[/C][C]0.649069847294315[/C][C]1.34[/C][/ROW]
[ROW][C]23[/C][C]17.605[/C][C]0.655362495112438[/C][C]1.39[/C][/ROW]
[ROW][C]24[/C][C]18.275[/C][C]0.179164728671689[/C][C]0.419999999999998[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14215&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14215&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
111.820.318642955882180.69
212.22250.1613226580490170.359999999999999
312.820.3595367389665020.85
412.880.3005550421026630.710000000000001
513.64250.4852748362182681.16
614.7650.3725139818405030.82
714.370.5528712930390461.31
814.8050.5524189231612791.32
915.69250.3367862823809780.74
1015.5550.3722454387452810.83
1116.120.6363961030678931.35
1217.36750.394239774756430.930000000000003
1317.130.5822370651203851.24000000000000
1417.580.421347046190350.89
1518.020.2576819745345020.539999999999999
1616.9950.6033517492585351.28
1717.29250.5235376458925051.15000000000000
1817.510.06218252702059080.139999999999997
1916.84750.6771693535101341.60000000000000
2017.04750.7398817473083121.61
2117.68750.3837859646556490.870000000000001
2217.33750.6490698472943151.34
2317.6050.6553624951124381.39
2418.2750.1791647286716890.419999999999998






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.120103735169187
beta0.0201765567270006
S.D.0.0187200036090157
T-STAT1.07780730967827
p-value0.292796446067173

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.120103735169187 \tabularnewline
beta & 0.0201765567270006 \tabularnewline
S.D. & 0.0187200036090157 \tabularnewline
T-STAT & 1.07780730967827 \tabularnewline
p-value & 0.292796446067173 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14215&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.120103735169187[/C][/ROW]
[ROW][C]beta[/C][C]0.0201765567270006[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0187200036090157[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.07780730967827[/C][/ROW]
[ROW][C]p-value[/C][C]0.292796446067173[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14215&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14215&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)
alpha0.120103735169187
beta0.0201765567270006
S.D.0.0187200036090157
T-STAT1.07780730967827
p-value0.292796446067173






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.36988699139126
beta0.519989517677218
S.D.0.894280981713318
T-STAT0.581461004214795
p-value0.566840358698232
Lambda0.480010482322782

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.36988699139126 \tabularnewline
beta & 0.519989517677218 \tabularnewline
S.D. & 0.894280981713318 \tabularnewline
T-STAT & 0.581461004214795 \tabularnewline
p-value & 0.566840358698232 \tabularnewline
Lambda & 0.480010482322782 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14215&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.36988699139126[/C][/ROW]
[ROW][C]beta[/C][C]0.519989517677218[/C][/ROW]
[ROW][C]S.D.[/C][C]0.894280981713318[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.581461004214795[/C][/ROW]
[ROW][C]p-value[/C][C]0.566840358698232[/C][/ROW]
[ROW][C]Lambda[/C][C]0.480010482322782[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14215&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14215&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-2.36988699139126
beta0.519989517677218
S.D.0.894280981713318
T-STAT0.581461004214795
p-value0.566840358698232
Lambda0.480010482322782


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 4 ;
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')