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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 computationFri, 18 Mar 2016 14:00:20 +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/2016/Mar/18/t1458309645pr212rioq89czyf.htm/, Retrieved Thu, 02 May 2024 12:06:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294255, Retrieved Thu, 02 May 2024 12:06:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact128

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] [consumptieprijsin...] [2016-03-18 14:00:20] [567a9be58124adae7ccc8a0c8709ba48] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
84.97
85.57
85.74
85.88
85.88
85.96
85.96
85.99
86.02
86.14
86.3
86.32
86.32
86.77
87.47
87.39
87.3
87.31
87.31
87.38
87.4
87.32
87.37
87.4
87.4
87.89
87.7
87.89
88.02
88.08
88.08
88.15
88.21
88.41
88.39
88.41
88.41
89.1
90.35
90.61
91.18
91.22
91.22
91.4
91.52
91.68
91.71
91.77
91.77
92.16
93.64
93.78
93.96
93.82
93.82
93.89
94.05
94.46
94.62
94.72
94.72
95.76
96.14
97.11
97.19
97.43
97.43
97.56
97.66
97.75
97.82
97.82
97.82
98.35
98.19
98.19
98.21
98.22
98.26
98.23
98.26
98.5
98.51
98.51
98.51
98.89
99.55
99.9
100.12
100.09
100.09
100.09
100.46
100.71
100.79
100.79
100.93
101.15
101.53
101.91
102.18
102.24
102.2
102.32
102.43
102.45
102.84
102.96
102.96
103.1
103.4
103.74
103.97
104.29
104.33
104.46
104.9
105.31
105.63
105.68

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' @ jenkins.wessa.net

\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' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294255&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294255&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294255&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' @ jenkins.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
185.89416666666670.3597336978006551.34999999999999
287.22833333333330.336906605168351.15000000000001
388.05250.3028988730132981.00999999999999
490.84751.075877020684233.36
593.72416666666670.8953867456258362.95
697.03250.9787480407503893.09999999999999
798.27083333333330.190141494363510.690000000000012
899.99916666666670.7177801427549612.28
9102.0950.6204910079196062.02999999999999
10104.3141666666670.9315525489821582.72000000000001

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 85.8941666666667 & 0.359733697800655 & 1.34999999999999 \tabularnewline
2 & 87.2283333333333 & 0.33690660516835 & 1.15000000000001 \tabularnewline
3 & 88.0525 & 0.302898873013298 & 1.00999999999999 \tabularnewline
4 & 90.8475 & 1.07587702068423 & 3.36 \tabularnewline
5 & 93.7241666666667 & 0.895386745625836 & 2.95 \tabularnewline
6 & 97.0325 & 0.978748040750389 & 3.09999999999999 \tabularnewline
7 & 98.2708333333333 & 0.19014149436351 & 0.690000000000012 \tabularnewline
8 & 99.9991666666667 & 0.717780142754961 & 2.28 \tabularnewline
9 & 102.095 & 0.620491007919606 & 2.02999999999999 \tabularnewline
10 & 104.314166666667 & 0.931552548982158 & 2.72000000000001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294255&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]85.8941666666667[/C][C]0.359733697800655[/C][C]1.34999999999999[/C][/ROW]
[ROW][C]2[/C][C]87.2283333333333[/C][C]0.33690660516835[/C][C]1.15000000000001[/C][/ROW]
[ROW][C]3[/C][C]88.0525[/C][C]0.302898873013298[/C][C]1.00999999999999[/C][/ROW]
[ROW][C]4[/C][C]90.8475[/C][C]1.07587702068423[/C][C]3.36[/C][/ROW]
[ROW][C]5[/C][C]93.7241666666667[/C][C]0.895386745625836[/C][C]2.95[/C][/ROW]
[ROW][C]6[/C][C]97.0325[/C][C]0.978748040750389[/C][C]3.09999999999999[/C][/ROW]
[ROW][C]7[/C][C]98.2708333333333[/C][C]0.19014149436351[/C][C]0.690000000000012[/C][/ROW]
[ROW][C]8[/C][C]99.9991666666667[/C][C]0.717780142754961[/C][C]2.28[/C][/ROW]
[ROW][C]9[/C][C]102.095[/C][C]0.620491007919606[/C][C]2.02999999999999[/C][/ROW]
[ROW][C]10[/C][C]104.314166666667[/C][C]0.931552548982158[/C][C]2.72000000000001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294255&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294255&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
185.89416666666670.3597336978006551.34999999999999
287.22833333333330.336906605168351.15000000000001
388.05250.3028988730132981.00999999999999
490.84751.075877020684233.36
593.72416666666670.8953867456258362.95
697.03250.9787480407503893.09999999999999
798.27083333333330.190141494363510.690000000000012
899.99916666666670.7177801427549612.28
9102.0950.6204910079196062.02999999999999
10104.3141666666670.9315525489821582.72000000000001






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-1.14735883239542
beta0.0188748189464978
S.D.0.0161811102963242
T-STAT1.16647242376102
p-value0.277016919287575

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -1.14735883239542 \tabularnewline
beta & 0.0188748189464978 \tabularnewline
S.D. & 0.0161811102963242 \tabularnewline
T-STAT & 1.16647242376102 \tabularnewline
p-value & 0.277016919287575 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294255&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.14735883239542[/C][/ROW]
[ROW][C]beta[/C][C]0.0188748189464978[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0161811102963242[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.16647242376102[/C][/ROW]
[ROW][C]p-value[/C][C]0.277016919287575[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294255&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294255&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-1.14735883239542
beta0.0188748189464978
S.D.0.0161811102963242
T-STAT1.16647242376102
p-value0.277016919287575






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-15.4595786959335
beta3.26865979965726
S.D.2.8549676713968
T-STAT1.14490256138629
p-value0.285344467164863
Lambda-2.26865979965726

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -15.4595786959335 \tabularnewline
beta & 3.26865979965726 \tabularnewline
S.D. & 2.8549676713968 \tabularnewline
T-STAT & 1.14490256138629 \tabularnewline
p-value & 0.285344467164863 \tabularnewline
Lambda & -2.26865979965726 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294255&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-15.4595786959335[/C][/ROW]
[ROW][C]beta[/C][C]3.26865979965726[/C][/ROW]
[ROW][C]S.D.[/C][C]2.8549676713968[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.14490256138629[/C][/ROW]
[ROW][C]p-value[/C][C]0.285344467164863[/C][/ROW]
[ROW][C]Lambda[/C][C]-2.26865979965726[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294255&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294255&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-15.4595786959335
beta3.26865979965726
S.D.2.8549676713968
T-STAT1.14490256138629
p-value0.285344467164863
Lambda-2.26865979965726


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')