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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 computationTue, 26 May 2009 06:13:52 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/May/26/t1243340083f3ihegtfzvp4g2d.htm/, Retrieved Sat, 04 May 2024 06:44:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=40363, Retrieved Sat, 04 May 2024 06:44:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact139

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] [cijferreeks - aan...] [2009-05-26 12:13:52] [10386bb3a6f73220c058f8d03d2f31cb] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
53
59
73
72
62
58
55
56
52
52
43
37
43
55
68
68
64
65
57
59
54
57
43
42
52
51
58
60
61
58
62
61
49
51
47
40
45
50
58
52
50
50
46
46
38
37
34
29
30
40
46
46
47
47
43
46
37
41
39
36
48
55
56
53
52
53
52
56
51
48
42
42
44
50
60
66
58
59
55
57
57
56
53
51
45
58
74
65
65
55
52
59
54
57
45
40
47
47
60
58
63
64
64
63
55
54
44

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'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40363&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40363&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40363&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'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
15610.29563014098736
256.259.4496272172744826
354.16666666666676.8865261506976422
444.58333333333338.4364828230870329
541.55.3512955100950717
650.66666666666674.8116021397778914
755.55.5840682465222622
855.759.6212359818363234

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 56 & 10.295630140987 & 36 \tabularnewline
2 & 56.25 & 9.44962721727448 & 26 \tabularnewline
3 & 54.1666666666667 & 6.88652615069764 & 22 \tabularnewline
4 & 44.5833333333333 & 8.43648282308703 & 29 \tabularnewline
5 & 41.5 & 5.35129551009507 & 17 \tabularnewline
6 & 50.6666666666667 & 4.81160213977789 & 14 \tabularnewline
7 & 55.5 & 5.58406824652226 & 22 \tabularnewline
8 & 55.75 & 9.62123598183632 & 34 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40363&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]56[/C][C]10.295630140987[/C][C]36[/C][/ROW]
[ROW][C]2[/C][C]56.25[/C][C]9.44962721727448[/C][C]26[/C][/ROW]
[ROW][C]3[/C][C]54.1666666666667[/C][C]6.88652615069764[/C][C]22[/C][/ROW]
[ROW][C]4[/C][C]44.5833333333333[/C][C]8.43648282308703[/C][C]29[/C][/ROW]
[ROW][C]5[/C][C]41.5[/C][C]5.35129551009507[/C][C]17[/C][/ROW]
[ROW][C]6[/C][C]50.6666666666667[/C][C]4.81160213977789[/C][C]14[/C][/ROW]
[ROW][C]7[/C][C]55.5[/C][C]5.58406824652226[/C][C]22[/C][/ROW]
[ROW][C]8[/C][C]55.75[/C][C]9.62123598183632[/C][C]34[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40363&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40363&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
15610.29563014098736
256.259.4496272172744826
354.16666666666676.8865261506976422
444.58333333333338.4364828230870329
541.55.3512955100950717
650.66666666666674.8116021397778914
755.55.5840682465222622
855.759.6212359818363234






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-1.08874265765091
beta0.166852385613879
S.D.0.137798332924188
T-STAT1.21084473282907
p-value0.271481119098057

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -1.08874265765091 \tabularnewline
beta & 0.166852385613879 \tabularnewline
S.D. & 0.137798332924188 \tabularnewline
T-STAT & 1.21084473282907 \tabularnewline
p-value & 0.271481119098057 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40363&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.08874265765091[/C][/ROW]
[ROW][C]beta[/C][C]0.166852385613879[/C][/ROW]
[ROW][C]S.D.[/C][C]0.137798332924188[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.21084473282907[/C][/ROW]
[ROW][C]p-value[/C][C]0.271481119098057[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40363&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40363&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-1.08874265765091
beta0.166852385613879
S.D.0.137798332924188
T-STAT1.21084473282907
p-value0.271481119098057






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.22395800417908
beta1.06757865607969
S.D.0.942812365080304
T-STAT1.13233416915227
p-value0.300707683230220
Lambda-0.0675786560796929

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.22395800417908 \tabularnewline
beta & 1.06757865607969 \tabularnewline
S.D. & 0.942812365080304 \tabularnewline
T-STAT & 1.13233416915227 \tabularnewline
p-value & 0.300707683230220 \tabularnewline
Lambda & -0.0675786560796929 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40363&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.22395800417908[/C][/ROW]
[ROW][C]beta[/C][C]1.06757865607969[/C][/ROW]
[ROW][C]S.D.[/C][C]0.942812365080304[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.13233416915227[/C][/ROW]
[ROW][C]p-value[/C][C]0.300707683230220[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.0675786560796929[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40363&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40363&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-2.22395800417908
beta1.06757865607969
S.D.0.942812365080304
T-STAT1.13233416915227
p-value0.300707683230220
Lambda-0.0675786560796929


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')