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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 computationWed, 13 Aug 2008 07:01:29 -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/13/t1218632544hzso5hzmg2ycqyj.htm/, Retrieved Tue, 14 May 2024 04:43:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=14035, Retrieved Tue, 14 May 2024 04:43:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact267

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] [Raf Mattheussen S...] [2008-08-13 13:01:29] [3b0a90e6bea50e83b08189298324fe13] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
16,8
16,91
16,91
17,16
17,02
17,23
17,22
17,29
17,3
17,22
17,19
17,23
17,36
17,39
17,29
17,28
17,4
17,51
17,54
17,64
17,65
17,5
17,37
17,56
17,49
17,61
17,79
17,83
17,56
17,95
18,09
18,38
18,38
18,44
18,84
19,01
19,06
19,06
18,97
18,98
19,41
19,55
19,64
19,71
19,48
19,48
19,41
19,25
19,14
19,21
19,3
19,53
19,14
19,16
19,24
19,38
19,27
19,27
19,07
19,15
19,24
19,36
19,57
19,59
19,36
19,46
19,65
19,46
19,51
19,64
19,64
19,69
19,28
19,67
19,65
19,6
19,53
19,64
19,67
19,81
19,73
19,87
19,97
20,12
19,94
20,31
20,13
20,22
20,38
20,44
20,34
20,14
19,97
19,82
19,98
20,12

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14035&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14035&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14035&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
116.9450.1524248448689820.359999999999999
217.190.1174734012447070.270000000000000
317.2350.04654746681256320.109999999999999
417.330.05354126134736330.109999999999999
517.52250.09878427675158370.240000000000002
617.520.1174734012447060.279999999999998
717.680.1587450786638750.34
817.9950.3408323145869050.82
918.66750.3063086678499330.630000000000003
1019.01750.049244289008980.0899999999999999
1119.57750.1294539815275430.300000000000001
1219.4050.108474267301820.230000000000000
1319.2950.1698038083593340.390000000000001
1419.230.1089342309224540.239999999999998
1519.190.0979795897113270.199999999999999
1619.440.1691153452528780.350000000000001
1719.48250.1212091855705110.289999999999999
1819.620.07702813338860870.180000000000000
1919.550.1823915202707260.390000000000001
2019.66250.1152894907034740.279999999999998
2119.92250.1643928222277360.390000000000001
2220.150.1581138830084180.369999999999997
2320.3250.130.300000000000001
2419.97250.1225765067213130.300000000000001

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 16.945 & 0.152424844868982 & 0.359999999999999 \tabularnewline
2 & 17.19 & 0.117473401244707 & 0.270000000000000 \tabularnewline
3 & 17.235 & 0.0465474668125632 & 0.109999999999999 \tabularnewline
4 & 17.33 & 0.0535412613473633 & 0.109999999999999 \tabularnewline
5 & 17.5225 & 0.0987842767515837 & 0.240000000000002 \tabularnewline
6 & 17.52 & 0.117473401244706 & 0.279999999999998 \tabularnewline
7 & 17.68 & 0.158745078663875 & 0.34 \tabularnewline
8 & 17.995 & 0.340832314586905 & 0.82 \tabularnewline
9 & 18.6675 & 0.306308667849933 & 0.630000000000003 \tabularnewline
10 & 19.0175 & 0.04924428900898 & 0.0899999999999999 \tabularnewline
11 & 19.5775 & 0.129453981527543 & 0.300000000000001 \tabularnewline
12 & 19.405 & 0.10847426730182 & 0.230000000000000 \tabularnewline
13 & 19.295 & 0.169803808359334 & 0.390000000000001 \tabularnewline
14 & 19.23 & 0.108934230922454 & 0.239999999999998 \tabularnewline
15 & 19.19 & 0.097979589711327 & 0.199999999999999 \tabularnewline
16 & 19.44 & 0.169115345252878 & 0.350000000000001 \tabularnewline
17 & 19.4825 & 0.121209185570511 & 0.289999999999999 \tabularnewline
18 & 19.62 & 0.0770281333886087 & 0.180000000000000 \tabularnewline
19 & 19.55 & 0.182391520270726 & 0.390000000000001 \tabularnewline
20 & 19.6625 & 0.115289490703474 & 0.279999999999998 \tabularnewline
21 & 19.9225 & 0.164392822227736 & 0.390000000000001 \tabularnewline
22 & 20.15 & 0.158113883008418 & 0.369999999999997 \tabularnewline
23 & 20.325 & 0.13 & 0.300000000000001 \tabularnewline
24 & 19.9725 & 0.122576506721313 & 0.300000000000001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14035&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]16.945[/C][C]0.152424844868982[/C][C]0.359999999999999[/C][/ROW]
[ROW][C]2[/C][C]17.19[/C][C]0.117473401244707[/C][C]0.270000000000000[/C][/ROW]
[ROW][C]3[/C][C]17.235[/C][C]0.0465474668125632[/C][C]0.109999999999999[/C][/ROW]
[ROW][C]4[/C][C]17.33[/C][C]0.0535412613473633[/C][C]0.109999999999999[/C][/ROW]
[ROW][C]5[/C][C]17.5225[/C][C]0.0987842767515837[/C][C]0.240000000000002[/C][/ROW]
[ROW][C]6[/C][C]17.52[/C][C]0.117473401244706[/C][C]0.279999999999998[/C][/ROW]
[ROW][C]7[/C][C]17.68[/C][C]0.158745078663875[/C][C]0.34[/C][/ROW]
[ROW][C]8[/C][C]17.995[/C][C]0.340832314586905[/C][C]0.82[/C][/ROW]
[ROW][C]9[/C][C]18.6675[/C][C]0.306308667849933[/C][C]0.630000000000003[/C][/ROW]
[ROW][C]10[/C][C]19.0175[/C][C]0.04924428900898[/C][C]0.0899999999999999[/C][/ROW]
[ROW][C]11[/C][C]19.5775[/C][C]0.129453981527543[/C][C]0.300000000000001[/C][/ROW]
[ROW][C]12[/C][C]19.405[/C][C]0.10847426730182[/C][C]0.230000000000000[/C][/ROW]
[ROW][C]13[/C][C]19.295[/C][C]0.169803808359334[/C][C]0.390000000000001[/C][/ROW]
[ROW][C]14[/C][C]19.23[/C][C]0.108934230922454[/C][C]0.239999999999998[/C][/ROW]
[ROW][C]15[/C][C]19.19[/C][C]0.097979589711327[/C][C]0.199999999999999[/C][/ROW]
[ROW][C]16[/C][C]19.44[/C][C]0.169115345252878[/C][C]0.350000000000001[/C][/ROW]
[ROW][C]17[/C][C]19.4825[/C][C]0.121209185570511[/C][C]0.289999999999999[/C][/ROW]
[ROW][C]18[/C][C]19.62[/C][C]0.0770281333886087[/C][C]0.180000000000000[/C][/ROW]
[ROW][C]19[/C][C]19.55[/C][C]0.182391520270726[/C][C]0.390000000000001[/C][/ROW]
[ROW][C]20[/C][C]19.6625[/C][C]0.115289490703474[/C][C]0.279999999999998[/C][/ROW]
[ROW][C]21[/C][C]19.9225[/C][C]0.164392822227736[/C][C]0.390000000000001[/C][/ROW]
[ROW][C]22[/C][C]20.15[/C][C]0.158113883008418[/C][C]0.369999999999997[/C][/ROW]
[ROW][C]23[/C][C]20.325[/C][C]0.13[/C][C]0.300000000000001[/C][/ROW]
[ROW][C]24[/C][C]19.9725[/C][C]0.122576506721313[/C][C]0.300000000000001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14035&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14035&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
116.9450.1524248448689820.359999999999999
217.190.1174734012447070.270000000000000
317.2350.04654746681256320.109999999999999
417.330.05354126134736330.109999999999999
517.52250.09878427675158370.240000000000002
617.520.1174734012447060.279999999999998
717.680.1587450786638750.34
817.9950.3408323145869050.82
918.66750.3063086678499330.630000000000003
1019.01750.049244289008980.0899999999999999
1119.57750.1294539815275430.300000000000001
1219.4050.108474267301820.230000000000000
1319.2950.1698038083593340.390000000000001
1419.230.1089342309224540.239999999999998
1519.190.0979795897113270.199999999999999
1619.440.1691153452528780.350000000000001
1719.48250.1212091855705110.289999999999999
1819.620.07702813338860870.180000000000000
1919.550.1823915202707260.390000000000001
2019.66250.1152894907034740.279999999999998
2119.92250.1643928222277360.390000000000001
2220.150.1581138830084180.369999999999997
2320.3250.130.300000000000001
2419.97250.1225765067213130.300000000000001






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.0788014550348941
beta0.00310870796372912
S.D.0.0135247694214224
T-STAT0.229852936258204
p-value0.820329725318831

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.0788014550348941 \tabularnewline
beta & 0.00310870796372912 \tabularnewline
S.D. & 0.0135247694214224 \tabularnewline
T-STAT & 0.229852936258204 \tabularnewline
p-value & 0.820329725318831 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14035&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.0788014550348941[/C][/ROW]
[ROW][C]beta[/C][C]0.00310870796372912[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0135247694214224[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.229852936258204[/C][/ROW]
[ROW][C]p-value[/C][C]0.820329725318831[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14035&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14035&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)
alpha0.0788014550348941
beta0.00310870796372912
S.D.0.0135247694214224
T-STAT0.229852936258204
p-value0.820329725318831






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-6.39897703186516
beta1.46721920575673
S.D.1.72592614172999
T-STAT0.85010544210545
p-value0.404423610150312
Lambda-0.467219205756727

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -6.39897703186516 \tabularnewline
beta & 1.46721920575673 \tabularnewline
S.D. & 1.72592614172999 \tabularnewline
T-STAT & 0.85010544210545 \tabularnewline
p-value & 0.404423610150312 \tabularnewline
Lambda & -0.467219205756727 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14035&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-6.39897703186516[/C][/ROW]
[ROW][C]beta[/C][C]1.46721920575673[/C][/ROW]
[ROW][C]S.D.[/C][C]1.72592614172999[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.85010544210545[/C][/ROW]
[ROW][C]p-value[/C][C]0.404423610150312[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.467219205756727[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14035&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14035&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-6.39897703186516
beta1.46721920575673
S.D.1.72592614172999
T-STAT0.85010544210545
p-value0.404423610150312
Lambda-0.467219205756727


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')