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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationMon, 09 Jan 2017 13:20:29 +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/2017/Jan/09/t1483968059jvxcv4rkm96qmz9.htm/, Retrieved Tue, 14 May 2024 02:20:36 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 14 May 2024 02:20:36 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0

Tree of Dependent Computations

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1.56
1.56
1.54
1.54
1.54
1.54
1.57
1.58
1.57
1.57
1.57
1.57
1.56
1.58
1.58
1.58
1.58
1.53
1.48
1.48
1.48
1.48
1.48
1.57
1.57
1.57
1.60
1.60
1.65
1.71
1.71
1.71
1.74
1.78
1.84
1.84
1.76
1.72
1.66
1.65
1.66
1.66
1.66
1.61
1.55
1.56
1.55
1.55
1.61
1.54
1.48
1.42
1.42
1.42
1.43
1.46
1.50
1.47
1.43
1.42
1.39
1.37
1.38
1.51
1.47
1.47
1.53
1.55
1.50
1.52
1.53
1.53
1.52
1.60
1.52
1.64
1.63
1.69
1.73
1.69
1.61
1.52
1.55
1.56
1.56
1.56
1.54
1.53
1.54
1.48
1.38
1.34
1.28
1.28
1.30
1.31
1.31
1.31
1.32
1.31
1.27
1.24
1.24
1.24
1.24
1.24
1.24
1.24
1.23
1.26
1.28
1.32
1.40
1.41
1.37
1.33
1.33
1.34
1.34
1.38
1.43
1.39
1.33
1.33
1.34
1.38
1.37
1.38
1.31
1.38
1.30
1.30
1.29
1.31
1.31
1.32
1.31
1.30
1.31
1.33
1.34
1.42
1.42
1.36
1.36
1.34
1.34
1.33
1.31
1.25
1.23
1.17
1.19
1.19
1.19
1.19

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

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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'Herman Ole Andreas Wold' @ wold.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
11.559166666666670.01505042031024890.04
21.531666666666670.04764133677487410.1
31.693333333333330.09689106660512510.27
41.63250.06969087588643280.21
51.466666666666670.05928871321888780.19
61.479166666666670.06444988656923980.18
71.6050.07305041845440470.21
81.4250.1195065612500760.28
91.266666666666670.03498917581542080.0800000000000001
101.33250.05479299888920780.18
111.353333333333330.04097301403104090.13
121.3350.04379705261980330.13
131.25750.07312815649753030.19

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 1.55916666666667 & 0.0150504203102489 & 0.04 \tabularnewline
2 & 1.53166666666667 & 0.0476413367748741 & 0.1 \tabularnewline
3 & 1.69333333333333 & 0.0968910666051251 & 0.27 \tabularnewline
4 & 1.6325 & 0.0696908758864328 & 0.21 \tabularnewline
5 & 1.46666666666667 & 0.0592887132188878 & 0.19 \tabularnewline
6 & 1.47916666666667 & 0.0644498865692398 & 0.18 \tabularnewline
7 & 1.605 & 0.0730504184544047 & 0.21 \tabularnewline
8 & 1.425 & 0.119506561250076 & 0.28 \tabularnewline
9 & 1.26666666666667 & 0.0349891758154208 & 0.0800000000000001 \tabularnewline
10 & 1.3325 & 0.0547929988892078 & 0.18 \tabularnewline
11 & 1.35333333333333 & 0.0409730140310409 & 0.13 \tabularnewline
12 & 1.335 & 0.0437970526198033 & 0.13 \tabularnewline
13 & 1.2575 & 0.0731281564975303 & 0.19 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]1.55916666666667[/C][C]0.0150504203102489[/C][C]0.04[/C][/ROW]
[ROW][C]2[/C][C]1.53166666666667[/C][C]0.0476413367748741[/C][C]0.1[/C][/ROW]
[ROW][C]3[/C][C]1.69333333333333[/C][C]0.0968910666051251[/C][C]0.27[/C][/ROW]
[ROW][C]4[/C][C]1.6325[/C][C]0.0696908758864328[/C][C]0.21[/C][/ROW]
[ROW][C]5[/C][C]1.46666666666667[/C][C]0.0592887132188878[/C][C]0.19[/C][/ROW]
[ROW][C]6[/C][C]1.47916666666667[/C][C]0.0644498865692398[/C][C]0.18[/C][/ROW]
[ROW][C]7[/C][C]1.605[/C][C]0.0730504184544047[/C][C]0.21[/C][/ROW]
[ROW][C]8[/C][C]1.425[/C][C]0.119506561250076[/C][C]0.28[/C][/ROW]
[ROW][C]9[/C][C]1.26666666666667[/C][C]0.0349891758154208[/C][C]0.0800000000000001[/C][/ROW]
[ROW][C]10[/C][C]1.3325[/C][C]0.0547929988892078[/C][C]0.18[/C][/ROW]
[ROW][C]11[/C][C]1.35333333333333[/C][C]0.0409730140310409[/C][C]0.13[/C][/ROW]
[ROW][C]12[/C][C]1.335[/C][C]0.0437970526198033[/C][C]0.13[/C][/ROW]
[ROW][C]13[/C][C]1.2575[/C][C]0.0731281564975303[/C][C]0.19[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
11.559166666666670.01505042031024890.04
21.531666666666670.04764133677487410.1
31.693333333333330.09689106660512510.27
41.63250.06969087588643280.21
51.466666666666670.05928871321888780.19
61.479166666666670.06444988656923980.18
71.6050.07305041845440470.21
81.4250.1195065612500760.28
91.266666666666670.03498917581542080.0800000000000001
101.33250.05479299888920780.18
111.353333333333330.04097301403104090.13
121.3350.04379705261980330.13
131.25750.07312815649753030.19






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.00941540837075084
beta0.0483511543626167
S.D.0.0554393091320369
T-STAT0.872145687231802
p-value0.401764684711145

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.00941540837075084 \tabularnewline
beta & 0.0483511543626167 \tabularnewline
S.D. & 0.0554393091320369 \tabularnewline
T-STAT & 0.872145687231802 \tabularnewline
p-value & 0.401764684711145 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.00941540837075084[/C][/ROW]
[ROW][C]beta[/C][C]0.0483511543626167[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0554393091320369[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.872145687231802[/C][/ROW]
[ROW][C]p-value[/C][C]0.401764684711145[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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-0.00941540837075084
beta0.0483511543626167
S.D.0.0554393091320369
T-STAT0.872145687231802
p-value0.401764684711145






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.20543103558752
beta0.812857762106569
S.D.1.57635606327518
T-STAT0.515656190275755
p-value0.61629996192358
Lambda0.187142237893431

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.20543103558752 \tabularnewline
beta & 0.812857762106569 \tabularnewline
S.D. & 1.57635606327518 \tabularnewline
T-STAT & 0.515656190275755 \tabularnewline
p-value & 0.61629996192358 \tabularnewline
Lambda & 0.187142237893431 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.20543103558752[/C][/ROW]
[ROW][C]beta[/C][C]0.812857762106569[/C][/ROW]
[ROW][C]S.D.[/C][C]1.57635606327518[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.515656190275755[/C][/ROW]
[ROW][C]p-value[/C][C]0.61629996192358[/C][/ROW]
[ROW][C]Lambda[/C][C]0.187142237893431[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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-3.20543103558752
beta0.812857762106569
S.D.1.57635606327518
T-STAT0.515656190275755
p-value0.61629996192358
Lambda0.187142237893431


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')