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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, 18 May 2008 08:15:48 -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/May/18/t1211120230y7dnzsrx1y9w17u.htm/, Retrieved Tue, 14 May 2024 10:58:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=12757, Retrieved Tue, 14 May 2024 10:58:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
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] [Standard Deviatio...] [2008-05-18 14:15:48] [b46ff5180a79ecd706507099e9497e04] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
117,99
118,13
117,06
118,03
118,57
118,44
118,02
118,18
116,79
116,91
117,19
117,3
116,35
117,04
116,26
115,91
115,75
115,21
115,07
114,17
113,96
113,59
114,47
113,52
113,56
113,59
113
112,07
111,11
109,61
109,51
109,21
108,86
107,99
108,74
108,74
107,74
107,8
106,96
106,73
106,27
105,69
105,39
105,09
104,94
104,75
104,38
103,65
103,49
103,39
103,48
103,33
103,61
103,21
102,85
103,25
102,88
102,51
101,99
101,6
101,21
100,74
100,36
100,26
100,37
100,23
100,02
99,8
99,58
99,69
99,53
99,37

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'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12757&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12757&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12757&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1117.80250.4984893847081041.06999999999999
2118.30250.2485122398058740.549999999999997
3117.04750.2375394704043910.509999999999991
4116.390.4730750469005991.13000000000001
5115.050.6558455102639121.58000000000000
6113.8850.4351628047830680.950000000000003
7113.0550.7105162442431141.52000000000001
8109.860.8504900548115391.90000000000001
9108.58250.3990300740545770.870000000000005
10107.30750.5427936993002011.06999999999999
11105.610.5035871324805641.17999999999999
12104.430.5696197562116881.28999999999999
13103.42250.07632168761236880.159999999999997
14103.230.3106981386061630.760000000000005
15102.2450.5640626442751451.28
16100.64250.4311515588127480.949999999999989
17100.1050.2490649179096390.570000000000007
1899.54250.1330100246848550.319999999999993

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 117.8025 & 0.498489384708104 & 1.06999999999999 \tabularnewline
2 & 118.3025 & 0.248512239805874 & 0.549999999999997 \tabularnewline
3 & 117.0475 & 0.237539470404391 & 0.509999999999991 \tabularnewline
4 & 116.39 & 0.473075046900599 & 1.13000000000001 \tabularnewline
5 & 115.05 & 0.655845510263912 & 1.58000000000000 \tabularnewline
6 & 113.885 & 0.435162804783068 & 0.950000000000003 \tabularnewline
7 & 113.055 & 0.710516244243114 & 1.52000000000001 \tabularnewline
8 & 109.86 & 0.850490054811539 & 1.90000000000001 \tabularnewline
9 & 108.5825 & 0.399030074054577 & 0.870000000000005 \tabularnewline
10 & 107.3075 & 0.542793699300201 & 1.06999999999999 \tabularnewline
11 & 105.61 & 0.503587132480564 & 1.17999999999999 \tabularnewline
12 & 104.43 & 0.569619756211688 & 1.28999999999999 \tabularnewline
13 & 103.4225 & 0.0763216876123688 & 0.159999999999997 \tabularnewline
14 & 103.23 & 0.310698138606163 & 0.760000000000005 \tabularnewline
15 & 102.245 & 0.564062644275145 & 1.28 \tabularnewline
16 & 100.6425 & 0.431151558812748 & 0.949999999999989 \tabularnewline
17 & 100.105 & 0.249064917909639 & 0.570000000000007 \tabularnewline
18 & 99.5425 & 0.133010024684855 & 0.319999999999993 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12757&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]117.8025[/C][C]0.498489384708104[/C][C]1.06999999999999[/C][/ROW]
[ROW][C]2[/C][C]118.3025[/C][C]0.248512239805874[/C][C]0.549999999999997[/C][/ROW]
[ROW][C]3[/C][C]117.0475[/C][C]0.237539470404391[/C][C]0.509999999999991[/C][/ROW]
[ROW][C]4[/C][C]116.39[/C][C]0.473075046900599[/C][C]1.13000000000001[/C][/ROW]
[ROW][C]5[/C][C]115.05[/C][C]0.655845510263912[/C][C]1.58000000000000[/C][/ROW]
[ROW][C]6[/C][C]113.885[/C][C]0.435162804783068[/C][C]0.950000000000003[/C][/ROW]
[ROW][C]7[/C][C]113.055[/C][C]0.710516244243114[/C][C]1.52000000000001[/C][/ROW]
[ROW][C]8[/C][C]109.86[/C][C]0.850490054811539[/C][C]1.90000000000001[/C][/ROW]
[ROW][C]9[/C][C]108.5825[/C][C]0.399030074054577[/C][C]0.870000000000005[/C][/ROW]
[ROW][C]10[/C][C]107.3075[/C][C]0.542793699300201[/C][C]1.06999999999999[/C][/ROW]
[ROW][C]11[/C][C]105.61[/C][C]0.503587132480564[/C][C]1.17999999999999[/C][/ROW]
[ROW][C]12[/C][C]104.43[/C][C]0.569619756211688[/C][C]1.28999999999999[/C][/ROW]
[ROW][C]13[/C][C]103.4225[/C][C]0.0763216876123688[/C][C]0.159999999999997[/C][/ROW]
[ROW][C]14[/C][C]103.23[/C][C]0.310698138606163[/C][C]0.760000000000005[/C][/ROW]
[ROW][C]15[/C][C]102.245[/C][C]0.564062644275145[/C][C]1.28[/C][/ROW]
[ROW][C]16[/C][C]100.6425[/C][C]0.431151558812748[/C][C]0.949999999999989[/C][/ROW]
[ROW][C]17[/C][C]100.105[/C][C]0.249064917909639[/C][C]0.570000000000007[/C][/ROW]
[ROW][C]18[/C][C]99.5425[/C][C]0.133010024684855[/C][C]0.319999999999993[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12757&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12757&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
1117.80250.4984893847081041.06999999999999
2118.30250.2485122398058740.549999999999997
3117.04750.2375394704043910.509999999999991
4116.390.4730750469005991.13000000000001
5115.050.6558455102639121.58000000000000
6113.8850.4351628047830680.950000000000003
7113.0550.7105162442431141.52000000000001
8109.860.8504900548115391.90000000000001
9108.58250.3990300740545770.870000000000005
10107.30750.5427936993002011.06999999999999
11105.610.5035871324805641.17999999999999
12104.430.5696197562116881.28999999999999
13103.42250.07632168761236880.159999999999997
14103.230.3106981386061630.760000000000005
15102.2450.5640626442751451.28
16100.64250.4311515588127480.949999999999989
17100.1050.2490649179096390.570000000000007
1899.54250.1330100246848550.319999999999993






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.398069523430130
beta0.00769442620360279
S.D.0.00741964805982544
T-STAT1.03703385141206
p-value0.315139736308151

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.398069523430130 \tabularnewline
beta & 0.00769442620360279 \tabularnewline
S.D. & 0.00741964805982544 \tabularnewline
T-STAT & 1.03703385141206 \tabularnewline
p-value & 0.315139736308151 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12757&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.398069523430130[/C][/ROW]
[ROW][C]beta[/C][C]0.00769442620360279[/C][/ROW]
[ROW][C]S.D.[/C][C]0.00741964805982544[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.03703385141206[/C][/ROW]
[ROW][C]p-value[/C][C]0.315139736308151[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12757&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12757&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-0.398069523430130
beta0.00769442620360279
S.D.0.00741964805982544
T-STAT1.03703385141206
p-value0.315139736308151






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-15.2483450092075
beta3.04752674622585
S.D.2.39128228412595
T-STAT1.27443203441779
p-value0.220709535298513
Lambda-2.04752674622585

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -15.2483450092075 \tabularnewline
beta & 3.04752674622585 \tabularnewline
S.D. & 2.39128228412595 \tabularnewline
T-STAT & 1.27443203441779 \tabularnewline
p-value & 0.220709535298513 \tabularnewline
Lambda & -2.04752674622585 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12757&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-15.2483450092075[/C][/ROW]
[ROW][C]beta[/C][C]3.04752674622585[/C][/ROW]
[ROW][C]S.D.[/C][C]2.39128228412595[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.27443203441779[/C][/ROW]
[ROW][C]p-value[/C][C]0.220709535298513[/C][/ROW]
[ROW][C]Lambda[/C][C]-2.04752674622585[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12757&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12757&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-15.2483450092075
beta3.04752674622585
S.D.2.39128228412595
T-STAT1.27443203441779
p-value0.220709535298513
Lambda-2.04752674622585


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')