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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, 11 Mar 2015 21:59:06 +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/2015/Mar/11/t1426111183wu1w9fhm4eulwef.htm/, Retrieved Sun, 19 May 2024 14:05:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278222, Retrieved Sun, 19 May 2024 14:05:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact126

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] [] [2015-03-11 21:59:06] [c6da619eabbd864125b02146bc2bbd84] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
35
37
34
33
33
34
34
34
36
37
39
38
35
38
33
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35
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34
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35
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35
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34
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35
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42
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35
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35
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40
36
37
33
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33
37
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39
40
36
38
33
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34
33
38
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37
39
33
34
33
35
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35
38
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40
37
38
34
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34
34
34
33
36
38
40
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37
37
33
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34
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36
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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 Maurice George Kendall' @ kendall.wessa.net

\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 Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278222&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 Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278222&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278222&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 Maurice George Kendall' @ kendall.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
135.33333333333332.015094553763196
235.41666666666672.429303429280747
336.16666666666672.167249338901666
436.752.734460225944558
5372.335496832484576
635.41666666666672.745519766433818
736.16666666666673.099364548751998
836.58333333333332.778434265858568
935.83333333333332.480224818744297

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 35.3333333333333 & 2.01509455376319 & 6 \tabularnewline
2 & 35.4166666666667 & 2.42930342928074 & 7 \tabularnewline
3 & 36.1666666666667 & 2.16724933890166 & 6 \tabularnewline
4 & 36.75 & 2.73446022594455 & 8 \tabularnewline
5 & 37 & 2.33549683248457 & 6 \tabularnewline
6 & 35.4166666666667 & 2.74551976643381 & 8 \tabularnewline
7 & 36.1666666666667 & 3.09936454875199 & 8 \tabularnewline
8 & 36.5833333333333 & 2.77843426585856 & 8 \tabularnewline
9 & 35.8333333333333 & 2.48022481874429 & 7 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278222&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]35.3333333333333[/C][C]2.01509455376319[/C][C]6[/C][/ROW]
[ROW][C]2[/C][C]35.4166666666667[/C][C]2.42930342928074[/C][C]7[/C][/ROW]
[ROW][C]3[/C][C]36.1666666666667[/C][C]2.16724933890166[/C][C]6[/C][/ROW]
[ROW][C]4[/C][C]36.75[/C][C]2.73446022594455[/C][C]8[/C][/ROW]
[ROW][C]5[/C][C]37[/C][C]2.33549683248457[/C][C]6[/C][/ROW]
[ROW][C]6[/C][C]35.4166666666667[/C][C]2.74551976643381[/C][C]8[/C][/ROW]
[ROW][C]7[/C][C]36.1666666666667[/C][C]3.09936454875199[/C][C]8[/C][/ROW]
[ROW][C]8[/C][C]36.5833333333333[/C][C]2.77843426585856[/C][C]8[/C][/ROW]
[ROW][C]9[/C][C]35.8333333333333[/C][C]2.48022481874429[/C][C]7[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278222&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278222&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
135.33333333333332.015094553763196
235.41666666666672.429303429280747
336.16666666666672.167249338901666
436.752.734460225944558
5372.335496832484576
635.41666666666672.745519766433818
736.16666666666673.099364548751998
836.58333333333332.778434265858568
935.83333333333332.480224818744297






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-2.4364420411538
beta0.137720101079715
S.D.0.200690774111361
T-STAT0.686230354581702
p-value0.514647605455875

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -2.4364420411538 \tabularnewline
beta & 0.137720101079715 \tabularnewline
S.D. & 0.200690774111361 \tabularnewline
T-STAT & 0.686230354581702 \tabularnewline
p-value & 0.514647605455875 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278222&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.4364420411538[/C][/ROW]
[ROW][C]beta[/C][C]0.137720101079715[/C][/ROW]
[ROW][C]S.D.[/C][C]0.200690774111361[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.686230354581702[/C][/ROW]
[ROW][C]p-value[/C][C]0.514647605455875[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278222&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278222&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-2.4364420411538
beta0.137720101079715
S.D.0.200690774111361
T-STAT0.686230354581702
p-value0.514647605455875






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-6.6234008164783
beta2.10412191747534
S.D.2.87620185172083
T-STAT0.731562673953652
p-value0.488196968423594
Lambda-1.10412191747534

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -6.6234008164783 \tabularnewline
beta & 2.10412191747534 \tabularnewline
S.D. & 2.87620185172083 \tabularnewline
T-STAT & 0.731562673953652 \tabularnewline
p-value & 0.488196968423594 \tabularnewline
Lambda & -1.10412191747534 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278222&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-6.6234008164783[/C][/ROW]
[ROW][C]beta[/C][C]2.10412191747534[/C][/ROW]
[ROW][C]S.D.[/C][C]2.87620185172083[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.731562673953652[/C][/ROW]
[ROW][C]p-value[/C][C]0.488196968423594[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.10412191747534[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278222&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278222&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-6.6234008164783
beta2.10412191747534
S.D.2.87620185172083
T-STAT0.731562673953652
p-value0.488196968423594
Lambda-1.10412191747534


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')