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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 computationFri, 16 Dec 2016 08:31:54 +0100
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/Dec/16/t1481873564tr8xhugiedo2wy9.htm/, Retrieved Thu, 02 May 2024 19:19:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300073, Retrieved Thu, 02 May 2024 19:19:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact98

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] [st dev of mean pl...] [2016-12-16 07:31:54] [afe7f6443461a2cd6ee0b843643e84a9] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3690
3878
3834
3780
3690
3202
3736
3480
3552
3372
3334
3502
3468
3480
3642
3600
3594
3834
3954
4006
4102
4236
4086
4350
4224
4576
4678
4624
4404
4190
4414
4414
3998
3554
3974
3820
4102
3926
4056
4072
4246
4232
4244
3944
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Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300073&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300073&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300073&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
13587.5214.20317457965676
23862.66666666667302.384864139404882
34239.16666666667346.2405452160611124
44102.75129.146373213829320
5NaNNA-Inf
6NaNNA-Inf
7NaNNA-Inf
8NaNNA-Inf
9NaNNA-Inf
10NaNNA-Inf
11NaNNA-Inf
12NaNNA-Inf

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 3587.5 & 214.20317457965 & 676 \tabularnewline
2 & 3862.66666666667 & 302.384864139404 & 882 \tabularnewline
3 & 4239.16666666667 & 346.240545216061 & 1124 \tabularnewline
4 & 4102.75 & 129.146373213829 & 320 \tabularnewline
5 & NaN & NA & -Inf \tabularnewline
6 & NaN & NA & -Inf \tabularnewline
7 & NaN & NA & -Inf \tabularnewline
8 & NaN & NA & -Inf \tabularnewline
9 & NaN & NA & -Inf \tabularnewline
10 & NaN & NA & -Inf \tabularnewline
11 & NaN & NA & -Inf \tabularnewline
12 & NaN & NA & -Inf \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300073&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]3587.5[/C][C]214.20317457965[/C][C]676[/C][/ROW]
[ROW][C]2[/C][C]3862.66666666667[/C][C]302.384864139404[/C][C]882[/C][/ROW]
[ROW][C]3[/C][C]4239.16666666667[/C][C]346.240545216061[/C][C]1124[/C][/ROW]
[ROW][C]4[/C][C]4102.75[/C][C]129.146373213829[/C][C]320[/C][/ROW]
[ROW][C]5[/C][C]NaN[/C][C]NA[/C][C]-Inf[/C][/ROW]
[ROW][C]6[/C][C]NaN[/C][C]NA[/C][C]-Inf[/C][/ROW]
[ROW][C]7[/C][C]NaN[/C][C]NA[/C][C]-Inf[/C][/ROW]
[ROW][C]8[/C][C]NaN[/C][C]NA[/C][C]-Inf[/C][/ROW]
[ROW][C]9[/C][C]NaN[/C][C]NA[/C][C]-Inf[/C][/ROW]
[ROW][C]10[/C][C]NaN[/C][C]NA[/C][C]-Inf[/C][/ROW]
[ROW][C]11[/C][C]NaN[/C][C]NA[/C][C]-Inf[/C][/ROW]
[ROW][C]12[/C][C]NaN[/C][C]NA[/C][C]-Inf[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300073&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300073&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
13587.5214.20317457965676
23862.66666666667302.384864139404882
34239.16666666667346.2405452160611124
44102.75129.146373213829320
5NaNNA-Inf
6NaNNA-Inf
7NaNNA-Inf
8NaNNA-Inf
9NaNNA-Inf
10NaNNA-Inf
11NaNNA-Inf
12NaNNA-Inf






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-36.9863646379832
beta0.0721830294103614
S.D.0.232515592758232
T-STAT0.310443822515666
p-value0.785588291064681

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -36.9863646379832 \tabularnewline
beta & 0.0721830294103614 \tabularnewline
S.D. & 0.232515592758232 \tabularnewline
T-STAT & 0.310443822515666 \tabularnewline
p-value & 0.785588291064681 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300073&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-36.9863646379832[/C][/ROW]
[ROW][C]beta[/C][C]0.0721830294103614[/C][/ROW]
[ROW][C]S.D.[/C][C]0.232515592758232[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.310443822515666[/C][/ROW]
[ROW][C]p-value[/C][C]0.785588291064681[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300073&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300073&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-36.9863646379832
beta0.0721830294103614
S.D.0.232515592758232
T-STAT0.310443822515666
p-value0.785588291064681






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha1.44305080749451
beta0.483590133748637
S.D.4.22099030492215
T-STAT0.11456793283432
p-value0.919252772682592
Lambda0.516409866251363

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.44305080749451 \tabularnewline
beta & 0.483590133748637 \tabularnewline
S.D. & 4.22099030492215 \tabularnewline
T-STAT & 0.11456793283432 \tabularnewline
p-value & 0.919252772682592 \tabularnewline
Lambda & 0.516409866251363 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300073&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.44305080749451[/C][/ROW]
[ROW][C]beta[/C][C]0.483590133748637[/C][/ROW]
[ROW][C]S.D.[/C][C]4.22099030492215[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.11456793283432[/C][/ROW]
[ROW][C]p-value[/C][C]0.919252772682592[/C][/ROW]
[ROW][C]Lambda[/C][C]0.516409866251363[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300073&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300073&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)
alpha1.44305080749451
beta0.483590133748637
S.D.4.22099030492215
T-STAT0.11456793283432
p-value0.919252772682592
Lambda0.516409866251363


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')