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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 computationTue, 02 Dec 2008 12:49:15 -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/02/t1228247414hj8rs5vne4qkr98.htm/, Retrieved Fri, 17 May 2024 01:41:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28285, Retrieved Fri, 17 May 2024 01:41:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsgsm
Estimated Impact167

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Law of Averages] [Random Walk Simul...] [2008-11-25 18:40:39] [b98453cac15ba1066b407e146608df68]
F       [Law of Averages] [WS7 Task 4] [2008-11-30 15:52:14] [11ac052cc87d77b9933b02bea117068e]
- RMPD    [Spectral Analysis] [WS7 Task 6d] [2008-12-02 18:21:54] [11ac052cc87d77b9933b02bea117068e]
- RMPD        [Standard Deviation-Mean Plot] [WS7 Task 8b] [2008-12-02 19:49:15] [99f79d508deef838ee89a56fb32f134e] [Current]
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Dataset

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

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=28285&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=28285&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28285&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
13.751.231037995130353.4
21.6750.338781238076620.9
31.808333333333330.2539088359425421
42.133333333333330.2534608929251690.8
51.558333333333330.2065224325624580.8
61.316666666666670.275790873780490.8
72.2250.8114241128467232
82.633333333333330.4163331998932271.1

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 3.75 & 1.23103799513035 & 3.4 \tabularnewline
2 & 1.675 & 0.33878123807662 & 0.9 \tabularnewline
3 & 1.80833333333333 & 0.253908835942542 & 1 \tabularnewline
4 & 2.13333333333333 & 0.253460892925169 & 0.8 \tabularnewline
5 & 1.55833333333333 & 0.206522432562458 & 0.8 \tabularnewline
6 & 1.31666666666667 & 0.27579087378049 & 0.8 \tabularnewline
7 & 2.225 & 0.811424112846723 & 2 \tabularnewline
8 & 2.63333333333333 & 0.416333199893227 & 1.1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28285&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]3.75[/C][C]1.23103799513035[/C][C]3.4[/C][/ROW]
[ROW][C]2[/C][C]1.675[/C][C]0.33878123807662[/C][C]0.9[/C][/ROW]
[ROW][C]3[/C][C]1.80833333333333[/C][C]0.253908835942542[/C][C]1[/C][/ROW]
[ROW][C]4[/C][C]2.13333333333333[/C][C]0.253460892925169[/C][C]0.8[/C][/ROW]
[ROW][C]5[/C][C]1.55833333333333[/C][C]0.206522432562458[/C][C]0.8[/C][/ROW]
[ROW][C]6[/C][C]1.31666666666667[/C][C]0.27579087378049[/C][C]0.8[/C][/ROW]
[ROW][C]7[/C][C]2.225[/C][C]0.811424112846723[/C][C]2[/C][/ROW]
[ROW][C]8[/C][C]2.63333333333333[/C][C]0.416333199893227[/C][C]1.1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28285&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28285&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
13.751.231037995130353.4
21.6750.338781238076620.9
31.808333333333330.2539088359425421
42.133333333333330.2534608929251690.8
51.558333333333330.2065224325624580.8
61.316666666666670.275790873780490.8
72.2250.8114241128467232
82.633333333333330.4163331998932271.1






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.382161876546515
beta0.400266350498812
S.D.0.0989701238459662
T-STAT4.04431494015076
p-value0.00676955103691133

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.382161876546515 \tabularnewline
beta & 0.400266350498812 \tabularnewline
S.D. & 0.0989701238459662 \tabularnewline
T-STAT & 4.04431494015076 \tabularnewline
p-value & 0.00676955103691133 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28285&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.382161876546515[/C][/ROW]
[ROW][C]beta[/C][C]0.400266350498812[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0989701238459662[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.04431494015076[/C][/ROW]
[ROW][C]p-value[/C][C]0.00676955103691133[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28285&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28285&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-0.382161876546515
beta0.400266350498812
S.D.0.0989701238459662
T-STAT4.04431494015076
p-value0.00676955103691133






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.02745785308628
beta1.52458765280609
S.D.0.468066679595465
T-STAT3.25720184595011
p-value0.0173093739387253
Lambda-0.524587652806088

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.02745785308628 \tabularnewline
beta & 1.52458765280609 \tabularnewline
S.D. & 0.468066679595465 \tabularnewline
T-STAT & 3.25720184595011 \tabularnewline
p-value & 0.0173093739387253 \tabularnewline
Lambda & -0.524587652806088 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28285&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.02745785308628[/C][/ROW]
[ROW][C]beta[/C][C]1.52458765280609[/C][/ROW]
[ROW][C]S.D.[/C][C]0.468066679595465[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.25720184595011[/C][/ROW]
[ROW][C]p-value[/C][C]0.0173093739387253[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.524587652806088[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28285&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28285&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-2.02745785308628
beta1.52458765280609
S.D.0.468066679595465
T-STAT3.25720184595011
p-value0.0173093739387253
Lambda-0.524587652806088


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')