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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 computationThu, 27 Dec 2007 07:09:56 -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/Dec/27/t119876338370n2mtjlvdjod7w.htm/, Retrieved Sun, 28 Apr 2024 04:37:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4904, Retrieved Sun, 28 Apr 2024 04:37:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact265

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] [s 0650692 paper] [2007-12-27 14:09:56] [011cc8cdd02d5893b5258ac3f5e21d83] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0,3
2,1
2,5
2,3
2,4
3
1,7
3,5
4
3,7
3,7
3
2,7
2,5
2,2
2,9
3,1
3
2,8
2,5
1,9
1,9
1,8
2
2,6
2,5
2,5
1,6
1,4
0,8
1,1
1,3
1,2
1,3
1,1
1,3
1,2
1,6
1,7
1,5
0,9
1,5
1,4
1,6
1,7
1,4
1,8
1,7
1,4
1,2
1
1,7
2,4
2
2,1
2
1,8
2,7
2,3
1,9
2
2,3
2,8
2,4
2,3
2,7
2,7
2,9
3
2,2
2,3
2,8

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'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4904&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4904&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4904&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'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
12.683333333333331.040832999733073.7
22.441666666666670.4679905463950651.3
31.558333333333330.6185883244545721.8
41.50.2522624895547560.9
51.8750.4956630086881791.7
62.533333333333330.3200378765462651

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 2.68333333333333 & 1.04083299973307 & 3.7 \tabularnewline
2 & 2.44166666666667 & 0.467990546395065 & 1.3 \tabularnewline
3 & 1.55833333333333 & 0.618588324454572 & 1.8 \tabularnewline
4 & 1.5 & 0.252262489554756 & 0.9 \tabularnewline
5 & 1.875 & 0.495663008688179 & 1.7 \tabularnewline
6 & 2.53333333333333 & 0.320037876546265 & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4904&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]2.68333333333333[/C][C]1.04083299973307[/C][C]3.7[/C][/ROW]
[ROW][C]2[/C][C]2.44166666666667[/C][C]0.467990546395065[/C][C]1.3[/C][/ROW]
[ROW][C]3[/C][C]1.55833333333333[/C][C]0.618588324454572[/C][C]1.8[/C][/ROW]
[ROW][C]4[/C][C]1.5[/C][C]0.252262489554756[/C][C]0.9[/C][/ROW]
[ROW][C]5[/C][C]1.875[/C][C]0.495663008688179[/C][C]1.7[/C][/ROW]
[ROW][C]6[/C][C]2.53333333333333[/C][C]0.320037876546265[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4904&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4904&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
12.683333333333331.040832999733073.7
22.441666666666670.4679905463950651.3
31.558333333333330.6185883244545721.8
41.50.2522624895547560.9
51.8750.4956630086881791.7
62.533333333333330.3200378765462651






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.0467790563249699
beta0.231478563130808
S.D.0.244577582438688
T-STAT0.946442273338096
p-value0.397514525776455

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.0467790563249699 \tabularnewline
beta & 0.231478563130808 \tabularnewline
S.D. & 0.244577582438688 \tabularnewline
T-STAT & 0.946442273338096 \tabularnewline
p-value & 0.397514525776455 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4904&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.0467790563249699[/C][/ROW]
[ROW][C]beta[/C][C]0.231478563130808[/C][/ROW]
[ROW][C]S.D.[/C][C]0.244577582438688[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.946442273338096[/C][/ROW]
[ROW][C]p-value[/C][C]0.397514525776455[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4904&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4904&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)
alpha0.0467790563249699
beta0.231478563130808
S.D.0.244577582438688
T-STAT0.946442273338096
p-value0.397514525776455






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.27268596470373
beta0.750659948663668
S.D.0.897299414012957
T-STAT0.83657688497368
p-value0.449896838100051
Lambda0.249340051336332

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.27268596470373 \tabularnewline
beta & 0.750659948663668 \tabularnewline
S.D. & 0.897299414012957 \tabularnewline
T-STAT & 0.83657688497368 \tabularnewline
p-value & 0.449896838100051 \tabularnewline
Lambda & 0.249340051336332 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4904&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.27268596470373[/C][/ROW]
[ROW][C]beta[/C][C]0.750659948663668[/C][/ROW]
[ROW][C]S.D.[/C][C]0.897299414012957[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.83657688497368[/C][/ROW]
[ROW][C]p-value[/C][C]0.449896838100051[/C][/ROW]
[ROW][C]Lambda[/C][C]0.249340051336332[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4904&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4904&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-1.27268596470373
beta0.750659948663668
S.D.0.897299414012957
T-STAT0.83657688497368
p-value0.449896838100051
Lambda0.249340051336332


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')