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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 computationThu, 26 Dec 2013 13:04:01 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Dec/26/t1388081065e5vcbqyde98pzh3.htm/, Retrieved Fri, 26 Apr 2024 05:15:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232624, Retrieved Fri, 26 Apr 2024 05:15:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact149

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] [] [2013-12-26 18:04:01] [b29dd38cb32721834f7fbb83663b016f] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
27,65
28,19
28,98
28,99
29,02
29
29,04
29,19
29,23
29,26
29,02
28,47
28,53
28,48
28,68
28,89
29,2
29,21
29,15
29,22
29,34
29,13
28,84
28,76
28,75
28,89
28,82
29,12
29,21
29,3
29,32
29,52
29,64
29,54
29,54
29,34
29,34
29,54
29,94
30,17
30,23
30,34
30,34
30,36
30,3
30,28
29,89
29,58
29,68
29,73
30,07
30,32
30,55
30,62
30,67
30,79
30,8
30,5
30,07
29,41
29,42
29,99
30,14
30,41
30,78
30,88
30,92
30,93
31,62
31,48
31,3
31,11
31,16
31,22
31,66
32,11
32,27
32,36
32,42
32,52
32,41
31,87
31,04
30,58

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'Gertrude Mary Cox' @ cox.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 & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232624&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232624&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232624&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'Gertrude Mary Cox' @ cox.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
128.83666666666670.4860664625960181.61
228.95250.293787956928740.859999999999999
329.24916666666670.3002562037307270.890000000000001
430.02583333333330.362101400497741.02
530.26750.4697025170737911.39
630.74833333333330.6491369561801182.2
731.80166666666670.6565728282436611.94

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 28.8366666666667 & 0.486066462596018 & 1.61 \tabularnewline
2 & 28.9525 & 0.29378795692874 & 0.859999999999999 \tabularnewline
3 & 29.2491666666667 & 0.300256203730727 & 0.890000000000001 \tabularnewline
4 & 30.0258333333333 & 0.36210140049774 & 1.02 \tabularnewline
5 & 30.2675 & 0.469702517073791 & 1.39 \tabularnewline
6 & 30.7483333333333 & 0.649136956180118 & 2.2 \tabularnewline
7 & 31.8016666666667 & 0.656572828243661 & 1.94 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232624&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]28.8366666666667[/C][C]0.486066462596018[/C][C]1.61[/C][/ROW]
[ROW][C]2[/C][C]28.9525[/C][C]0.29378795692874[/C][C]0.859999999999999[/C][/ROW]
[ROW][C]3[/C][C]29.2491666666667[/C][C]0.300256203730727[/C][C]0.890000000000001[/C][/ROW]
[ROW][C]4[/C][C]30.0258333333333[/C][C]0.36210140049774[/C][C]1.02[/C][/ROW]
[ROW][C]5[/C][C]30.2675[/C][C]0.469702517073791[/C][C]1.39[/C][/ROW]
[ROW][C]6[/C][C]30.7483333333333[/C][C]0.649136956180118[/C][C]2.2[/C][/ROW]
[ROW][C]7[/C][C]31.8016666666667[/C][C]0.656572828243661[/C][C]1.94[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232624&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232624&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
128.83666666666670.4860664625960181.61
228.95250.293787956928740.859999999999999
329.24916666666670.3002562037307270.890000000000001
430.02583333333330.362101400497741.02
530.26750.4697025170737911.39
630.74833333333330.6491369561801182.2
731.80166666666670.6565728282436611.94






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-2.84493154184857
beta0.110215177369109
S.D.0.039667712986544
T-STAT2.77846059354356
p-value0.0389730009138628

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -2.84493154184857 \tabularnewline
beta & 0.110215177369109 \tabularnewline
S.D. & 0.039667712986544 \tabularnewline
T-STAT & 2.77846059354356 \tabularnewline
p-value & 0.0389730009138628 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232624&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.84493154184857[/C][/ROW]
[ROW][C]beta[/C][C]0.110215177369109[/C][/ROW]
[ROW][C]S.D.[/C][C]0.039667712986544[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.77846059354356[/C][/ROW]
[ROW][C]p-value[/C][C]0.0389730009138628[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232624&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232624&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-2.84493154184857
beta0.110215177369109
S.D.0.039667712986544
T-STAT2.77846059354356
p-value0.0389730009138628






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-24.8805242809307
beta7.07501589077271
S.D.2.79451471764925
T-STAT2.53175116455433
p-value0.0524179556508029
Lambda-6.07501589077271

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -24.8805242809307 \tabularnewline
beta & 7.07501589077271 \tabularnewline
S.D. & 2.79451471764925 \tabularnewline
T-STAT & 2.53175116455433 \tabularnewline
p-value & 0.0524179556508029 \tabularnewline
Lambda & -6.07501589077271 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232624&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-24.8805242809307[/C][/ROW]
[ROW][C]beta[/C][C]7.07501589077271[/C][/ROW]
[ROW][C]S.D.[/C][C]2.79451471764925[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.53175116455433[/C][/ROW]
[ROW][C]p-value[/C][C]0.0524179556508029[/C][/ROW]
[ROW][C]Lambda[/C][C]-6.07501589077271[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232624&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232624&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-24.8805242809307
beta7.07501589077271
S.D.2.79451471764925
T-STAT2.53175116455433
p-value0.0524179556508029
Lambda-6.07501589077271


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
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')