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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 computationWed, 28 Nov 2007 12:37:00 -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/2007/Nov/28/t1196278115esgt6p2xxy2gt67.htm/, Retrieved Thu, 02 May 2024 01:32:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7256, Retrieved Thu, 02 May 2024 01:32:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsInducing stationarity time series
Estimated Impact176

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] [Case IV Question I.2] [2007-11-28 19:37:00] [fd802f308f037a9692de8c23f8b60e49] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
73,8
55,2
54,4
80,8
88
74,5
55,1
47,2
54,2
70,6
78,5
77,1
56,6
39,8
44,1
66,9
75,3
74,9
48,8
37
49,8
63,2
75,9
68,5
49,2
40,3
38,6
54,2
70,6
68
43
42,3
47,7
57,7
75,8
57,2
43,6
40
35,9
59,5
72,7
70,9
44,9
44,5
48
60,4
71,8
63,2
32,4
33,9
24,2
64,7
73
61,7
31,9
30,8
36,7
47,4
54
41,1

Tables (Output of Computation)





Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7256&T=0

[TABLE]
[ROW][C]Summary of compuational 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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7256&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7256&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
167.4513.396777088674655.6
258.414.267509179314342
353.716666666666712.487363309531951.6
454.616666666666713.294758593543818.5
544.316666666666715.67887016646832.40000000000001

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 67.45 & 13.3967770886746 & 55.6 \tabularnewline
2 & 58.4 & 14.2675091793143 & 42 \tabularnewline
3 & 53.7166666666667 & 12.4873633095319 & 51.6 \tabularnewline
4 & 54.6166666666667 & 13.2947585935438 & 18.5 \tabularnewline
5 & 44.3166666666667 & 15.6788701664683 & 2.40000000000001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7256&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]67.45[/C][C]13.3967770886746[/C][C]55.6[/C][/ROW]
[ROW][C]2[/C][C]58.4[/C][C]14.2675091793143[/C][C]42[/C][/ROW]
[ROW][C]3[/C][C]53.7166666666667[/C][C]12.4873633095319[/C][C]51.6[/C][/ROW]
[ROW][C]4[/C][C]54.6166666666667[/C][C]13.2947585935438[/C][C]18.5[/C][/ROW]
[ROW][C]5[/C][C]44.3166666666667[/C][C]15.6788701664683[/C][C]2.40000000000001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7256&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7256&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
167.4513.396777088674655.6
258.414.267509179314342
353.716666666666712.487363309531951.6
454.616666666666713.294758593543818.5
544.316666666666715.67887016646832.40000000000001






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha18.14370692609
beta-0.0775341339063457
S.D.0.070730702733204
T-STAT-1.09618780685390
p-value0.353109024884462

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 18.14370692609 \tabularnewline
beta & -0.0775341339063457 \tabularnewline
S.D. & 0.070730702733204 \tabularnewline
T-STAT & -1.09618780685390 \tabularnewline
p-value & 0.353109024884462 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7256&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]18.14370692609[/C][/ROW]
[ROW][C]beta[/C][C]-0.0775341339063457[/C][/ROW]
[ROW][C]S.D.[/C][C]0.070730702733204[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.09618780685390[/C][/ROW]
[ROW][C]p-value[/C][C]0.353109024884462[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7256&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7256&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)
alpha18.14370692609
beta-0.0775341339063457
S.D.0.070730702733204
T-STAT-1.09618780685390
p-value0.353109024884462






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha3.88103907780747
beta-0.313541234879793
S.D.0.272377783527652
T-STAT-1.15112631734872
p-value0.333103106936133
Lambda1.31354123487979

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 3.88103907780747 \tabularnewline
beta & -0.313541234879793 \tabularnewline
S.D. & 0.272377783527652 \tabularnewline
T-STAT & -1.15112631734872 \tabularnewline
p-value & 0.333103106936133 \tabularnewline
Lambda & 1.31354123487979 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7256&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.88103907780747[/C][/ROW]
[ROW][C]beta[/C][C]-0.313541234879793[/C][/ROW]
[ROW][C]S.D.[/C][C]0.272377783527652[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.15112631734872[/C][/ROW]
[ROW][C]p-value[/C][C]0.333103106936133[/C][/ROW]
[ROW][C]Lambda[/C][C]1.31354123487979[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7256&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7256&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)
alpha3.88103907780747
beta-0.313541234879793
S.D.0.272377783527652
T-STAT-1.15112631734872
p-value0.333103106936133
Lambda1.31354123487979


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')