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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 computationSun, 26 Dec 2010 16:00:23 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/26/t12933791833tv28ic21u27yyh.htm/, Retrieved Mon, 06 May 2024 13:43:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115696, Retrieved Mon, 06 May 2024 13:43:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact117

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
- RMP         [Standard Deviation-Mean Plot] [Births] [2010-11-29 10:52:49] [b98453cac15ba1066b407e146608df68]
- R PD          [Standard Deviation-Mean Plot] [WS9 - Standard De...] [2010-12-07 09:15:36] [1f5baf2b24e732d76900bb8178fc04e7]
-    D            [Standard Deviation-Mean Plot] [Paper - Standard ...] [2010-12-14 16:20:25] [1f5baf2b24e732d76900bb8178fc04e7]
-    D                [Standard Deviation-Mean Plot] [paper lambda waar...] [2010-12-26 16:00:23] [6df2229e3f2091de42c4a9cf9a617420] [Current]
-   PD                  [Standard Deviation-Mean Plot] [paper Standard De...] [2010-12-26 17:09:45] [eeb33d252044f8583501f5ba0605ad6d]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2,08
2,09
2,07
2,04
2,35
2,33
2,37
2,59
2,62
2,6
2,83
2,78
3,01
3,06
3,33
3,32
3,6
3,57
3,57
3,83
3,84
3,8
4,07
4,05
4,272
3,858
4,067
3,964
3,782
4,114
4,009
4,025
4,082
4,044
3,916
4,289
4,296
4,193
3,48
2,934
2,221
1,211
1,28
0,96
0,5
0,687
0,344
0,346
0,334
0,34
0,328
0,344
0,341
0,32
0,314
0,325
0,339
0,329
0,48
0,399
0,37

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'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115696&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115696&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115696&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'RServer@AstonUniversity' @ vre.aston.ac.uk






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
12.395833333333330.285862596788080.79
23.58750.3522428139792211.06
34.035166666666670.1494096463560580.507
41.8711.497492206687873.952
50.3494166666666670.04635526513849970.166

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 2.39583333333333 & 0.28586259678808 & 0.79 \tabularnewline
2 & 3.5875 & 0.352242813979221 & 1.06 \tabularnewline
3 & 4.03516666666667 & 0.149409646356058 & 0.507 \tabularnewline
4 & 1.871 & 1.49749220668787 & 3.952 \tabularnewline
5 & 0.349416666666667 & 0.0463552651384997 & 0.166 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115696&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]2.39583333333333[/C][C]0.28586259678808[/C][C]0.79[/C][/ROW]
[ROW][C]2[/C][C]3.5875[/C][C]0.352242813979221[/C][C]1.06[/C][/ROW]
[ROW][C]3[/C][C]4.03516666666667[/C][C]0.149409646356058[/C][C]0.507[/C][/ROW]
[ROW][C]4[/C][C]1.871[/C][C]1.49749220668787[/C][C]3.952[/C][/ROW]
[ROW][C]5[/C][C]0.349416666666667[/C][C]0.0463552651384997[/C][C]0.166[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115696&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115696&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
12.395833333333330.285862596788080.79
23.58750.3522428139792211.06
34.035166666666670.1494096463560580.507
41.8711.497492206687873.952
50.3494166666666670.04635526513849970.166






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.562734049188074
beta-0.0394077131274398
S.D.0.231213728423786
T-STAT-0.17043846572644
p-value0.875511612053709

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.562734049188074 \tabularnewline
beta & -0.0394077131274398 \tabularnewline
S.D. & 0.231213728423786 \tabularnewline
T-STAT & -0.17043846572644 \tabularnewline
p-value & 0.875511612053709 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115696&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.562734049188074[/C][/ROW]
[ROW][C]beta[/C][C]-0.0394077131274398[/C][/ROW]
[ROW][C]S.D.[/C][C]0.231213728423786[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.17043846572644[/C][/ROW]
[ROW][C]p-value[/C][C]0.875511612053709[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115696&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115696&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)
alpha0.562734049188074
beta-0.0394077131274398
S.D.0.231213728423786
T-STAT-0.17043846572644
p-value0.875511612053709






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.80416884612881
beta0.69090793023931
S.D.0.626796963988539
T-STAT1.10228346647184
p-value0.350831852712326
Lambda0.30909206976069

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.80416884612881 \tabularnewline
beta & 0.69090793023931 \tabularnewline
S.D. & 0.626796963988539 \tabularnewline
T-STAT & 1.10228346647184 \tabularnewline
p-value & 0.350831852712326 \tabularnewline
Lambda & 0.30909206976069 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115696&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.80416884612881[/C][/ROW]
[ROW][C]beta[/C][C]0.69090793023931[/C][/ROW]
[ROW][C]S.D.[/C][C]0.626796963988539[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.10228346647184[/C][/ROW]
[ROW][C]p-value[/C][C]0.350831852712326[/C][/ROW]
[ROW][C]Lambda[/C][C]0.30909206976069[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115696&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115696&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-1.80416884612881
beta0.69090793023931
S.D.0.626796963988539
T-STAT1.10228346647184
p-value0.350831852712326
Lambda0.30909206976069


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')