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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 computationFri, 27 Nov 2009 06:27:15 -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/2009/Nov/27/t1259328467g8imvxul869cqgj.htm/, Retrieved Mon, 29 Apr 2024 20:14:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=60734, Retrieved Mon, 29 Apr 2024 20:14:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact125

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Standard Deviation-Mean Plot] [Identifying Integ...] [2009-11-22 12:50:05] [b98453cac15ba1066b407e146608df68]
-   PD          [Standard Deviation-Mean Plot] [Workshop 8] [2009-11-27 13:27:15] [0bdf648420800d03e6dbfbd39fe2311c] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
62
64
62
64
64
69
69
65
56
58
53
62
55
60
59
58
53
57
57
53
54
53
57
57
55
49
50
49
54
58
58
52
56
52
59
53
52
53
51
50
56
52
46
48
46
48
48
49
53
48
51
48
50
55
52
53
52
55
53
53
56
54
52
55
54
59
56
56
51
53
52
51
46
49
46
55
57
53
52
53
50
54
53
50
51
52
47
51
49
53
52
45
53
51
48
48
48
48
40
43
40
39
39
36
41
39
40
39
46
40
37
37
44
41
40
36
38
43
42
45
46

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=60734&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=60734&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60734&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
162.33333333333334.7736651315188416
256.08333333333332.429303429280747
353.753.5194266061907910
449.91666666666672.9987371079213110
551.91666666666672.314316444667977
654.08333333333332.429303429280748
751.53.3978602892783211
8502.558408596267338
9413.6431754380934312
1040.753.3337120996925310

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 62.3333333333333 & 4.77366513151884 & 16 \tabularnewline
2 & 56.0833333333333 & 2.42930342928074 & 7 \tabularnewline
3 & 53.75 & 3.51942660619079 & 10 \tabularnewline
4 & 49.9166666666667 & 2.99873710792131 & 10 \tabularnewline
5 & 51.9166666666667 & 2.31431644466797 & 7 \tabularnewline
6 & 54.0833333333333 & 2.42930342928074 & 8 \tabularnewline
7 & 51.5 & 3.39786028927832 & 11 \tabularnewline
8 & 50 & 2.55840859626733 & 8 \tabularnewline
9 & 41 & 3.64317543809343 & 12 \tabularnewline
10 & 40.75 & 3.33371209969253 & 10 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60734&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]62.3333333333333[/C][C]4.77366513151884[/C][C]16[/C][/ROW]
[ROW][C]2[/C][C]56.0833333333333[/C][C]2.42930342928074[/C][C]7[/C][/ROW]
[ROW][C]3[/C][C]53.75[/C][C]3.51942660619079[/C][C]10[/C][/ROW]
[ROW][C]4[/C][C]49.9166666666667[/C][C]2.99873710792131[/C][C]10[/C][/ROW]
[ROW][C]5[/C][C]51.9166666666667[/C][C]2.31431644466797[/C][C]7[/C][/ROW]
[ROW][C]6[/C][C]54.0833333333333[/C][C]2.42930342928074[/C][C]8[/C][/ROW]
[ROW][C]7[/C][C]51.5[/C][C]3.39786028927832[/C][C]11[/C][/ROW]
[ROW][C]8[/C][C]50[/C][C]2.55840859626733[/C][C]8[/C][/ROW]
[ROW][C]9[/C][C]41[/C][C]3.64317543809343[/C][C]12[/C][/ROW]
[ROW][C]10[/C][C]40.75[/C][C]3.33371209969253[/C][C]10[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60734&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60734&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
162.33333333333334.7736651315188416
256.08333333333332.429303429280747
353.753.5194266061907910
449.91666666666672.9987371079213110
551.91666666666672.314316444667977
654.08333333333332.429303429280748
751.53.3978602892783211
8502.558408596267338
9413.6431754380934312
1040.753.3337120996925310






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha2.21765572211708
beta0.0180339335417624
S.D.0.0409726272990935
T-STAT0.440145890819195
p-value0.671480856242339

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 2.21765572211708 \tabularnewline
beta & 0.0180339335417624 \tabularnewline
S.D. & 0.0409726272990935 \tabularnewline
T-STAT & 0.440145890819195 \tabularnewline
p-value & 0.671480856242339 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60734&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.21765572211708[/C][/ROW]
[ROW][C]beta[/C][C]0.0180339335417624[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0409726272990935[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.440145890819195[/C][/ROW]
[ROW][C]p-value[/C][C]0.671480856242339[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60734&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60734&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)
alpha2.21765572211708
beta0.0180339335417624
S.D.0.0409726272990935
T-STAT0.440145890819195
p-value0.671480856242339






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha1.02064807258745
beta0.0251323974152459
S.D.0.625107933508044
T-STAT0.0402048927362118
p-value0.968915035666735
Lambda0.974867602584754

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.02064807258745 \tabularnewline
beta & 0.0251323974152459 \tabularnewline
S.D. & 0.625107933508044 \tabularnewline
T-STAT & 0.0402048927362118 \tabularnewline
p-value & 0.968915035666735 \tabularnewline
Lambda & 0.974867602584754 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60734&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.02064807258745[/C][/ROW]
[ROW][C]beta[/C][C]0.0251323974152459[/C][/ROW]
[ROW][C]S.D.[/C][C]0.625107933508044[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.0402048927362118[/C][/ROW]
[ROW][C]p-value[/C][C]0.968915035666735[/C][/ROW]
[ROW][C]Lambda[/C][C]0.974867602584754[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60734&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60734&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)
alpha1.02064807258745
beta0.0251323974152459
S.D.0.625107933508044
T-STAT0.0402048927362118
p-value0.968915035666735
Lambda0.974867602584754


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 2 ; par3 = 0 ; par4 = 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')