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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, 03 Dec 2008 12:49:48 -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/03/t1228333821e2hhwqpoq7d7xan.htm/, Retrieved Fri, 17 May 2024 16:10:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28867, Retrieved Fri, 17 May 2024 16:10:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact185

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMPD    [Standard Deviation-Mean Plot] [T8 16] [2008-12-03 19:49:48] [fb0ffb935e9c1a725d69519be28b148f] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
33
34
44
38
37
30
35
32
32
37
27
28
27
38
32
38
33
36
40
36
38
33
30
34
33
31
39
41
34
41
37
37
39
37
32
44
48
39
52
39
40
55
39
37
41
46
39
43
41
44
52
49
57
55
41
49
52
47
44
57
57
50
60
49
53
55
46
47
50
52
41
46
47
42
51
41
40
50
41
45
37
55
42
37

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=28867&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=28867&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28867&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
133.91666666666674.718596350097317
234.58333333333333.8009169547583813
337.08333333333333.9876703915337813
443.16666666666675.8127341920888518
5495.7524698252932316
650.55.2829055366427819
7445.6889046716952818

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 33.9166666666667 & 4.7185963500973 & 17 \tabularnewline
2 & 34.5833333333333 & 3.80091695475838 & 13 \tabularnewline
3 & 37.0833333333333 & 3.98767039153378 & 13 \tabularnewline
4 & 43.1666666666667 & 5.81273419208885 & 18 \tabularnewline
5 & 49 & 5.75246982529323 & 16 \tabularnewline
6 & 50.5 & 5.28290553664278 & 19 \tabularnewline
7 & 44 & 5.68890467169528 & 18 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28867&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]33.9166666666667[/C][C]4.7185963500973[/C][C]17[/C][/ROW]
[ROW][C]2[/C][C]34.5833333333333[/C][C]3.80091695475838[/C][C]13[/C][/ROW]
[ROW][C]3[/C][C]37.0833333333333[/C][C]3.98767039153378[/C][C]13[/C][/ROW]
[ROW][C]4[/C][C]43.1666666666667[/C][C]5.81273419208885[/C][C]18[/C][/ROW]
[ROW][C]5[/C][C]49[/C][C]5.75246982529323[/C][C]16[/C][/ROW]
[ROW][C]6[/C][C]50.5[/C][C]5.28290553664278[/C][C]19[/C][/ROW]
[ROW][C]7[/C][C]44[/C][C]5.68890467169528[/C][C]18[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28867&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28867&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
133.91666666666674.718596350097317
234.58333333333333.8009169547583813
337.08333333333333.9876703915337813
443.16666666666675.8127341920888518
5495.7524698252932316
650.55.2829055366427819
7445.6889046716952818






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.97247474543722
beta0.096618904034385
S.D.0.0364264433204783
T-STAT2.65243859205073
p-value0.0452934781361247

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.97247474543722 \tabularnewline
beta & 0.096618904034385 \tabularnewline
S.D. & 0.0364264433204783 \tabularnewline
T-STAT & 2.65243859205073 \tabularnewline
p-value & 0.0452934781361247 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28867&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.97247474543722[/C][/ROW]
[ROW][C]beta[/C][C]0.096618904034385[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0364264433204783[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.65243859205073[/C][/ROW]
[ROW][C]p-value[/C][C]0.0452934781361247[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28867&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28867&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)
alpha0.97247474543722
beta0.096618904034385
S.D.0.0364264433204783
T-STAT2.65243859205073
p-value0.0452934781361247






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.57384292635539
beta0.852402231353707
S.D.0.311231203443416
T-STAT2.73880710520942
p-value0.0408499632356267
Lambda0.147597768646293

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.57384292635539 \tabularnewline
beta & 0.852402231353707 \tabularnewline
S.D. & 0.311231203443416 \tabularnewline
T-STAT & 2.73880710520942 \tabularnewline
p-value & 0.0408499632356267 \tabularnewline
Lambda & 0.147597768646293 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28867&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.57384292635539[/C][/ROW]
[ROW][C]beta[/C][C]0.852402231353707[/C][/ROW]
[ROW][C]S.D.[/C][C]0.311231203443416[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.73880710520942[/C][/ROW]
[ROW][C]p-value[/C][C]0.0408499632356267[/C][/ROW]
[ROW][C]Lambda[/C][C]0.147597768646293[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28867&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28867&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-1.57384292635539
beta0.852402231353707
S.D.0.311231203443416
T-STAT2.73880710520942
p-value0.0408499632356267
Lambda0.147597768646293


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')