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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, 10 Dec 2008 06:47:28 -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/10/t1228917002d4s7t5xto7hu9xr.htm/, Retrieved Wed, 15 May 2024 18:01:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=31954, Retrieved Wed, 15 May 2024 18:01:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact205

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [test 3] [2007-10-13 09:57:27] [74be16979710d4c4e7c6647856088456]
- RMPD    [Standard Deviation-Mean Plot] [paper standard de...] [2008-12-10 13:47:28] [e1dd70d3b1099218056e8ae5041dcc2f] [Current]
-  M D      [Standard Deviation-Mean Plot] [paper sdmeanplot WLH] [2009-12-27 13:06:33] [db72903d7941c8279d5ce0e4e873d517]
- RM D      [Variance Reduction Matrix] [paper VRM WLH] [2009-12-27 13:28:57] [db72903d7941c8279d5ce0e4e873d517]
- RM D      [Variance Reduction Matrix] [paper VRM WLH] [2009-12-27 13:32:35] [db72903d7941c8279d5ce0e4e873d517]
- RMPD      [(Partial) Autocorrelation Function] [paper ACF WLH] [2009-12-27 13:56:04] [db72903d7941c8279d5ce0e4e873d517]
- RMPD      [Spectral Analysis] [paper spectrum WLH] [2009-12-27 14:33:28] [db72903d7941c8279d5ce0e4e873d517]
- RMPD      [(Partial) Autocorrelation Function] [paper diffACF WLH] [2009-12-27 14:56:24] [db72903d7941c8279d5ce0e4e873d517]
- RMPD      [(Partial) Autocorrelation Function] [paper diff2ACF WLH] [2009-12-27 14:59:10] [db72903d7941c8279d5ce0e4e873d517]
- RMPD      [Spectral Analysis] [paper diffSPEC WLH] [2009-12-27 15:07:25] [db72903d7941c8279d5ce0e4e873d517]
- RMPD      [Spectral Analysis] [paper diff2SPEC WLH] [2009-12-27 15:19:55] [db72903d7941c8279d5ce0e4e873d517]
- RMPD      [Spectral Analysis] [paper diff3spec wlh] [2009-12-27 15:33:33] [db72903d7941c8279d5ce0e4e873d517]
- RMPD      [(Partial) Autocorrelation Function] [paper diff3ACF WLH] [2009-12-27 15:37:59] [db72903d7941c8279d5ce0e4e873d517]
- RMPD      [(Partial) Autocorrelation Function] [paper diff3 ACF WLH] [2009-12-27 15:41:15] [db72903d7941c8279d5ce0e4e873d517]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
12.5
14.8
15.9
14.8
12.9
14.3
14.2
15.9
15.3
15.5
15.1
15
12.1
15.8
16.9
15.1
13.7
14.8
14.7
16
15.4
15
15.5
15.1
11.7
16.3
16.7
15
14.9
14.6
15.3
17.9
16.4
15.4
17.9
15.9
13.9
17.8
17.9
17.4
16.7
16
16.6
19.1
17.8
17.2
18.6
16.3
15.1
19.2
17.7
19.1
18
17.5
17.8
21.1
17.2
19.4
19.8
17.6
16.2
19.5
19.9
20
17.3
18.9
18.6
21.4
18.6
19.8
20.8
19.6
17.7
19.8
22.2
20.7
17.9
21.2
21.4
21.7
23.2
21.5
22.9
23.2
18.6

Tables (Output of Computation)





Summary of computational 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 computational 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=31954&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]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=31954&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31954&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
114.68333333333331.071815226047793.4
215.00833333333331.202617095665904.8
315.66666666666671.655477592903656.2
417.10833333333331.364123650309365.2
518.29166666666671.538274318445156
619.21666666666671.431993736231435.2
721.11666666666671.847274815078755.5

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 14.6833333333333 & 1.07181522604779 & 3.4 \tabularnewline
2 & 15.0083333333333 & 1.20261709566590 & 4.8 \tabularnewline
3 & 15.6666666666667 & 1.65547759290365 & 6.2 \tabularnewline
4 & 17.1083333333333 & 1.36412365030936 & 5.2 \tabularnewline
5 & 18.2916666666667 & 1.53827431844515 & 6 \tabularnewline
6 & 19.2166666666667 & 1.43199373623143 & 5.2 \tabularnewline
7 & 21.1166666666667 & 1.84727481507875 & 5.5 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31954&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]14.6833333333333[/C][C]1.07181522604779[/C][C]3.4[/C][/ROW]
[ROW][C]2[/C][C]15.0083333333333[/C][C]1.20261709566590[/C][C]4.8[/C][/ROW]
[ROW][C]3[/C][C]15.6666666666667[/C][C]1.65547759290365[/C][C]6.2[/C][/ROW]
[ROW][C]4[/C][C]17.1083333333333[/C][C]1.36412365030936[/C][C]5.2[/C][/ROW]
[ROW][C]5[/C][C]18.2916666666667[/C][C]1.53827431844515[/C][C]6[/C][/ROW]
[ROW][C]6[/C][C]19.2166666666667[/C][C]1.43199373623143[/C][C]5.2[/C][/ROW]
[ROW][C]7[/C][C]21.1166666666667[/C][C]1.84727481507875[/C][C]5.5[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31954&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31954&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
114.68333333333331.071815226047793.4
215.00833333333331.202617095665904.8
315.66666666666671.655477592903656.2
417.10833333333331.364123650309365.2
518.29166666666671.538274318445156
619.21666666666671.431993736231435.2
721.11666666666671.847274815078755.5






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.0176864865694715
beta0.0824810765565678
S.D.0.0332468258311582
T-STAT2.48087071455911
p-value0.0557815174440521

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.0176864865694715 \tabularnewline
beta & 0.0824810765565678 \tabularnewline
S.D. & 0.0332468258311582 \tabularnewline
T-STAT & 2.48087071455911 \tabularnewline
p-value & 0.0557815174440521 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31954&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.0176864865694715[/C][/ROW]
[ROW][C]beta[/C][C]0.0824810765565678[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0332468258311582[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.48087071455911[/C][/ROW]
[ROW][C]p-value[/C][C]0.0557815174440521[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31954&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31954&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)
alpha0.0176864865694715
beta0.0824810765565678
S.D.0.0332468258311582
T-STAT2.48087071455911
p-value0.0557815174440521






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.55166133862382
beta1.02185164615932
S.D.0.408436600001127
T-STAT2.50186111175273
p-value0.0543662054122707
Lambda-0.0218516461593237

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.55166133862382 \tabularnewline
beta & 1.02185164615932 \tabularnewline
S.D. & 0.408436600001127 \tabularnewline
T-STAT & 2.50186111175273 \tabularnewline
p-value & 0.0543662054122707 \tabularnewline
Lambda & -0.0218516461593237 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31954&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.55166133862382[/C][/ROW]
[ROW][C]beta[/C][C]1.02185164615932[/C][/ROW]
[ROW][C]S.D.[/C][C]0.408436600001127[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.50186111175273[/C][/ROW]
[ROW][C]p-value[/C][C]0.0543662054122707[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.0218516461593237[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31954&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31954&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-2.55166133862382
beta1.02185164615932
S.D.0.408436600001127
T-STAT2.50186111175273
p-value0.0543662054122707
Lambda-0.0218516461593237


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')