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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 computationMon, 01 Dec 2008 13:45:37 -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/01/t122816436848uf8mpul67zihr.htm/, Retrieved Sun, 05 May 2024 14:56:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27381, Retrieved Sun, 05 May 2024 14:56:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact209

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [Airline data] [2007-10-18 09:58:47] [42daae401fd3def69a25014f2252b4c2]
- RMPD  [Variance Reduction Matrix] [Q6 reproduce vari...] [2008-12-01 20:00:25] [4242609301e759e844b9196c1994e4ef]
-    D    [Variance Reduction Matrix] [Q8 tabak variantie] [2008-12-01 20:36:19] [4242609301e759e844b9196c1994e4ef]
- RM D        [Standard Deviation-Mean Plot] [Q8 tabak lambda] [2008-12-01 20:45:37] [c040f376c7eef5bfe1cb52dcc7980437] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
41.1
58
63
53.8
54.7
55.5
56.1
69.6
69.4
57.2
68
53.3
47.9
60.8
61.7
57.8
51.4
50.5
48.1
58.7
54
56.1
60.4
51.2
50.7
56.4
53.3
52.6
47.7
49.5
48.5
55.3
49.8
57.4
64.6
53
41.5
55.9
58.4
53.5
50.6
58.5
49.1
61.1
52.3
58.4
65.5
61.7
45.1
52.1
59.3
57.9
45
64.9
63.8
69.4
71.1
62.9
73.5
62.6

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=27381&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=27381&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27381&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
158.30833333333338.1748459349767628.5
254.88333333333335.0175751719391913.8
353.23333333333334.7336961021889416.9
455.54166666666676.5433461461150624
560.63333333333339.3271191433985428.5

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 58.3083333333333 & 8.17484593497676 & 28.5 \tabularnewline
2 & 54.8833333333333 & 5.01757517193919 & 13.8 \tabularnewline
3 & 53.2333333333333 & 4.73369610218894 & 16.9 \tabularnewline
4 & 55.5416666666667 & 6.54334614611506 & 24 \tabularnewline
5 & 60.6333333333333 & 9.32711914339854 & 28.5 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27381&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]58.3083333333333[/C][C]8.17484593497676[/C][C]28.5[/C][/ROW]
[ROW][C]2[/C][C]54.8833333333333[/C][C]5.01757517193919[/C][C]13.8[/C][/ROW]
[ROW][C]3[/C][C]53.2333333333333[/C][C]4.73369610218894[/C][C]16.9[/C][/ROW]
[ROW][C]4[/C][C]55.5416666666667[/C][C]6.54334614611506[/C][C]24[/C][/ROW]
[ROW][C]5[/C][C]60.6333333333333[/C][C]9.32711914339854[/C][C]28.5[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27381&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27381&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
158.30833333333338.1748459349767628.5
254.88333333333335.0175751719391913.8
353.23333333333334.7336961021889416.9
455.54166666666676.5433461461150624
560.63333333333339.3271191433985428.5






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-30.5543924166546
beta0.660185932703084
S.D.0.0833304608978785
T-STAT7.92250427502305
p-value0.00419293823383315

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -30.5543924166546 \tabularnewline
beta & 0.660185932703084 \tabularnewline
S.D. & 0.0833304608978785 \tabularnewline
T-STAT & 7.92250427502305 \tabularnewline
p-value & 0.00419293823383315 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27381&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-30.5543924166546[/C][/ROW]
[ROW][C]beta[/C][C]0.660185932703084[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0833304608978785[/C][/ROW]
[ROW][C]T-STAT[/C][C]7.92250427502305[/C][/ROW]
[ROW][C]p-value[/C][C]0.00419293823383315[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27381&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27381&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-30.5543924166546
beta0.660185932703084
S.D.0.0833304608978785
T-STAT7.92250427502305
p-value0.00419293823383315






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-20.4619453081919
beta5.538076807797
S.D.0.859533840889677
T-STAT6.44311665735546
p-value0.00758136674466575
Lambda-4.538076807797

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -20.4619453081919 \tabularnewline
beta & 5.538076807797 \tabularnewline
S.D. & 0.859533840889677 \tabularnewline
T-STAT & 6.44311665735546 \tabularnewline
p-value & 0.00758136674466575 \tabularnewline
Lambda & -4.538076807797 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27381&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-20.4619453081919[/C][/ROW]
[ROW][C]beta[/C][C]5.538076807797[/C][/ROW]
[ROW][C]S.D.[/C][C]0.859533840889677[/C][/ROW]
[ROW][C]T-STAT[/C][C]6.44311665735546[/C][/ROW]
[ROW][C]p-value[/C][C]0.00758136674466575[/C][/ROW]
[ROW][C]Lambda[/C][C]-4.538076807797[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27381&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27381&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-20.4619453081919
beta5.538076807797
S.D.0.859533840889677
T-STAT6.44311665735546
p-value0.00758136674466575
Lambda-4.538076807797


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')