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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, 19 Dec 2008 10:13:34 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/19/t1229706852r346pby54y506ew.htm/, Retrieved Wed, 15 May 2024 14:37:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35225, Retrieved Wed, 15 May 2024 14:37:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact220

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
F RMP   [(Partial) Autocorrelation Function] [Taak 10 Stap 4] [2008-12-03 16:24:10] [6fea0e9a9b3b29a63badf2c274e82506]
-   P     [(Partial) Autocorrelation Function] [Identification an...] [2008-12-08 19:12:52] [79c17183721a40a589db5f9f561947d8]
- RMPD      [ARIMA Backward Selection] [arima backward el...] [2008-12-19 16:45:52] [44a98561a4b3e6ab8cd5a857b48b0914]
- RMPD          [Standard Deviation-Mean Plot] [standdev olie] [2008-12-19 17:13:34] [1aceffc2fa350402d9e8f8edd757a2e8] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
20,72
21,45
22,09
21,53
23,35
23,57
26,42
25,21
26,44
29,34
29,40
33,05
28,38
26,01
29,31
30,36
35,75
36,15
34,21
37,91
38,70
42,12
42,16
39,80
37,36
38,35
42,60
41,25
42,16
46,94
47,43
47,06
50,18
50,13
43,23
40,04
40,37
42,21
37,00
39,74
42,68
46,29
46,97
48,73
52,37
50,05
54,04
57,78
64,72
63,41
64,36
66,03
72,14
76,60
86,97
93,48
95,59
81,89
70,55
50,38
36,25

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35225&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35225&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35225&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
125.21416666666673.8468297651994212.33
235.07166666666675.4618991591059616.15
343.89416666666674.3755694867449412.82
446.51916666666676.3453912528318720.78
573.843333333333313.519415219556945.21

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 25.2141666666667 & 3.84682976519942 & 12.33 \tabularnewline
2 & 35.0716666666667 & 5.46189915910596 & 16.15 \tabularnewline
3 & 43.8941666666667 & 4.37556948674494 & 12.82 \tabularnewline
4 & 46.5191666666667 & 6.34539125283187 & 20.78 \tabularnewline
5 & 73.8433333333333 & 13.5194152195569 & 45.21 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35225&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]25.2141666666667[/C][C]3.84682976519942[/C][C]12.33[/C][/ROW]
[ROW][C]2[/C][C]35.0716666666667[/C][C]5.46189915910596[/C][C]16.15[/C][/ROW]
[ROW][C]3[/C][C]43.8941666666667[/C][C]4.37556948674494[/C][C]12.82[/C][/ROW]
[ROW][C]4[/C][C]46.5191666666667[/C][C]6.34539125283187[/C][C]20.78[/C][/ROW]
[ROW][C]5[/C][C]73.8433333333333[/C][C]13.5194152195569[/C][C]45.21[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35225&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35225&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
125.21416666666673.8468297651994212.33
235.07166666666675.4618991591059616.15
343.89416666666674.3755694867449412.82
446.51916666666676.3453912528318720.78
573.843333333333313.519415219556945.21






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-2.35251442716604
beta0.201795548812672
S.D.0.0440924880739955
T-STAT4.57664236307147
p-value0.0195795615501518

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -2.35251442716604 \tabularnewline
beta & 0.201795548812672 \tabularnewline
S.D. & 0.0440924880739955 \tabularnewline
T-STAT & 4.57664236307147 \tabularnewline
p-value & 0.0195795615501518 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35225&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.35251442716604[/C][/ROW]
[ROW][C]beta[/C][C]0.201795548812672[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0440924880739955[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.57664236307147[/C][/ROW]
[ROW][C]p-value[/C][C]0.0195795615501518[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35225&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35225&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-2.35251442716604
beta0.201795548812672
S.D.0.0440924880739955
T-STAT4.57664236307147
p-value0.0195795615501518






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.36895046043236
beta1.11274616301469
S.D.0.324512888375723
T-STAT3.42897371067229
p-value0.0415692109985351
Lambda-0.112746163014688

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.36895046043236 \tabularnewline
beta & 1.11274616301469 \tabularnewline
S.D. & 0.324512888375723 \tabularnewline
T-STAT & 3.42897371067229 \tabularnewline
p-value & 0.0415692109985351 \tabularnewline
Lambda & -0.112746163014688 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35225&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.36895046043236[/C][/ROW]
[ROW][C]beta[/C][C]1.11274616301469[/C][/ROW]
[ROW][C]S.D.[/C][C]0.324512888375723[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.42897371067229[/C][/ROW]
[ROW][C]p-value[/C][C]0.0415692109985351[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.112746163014688[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35225&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35225&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-2.36895046043236
beta1.11274616301469
S.D.0.324512888375723
T-STAT3.42897371067229
p-value0.0415692109985351
Lambda-0.112746163014688


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')