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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 computationThu, 16 Dec 2010 19:52:36 +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/16/t1292529262rcwsihnj1dcotnf.htm/, Retrieved Fri, 03 May 2024 05:00:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111242, Retrieved Fri, 03 May 2024 05:00:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact122

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] [] [2010-12-16 19:52:36] [40b262140b988d7b8204c4955f8b7651] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
-2.0
2.6
0.2
0.1
-0.1
0.1
-1.6
2.3
-0.3
0.0
0.1
0.4
-1.9
2.4
0.0
0.4
0.1
0.2
-1.3
2.1
-0.1
0.3
0.3
0.2
-1.9
2.7
0.0
-0.2
0.2
0.1
-1.5
2.1
-0.3
-0.2
0.2
0.3
-2.0
2.6
0.0
0.5
-0.1
0.2
-1.6
2.1
-0.2
0.0
0.2
0.2
-2.2
2.7
-0.3
0.4
-0.1
0.0
-1.6
2.2
-0.3
0.0
0.1
0.1
-1.9
2.5
0.1
-0.1
0.3
0.1
-1.9
2.5
-0.3
0.2
0.2
0.1
-2.4
3.1
-0.3
0.2
0.1
0.2
-1.8
2.4
-0.4
0.0
0.0
0.2
-2.4
3.2
0.0
0.1
0.1
0.1
-1.8
2.5
-0.6
0.0
0.0
0.4
-2.5
3.1
0.2
-0.3
0.3
0.4
-1.8
2.6
-0.3
0.3
0.0
0.4
-2.9
3.6
-0.1
0.3
0.0
0.3
-2.1
2.6
-0.2
0.0
-0.2
0.3
-3.1
3.4
-0.1
0.1
0.3
0.1
-2.5
3.1
-0.1
0.1
0.0

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=111242&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=111242&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111242&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
10.151.302794199892194.6
20.2251.179464439326754.3
30.1251.269305465062044.6
40.1583333333333331.273833393796664.6
50.08333333333333331.342205331354024.9
60.151.339945724816704.4
70.1083333333333331.495726234876215.5
80.1333333333333331.532278952370885.6
90.21.540365954157415.6
100.1333333333333331.723808327951566.5

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 0.15 & 1.30279419989219 & 4.6 \tabularnewline
2 & 0.225 & 1.17946443932675 & 4.3 \tabularnewline
3 & 0.125 & 1.26930546506204 & 4.6 \tabularnewline
4 & 0.158333333333333 & 1.27383339379666 & 4.6 \tabularnewline
5 & 0.0833333333333333 & 1.34220533135402 & 4.9 \tabularnewline
6 & 0.15 & 1.33994572481670 & 4.4 \tabularnewline
7 & 0.108333333333333 & 1.49572623487621 & 5.5 \tabularnewline
8 & 0.133333333333333 & 1.53227895237088 & 5.6 \tabularnewline
9 & 0.2 & 1.54036595415741 & 5.6 \tabularnewline
10 & 0.133333333333333 & 1.72380832795156 & 6.5 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111242&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]0.15[/C][C]1.30279419989219[/C][C]4.6[/C][/ROW]
[ROW][C]2[/C][C]0.225[/C][C]1.17946443932675[/C][C]4.3[/C][/ROW]
[ROW][C]3[/C][C]0.125[/C][C]1.26930546506204[/C][C]4.6[/C][/ROW]
[ROW][C]4[/C][C]0.158333333333333[/C][C]1.27383339379666[/C][C]4.6[/C][/ROW]
[ROW][C]5[/C][C]0.0833333333333333[/C][C]1.34220533135402[/C][C]4.9[/C][/ROW]
[ROW][C]6[/C][C]0.15[/C][C]1.33994572481670[/C][C]4.4[/C][/ROW]
[ROW][C]7[/C][C]0.108333333333333[/C][C]1.49572623487621[/C][C]5.5[/C][/ROW]
[ROW][C]8[/C][C]0.133333333333333[/C][C]1.53227895237088[/C][C]5.6[/C][/ROW]
[ROW][C]9[/C][C]0.2[/C][C]1.54036595415741[/C][C]5.6[/C][/ROW]
[ROW][C]10[/C][C]0.133333333333333[/C][C]1.72380832795156[/C][C]6.5[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111242&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111242&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
10.151.302794199892194.6
20.2251.179464439326754.3
30.1251.269305465062044.6
40.1583333333333331.273833393796664.6
50.08333333333333331.342205331354024.9
60.151.339945724816704.4
70.1083333333333331.495726234876215.5
80.1333333333333331.532278952370885.6
90.21.540365954157415.6
100.1333333333333331.723808327951566.5






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha1.5428354605484
beta-0.974063578554262
S.D.1.37792664178094
T-STAT-0.70690525099022
p-value0.499694552010831

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.5428354605484 \tabularnewline
beta & -0.974063578554262 \tabularnewline
S.D. & 1.37792664178094 \tabularnewline
T-STAT & -0.70690525099022 \tabularnewline
p-value & 0.499694552010831 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111242&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.5428354605484[/C][/ROW]
[ROW][C]beta[/C][C]-0.974063578554262[/C][/ROW]
[ROW][C]S.D.[/C][C]1.37792664178094[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.70690525099022[/C][/ROW]
[ROW][C]p-value[/C][C]0.499694552010831[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111242&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111242&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)
alpha1.5428354605484
beta-0.974063578554262
S.D.1.37792664178094
T-STAT-0.70690525099022
p-value0.499694552010831






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha0.156473827151108
beta-0.0888874476641525
S.D.0.140845381640779
T-STAT-0.631099483906802
p-value0.545579715139345
Lambda1.08888744766415

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.156473827151108 \tabularnewline
beta & -0.0888874476641525 \tabularnewline
S.D. & 0.140845381640779 \tabularnewline
T-STAT & -0.631099483906802 \tabularnewline
p-value & 0.545579715139345 \tabularnewline
Lambda & 1.08888744766415 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111242&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.156473827151108[/C][/ROW]
[ROW][C]beta[/C][C]-0.0888874476641525[/C][/ROW]
[ROW][C]S.D.[/C][C]0.140845381640779[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.631099483906802[/C][/ROW]
[ROW][C]p-value[/C][C]0.545579715139345[/C][/ROW]
[ROW][C]Lambda[/C][C]1.08888744766415[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111242&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111242&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)
alpha0.156473827151108
beta-0.0888874476641525
S.D.0.140845381640779
T-STAT-0.631099483906802
p-value0.545579715139345
Lambda1.08888744766415


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')