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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, 23 Jan 2017 12:25:08 +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/Jan/23/t1485170725t5xd77jr699rmvn.htm/, Retrieved Wed, 15 May 2024 11:53:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=305048, Retrieved Wed, 15 May 2024 11:53:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact40

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] [] [2017-01-23 11:25:08] [1cdbb99454d86b60323f5d77f6a65c9b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
14
19
17
17
15
20
15
19
15
15
19
NA
20
18
15
14
20
NA
16
16
16
10
19
19
16
15
18
17
19
17
NA
19
20
5
19
16
15
16
18
16
15
17
NA
20
19
7
13
16
16
NA
18
18
16
17
19
16
19
13
16
13
12
17
17
17
16
16
14
16
13
16
14
20
12
13
18
14
19
18
14
18
19
15
14
17
19
13
19
18
20
15
15
15
20
15
19
18
18
15
20
17
12
18
19
20
NA
17
15
16
18
18
14
15
12
17
14
18
17
17
20
16
14
15
18
20
17
17
17
17
15
17
18
17
20
15
16
15
18
11
15
18
20
19
14
16
15
17
18
20
17
18
15
16
11
15
18
17
16
12
19
18
15
17
19
18
19
16
16
16
14

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=305048&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=305048&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=305048&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
116.81818181818182.136266922375666
216.63636363636363.009077176568510
316.45454545454554.1076425444197615
415.63636363636363.4719656470860213
516.45454545454552.067057636527656
615.66666666666672.146173479954648
715.91666666666672.503028468705767
817.16666666666672.405801069888947
9172.408318915758468
1016.33333333333332.229281716090858
1116.83333333333331.585922922197526
1216.41666666666672.678477631835379
1316.41666666666672.274696116900559
1416.752.050498830661817

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 16.8181818181818 & 2.13626692237566 & 6 \tabularnewline
2 & 16.6363636363636 & 3.0090771765685 & 10 \tabularnewline
3 & 16.4545454545455 & 4.10764254441976 & 15 \tabularnewline
4 & 15.6363636363636 & 3.47196564708602 & 13 \tabularnewline
5 & 16.4545454545455 & 2.06705763652765 & 6 \tabularnewline
6 & 15.6666666666667 & 2.14617347995464 & 8 \tabularnewline
7 & 15.9166666666667 & 2.50302846870576 & 7 \tabularnewline
8 & 17.1666666666667 & 2.40580106988894 & 7 \tabularnewline
9 & 17 & 2.40831891575846 & 8 \tabularnewline
10 & 16.3333333333333 & 2.22928171609085 & 8 \tabularnewline
11 & 16.8333333333333 & 1.58592292219752 & 6 \tabularnewline
12 & 16.4166666666667 & 2.67847763183537 & 9 \tabularnewline
13 & 16.4166666666667 & 2.27469611690055 & 9 \tabularnewline
14 & 16.75 & 2.05049883066181 & 7 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=305048&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]16.8181818181818[/C][C]2.13626692237566[/C][C]6[/C][/ROW]
[ROW][C]2[/C][C]16.6363636363636[/C][C]3.0090771765685[/C][C]10[/C][/ROW]
[ROW][C]3[/C][C]16.4545454545455[/C][C]4.10764254441976[/C][C]15[/C][/ROW]
[ROW][C]4[/C][C]15.6363636363636[/C][C]3.47196564708602[/C][C]13[/C][/ROW]
[ROW][C]5[/C][C]16.4545454545455[/C][C]2.06705763652765[/C][C]6[/C][/ROW]
[ROW][C]6[/C][C]15.6666666666667[/C][C]2.14617347995464[/C][C]8[/C][/ROW]
[ROW][C]7[/C][C]15.9166666666667[/C][C]2.50302846870576[/C][C]7[/C][/ROW]
[ROW][C]8[/C][C]17.1666666666667[/C][C]2.40580106988894[/C][C]7[/C][/ROW]
[ROW][C]9[/C][C]17[/C][C]2.40831891575846[/C][C]8[/C][/ROW]
[ROW][C]10[/C][C]16.3333333333333[/C][C]2.22928171609085[/C][C]8[/C][/ROW]
[ROW][C]11[/C][C]16.8333333333333[/C][C]1.58592292219752[/C][C]6[/C][/ROW]
[ROW][C]12[/C][C]16.4166666666667[/C][C]2.67847763183537[/C][C]9[/C][/ROW]
[ROW][C]13[/C][C]16.4166666666667[/C][C]2.27469611690055[/C][C]9[/C][/ROW]
[ROW][C]14[/C][C]16.75[/C][C]2.05049883066181[/C][C]7[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=305048&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=305048&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
116.81818181818182.136266922375666
216.63636363636363.009077176568510
316.45454545454554.1076425444197615
415.63636363636363.4719656470860213
516.45454545454552.067057636527656
615.66666666666672.146173479954648
715.91666666666672.503028468705767
817.16666666666672.405801069888947
9172.408318915758468
1016.33333333333332.229281716090858
1116.83333333333331.585922922197526
1216.41666666666672.678477631835379
1316.41666666666672.274696116900559
1416.752.050498830661817






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha9.09991466812289
beta-0.400540547829713
S.D.0.385814933834162
T-STAT-1.03816755833998
p-value0.319659290937829

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 9.09991466812289 \tabularnewline
beta & -0.400540547829713 \tabularnewline
S.D. & 0.385814933834162 \tabularnewline
T-STAT & -1.03816755833998 \tabularnewline
p-value & 0.319659290937829 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=305048&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]9.09991466812289[/C][/ROW]
[ROW][C]beta[/C][C]-0.400540547829713[/C][/ROW]
[ROW][C]S.D.[/C][C]0.385814933834162[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.03816755833998[/C][/ROW]
[ROW][C]p-value[/C][C]0.319659290937829[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=305048&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=305048&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)
alpha9.09991466812289
beta-0.400540547829713
S.D.0.385814933834162
T-STAT-1.03816755833998
p-value0.319659290937829






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha7.96653303278732
beta-2.52632639568339
S.D.2.31464216919906
T-STAT-1.09145440677665
p-value0.2965027673055
Lambda3.52632639568339

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 7.96653303278732 \tabularnewline
beta & -2.52632639568339 \tabularnewline
S.D. & 2.31464216919906 \tabularnewline
T-STAT & -1.09145440677665 \tabularnewline
p-value & 0.2965027673055 \tabularnewline
Lambda & 3.52632639568339 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=305048&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]7.96653303278732[/C][/ROW]
[ROW][C]beta[/C][C]-2.52632639568339[/C][/ROW]
[ROW][C]S.D.[/C][C]2.31464216919906[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.09145440677665[/C][/ROW]
[ROW][C]p-value[/C][C]0.2965027673055[/C][/ROW]
[ROW][C]Lambda[/C][C]3.52632639568339[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=305048&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=305048&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)
alpha7.96653303278732
beta-2.52632639568339
S.D.2.31464216919906
T-STAT-1.09145440677665
p-value0.2965027673055
Lambda3.52632639568339


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')