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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 computationTue, 19 Dec 2017 12:57:27 +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/2017/Dec/19/t1513685344jbpflvstv2rnb8w.htm/, Retrieved Wed, 15 May 2024 08:54:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=310316, Retrieved Wed, 15 May 2024 08:54:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact66

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] [ff] [2017-12-19 11:57:27] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
26
21
34
25
20
35
40
24
14
25
31
17
33
26
30
19
36
27
28
38
26
25
30
29
28
41
46
28
35
23
35
31
35
25
31
18
35
21
30
29
30
23
41
35
31
31
31
31
38
23
33
34
39
38
59
28
24
48
37
35
44
27
26
38
24
17
41
29
28
32
33
42
34
19
35
23
16
21
20
22
22
29
37
28
21
14
29
22
28
31
26
29
22
19
21
24
35
25
25
16
20
25
14
22
25
22
19

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=310316&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=310316&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310316&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
1267.7342214746011726
228.91666666666675.1071844820148519
331.33333333333337.7381385280174428
430.66666666666675.2281290471193720
536.33333333333339.9117316470142736
631.758.1811868443287727
725.56.9216393223781121
823.83333333333334.9512777659056417

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 26 & 7.73422147460117 & 26 \tabularnewline
2 & 28.9166666666667 & 5.10718448201485 & 19 \tabularnewline
3 & 31.3333333333333 & 7.73813852801744 & 28 \tabularnewline
4 & 30.6666666666667 & 5.22812904711937 & 20 \tabularnewline
5 & 36.3333333333333 & 9.91173164701427 & 36 \tabularnewline
6 & 31.75 & 8.18118684432877 & 27 \tabularnewline
7 & 25.5 & 6.92163932237811 & 21 \tabularnewline
8 & 23.8333333333333 & 4.95127776590564 & 17 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310316&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]26[/C][C]7.73422147460117[/C][C]26[/C][/ROW]
[ROW][C]2[/C][C]28.9166666666667[/C][C]5.10718448201485[/C][C]19[/C][/ROW]
[ROW][C]3[/C][C]31.3333333333333[/C][C]7.73813852801744[/C][C]28[/C][/ROW]
[ROW][C]4[/C][C]30.6666666666667[/C][C]5.22812904711937[/C][C]20[/C][/ROW]
[ROW][C]5[/C][C]36.3333333333333[/C][C]9.91173164701427[/C][C]36[/C][/ROW]
[ROW][C]6[/C][C]31.75[/C][C]8.18118684432877[/C][C]27[/C][/ROW]
[ROW][C]7[/C][C]25.5[/C][C]6.92163932237811[/C][C]21[/C][/ROW]
[ROW][C]8[/C][C]23.8333333333333[/C][C]4.95127776590564[/C][C]17[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310316&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310316&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
1267.7342214746011726
228.91666666666675.1071844820148519
331.33333333333337.7381385280174428
430.66666666666675.2281290471193720
536.33333333333339.9117316470142736
631.758.1811868443287727
725.56.9216393223781121
823.83333333333334.9512777659056417






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-1.11397086905889
beta0.276039584909747
S.D.0.13604423786689
T-STAT2.02904282634766
p-value0.0887814055558663

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -1.11397086905889 \tabularnewline
beta & 0.276039584909747 \tabularnewline
S.D. & 0.13604423786689 \tabularnewline
T-STAT & 2.02904282634766 \tabularnewline
p-value & 0.0887814055558663 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310316&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.11397086905889[/C][/ROW]
[ROW][C]beta[/C][C]0.276039584909747[/C][/ROW]
[ROW][C]S.D.[/C][C]0.13604423786689[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.02904282634766[/C][/ROW]
[ROW][C]p-value[/C][C]0.0887814055558663[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310316&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310316&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-1.11397086905889
beta0.276039584909747
S.D.0.13604423786689
T-STAT2.02904282634766
p-value0.0887814055558663






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.67241982946549
beta1.06437537425675
S.D.0.616740866327464
T-STAT1.72580646486885
p-value0.135135831364684
Lambda-0.0643753742567537

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.67241982946549 \tabularnewline
beta & 1.06437537425675 \tabularnewline
S.D. & 0.616740866327464 \tabularnewline
T-STAT & 1.72580646486885 \tabularnewline
p-value & 0.135135831364684 \tabularnewline
Lambda & -0.0643753742567537 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310316&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.67241982946549[/C][/ROW]
[ROW][C]beta[/C][C]1.06437537425675[/C][/ROW]
[ROW][C]S.D.[/C][C]0.616740866327464[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.72580646486885[/C][/ROW]
[ROW][C]p-value[/C][C]0.135135831364684[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.0643753742567537[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310316&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310316&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-1.67241982946549
beta1.06437537425675
S.D.0.616740866327464
T-STAT1.72580646486885
p-value0.135135831364684
Lambda-0.0643753742567537


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')