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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, 23 Dec 2016 13:27:27 +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/2016/Dec/23/t1482496627nojkpfkani4iuns.htm/, Retrieved Fri, 04 Apr 2025 11:43:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302901, Retrieved Fri, 04 Apr 2025 11:43:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact130

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] [] [2016-12-23 12:27:27] [219800a2f11ddd28e3280d87dbde8c8d] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4778
4838
4899
4935
4995
5032
5083
5104
5127
5180
5193
5210
5251
5275
5309
5339
5363
5402
5410
5408
5441
5438
5474
5521
5561
5632
5666
5699
5748
5833
5892
5965
6040
6077
6126
6199
6209
6252
6338
6411
6520
6611
6703
6799
6874
6950
7066
7245
7302
7310
7336
7436
7468
7430
7430
7460
7481
7568
7537
7501
7576
7582
7618
7690
7723
7789
7831
7837
7838
7848
7856
7874
7864
7847
7834
7805
7754
7738
7792
7798
7821
7875
7886
7947
7959
7988
8023
8066
8052
8108
8110
8166
8222
8204
8225
8264
8275
8337
8407
8427
8497
8592
8622
8679
8714
8781
8891
8977
9110
9273
9378
9437
9527
9547
9642
9761

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=302901&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=302901&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302901&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
15031.16666666667143.631367385295432
25385.9166666666781.0313725252962270
35869.83333333333211.975484574528638
46664.83333333333332.401409397881036
57438.2584.9161350981072266
67755.16666666667112.631202953657298
77830.0833333333358.5622564352491209
88115.58333333333100.743110148656305
98599.91666666667219.904300810947702

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 5031.16666666667 & 143.631367385295 & 432 \tabularnewline
2 & 5385.91666666667 & 81.0313725252962 & 270 \tabularnewline
3 & 5869.83333333333 & 211.975484574528 & 638 \tabularnewline
4 & 6664.83333333333 & 332.40140939788 & 1036 \tabularnewline
5 & 7438.25 & 84.9161350981072 & 266 \tabularnewline
6 & 7755.16666666667 & 112.631202953657 & 298 \tabularnewline
7 & 7830.08333333333 & 58.5622564352491 & 209 \tabularnewline
8 & 8115.58333333333 & 100.743110148656 & 305 \tabularnewline
9 & 8599.91666666667 & 219.904300810947 & 702 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302901&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]5031.16666666667[/C][C]143.631367385295[/C][C]432[/C][/ROW]
[ROW][C]2[/C][C]5385.91666666667[/C][C]81.0313725252962[/C][C]270[/C][/ROW]
[ROW][C]3[/C][C]5869.83333333333[/C][C]211.975484574528[/C][C]638[/C][/ROW]
[ROW][C]4[/C][C]6664.83333333333[/C][C]332.40140939788[/C][C]1036[/C][/ROW]
[ROW][C]5[/C][C]7438.25[/C][C]84.9161350981072[/C][C]266[/C][/ROW]
[ROW][C]6[/C][C]7755.16666666667[/C][C]112.631202953657[/C][C]298[/C][/ROW]
[ROW][C]7[/C][C]7830.08333333333[/C][C]58.5622564352491[/C][C]209[/C][/ROW]
[ROW][C]8[/C][C]8115.58333333333[/C][C]100.743110148656[/C][C]305[/C][/ROW]
[ROW][C]9[/C][C]8599.91666666667[/C][C]219.904300810947[/C][C]702[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302901&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302901&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
15031.16666666667143.631367385295432
25385.9166666666781.0313725252962270
35869.83333333333211.975484574528638
46664.83333333333332.401409397881036
57438.2584.9161350981072266
67755.16666666667112.631202953657298
77830.0833333333358.5622564352491209
88115.58333333333100.743110148656305
98599.91666666667219.904300810947702






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha193.725965650223
beta-0.00634442962514239
S.D.0.0261292830268447
T-STAT-0.242809173853881
p-value0.815114384863737

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 193.725965650223 \tabularnewline
beta & -0.00634442962514239 \tabularnewline
S.D. & 0.0261292830268447 \tabularnewline
T-STAT & -0.242809173853881 \tabularnewline
p-value & 0.815114384863737 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302901&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]193.725965650223[/C][/ROW]
[ROW][C]beta[/C][C]-0.00634442962514239[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0261292830268447[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.242809173853881[/C][/ROW]
[ROW][C]p-value[/C][C]0.815114384863737[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302901&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302901&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)
alpha193.725965650223
beta-0.00634442962514239
S.D.0.0261292830268447
T-STAT-0.242809173853881
p-value0.815114384863737






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha7.86818166900929
beta-0.340238935318969
S.D.1.09396061193763
T-STAT-0.311015708980908
p-value0.764845872831083
Lambda1.34023893531897

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 7.86818166900929 \tabularnewline
beta & -0.340238935318969 \tabularnewline
S.D. & 1.09396061193763 \tabularnewline
T-STAT & -0.311015708980908 \tabularnewline
p-value & 0.764845872831083 \tabularnewline
Lambda & 1.34023893531897 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302901&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]7.86818166900929[/C][/ROW]
[ROW][C]beta[/C][C]-0.340238935318969[/C][/ROW]
[ROW][C]S.D.[/C][C]1.09396061193763[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.311015708980908[/C][/ROW]
[ROW][C]p-value[/C][C]0.764845872831083[/C][/ROW]
[ROW][C]Lambda[/C][C]1.34023893531897[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302901&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302901&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)
alpha7.86818166900929
beta-0.340238935318969
S.D.1.09396061193763
T-STAT-0.311015708980908
p-value0.764845872831083
Lambda1.34023893531897


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')