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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 computationThu, 28 May 2009 13:22:03 -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/28/t1243538634ifuos8ytzwv1e4x.htm/, Retrieved Mon, 06 May 2024 01:29:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=40701, Retrieved Mon, 06 May 2024 01:29:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact123

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] [Standard Deviatio...] [2009-05-28 19:22:03] [508db52847fe44fb658c0de5bd3816a5] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
20.73
20.73
20.74
20.74
20.75
20.75
20.77
20.78
20.78
20.8
20.84
20.85
20.86
20.86
20.86
20.86
20.9
20.92
20.95
20.95
20.95
20.96
21.1
21.18
21.19
21.19
21.19
21.19
21.19
21.21
21.22
21.22
21.22
21.23
21.41
21.42
21.43
21.44
21.44
21.44
21.48
21.53
21.54
21.54
21.54
21.54
21.54
21.54
21.54
21.54
21.54
21.54
21.57
21.6
21.61
21.6
21.6
21.71
21.75
21.84
21.85
21.92
21.92
21.93
22
22
21.99
22.01
22.01
22.06
22.03
22.05
22.05
22.06
22.06
22.13
22.06
22.25
22.28
22.18

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=40701&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=40701&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40701&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
120.77166666666670.04063883796954820.120000000000001
220.94583333333330.1004949870602630.32
321.240.08312094145936340.230000000000000
421.50.04917501213199390.109999999999999
521.620.09667189118587980.300000000000001
621.98083333333330.06258933010045870.209999999999997

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 20.7716666666667 & 0.0406388379695482 & 0.120000000000001 \tabularnewline
2 & 20.9458333333333 & 0.100494987060263 & 0.32 \tabularnewline
3 & 21.24 & 0.0831209414593634 & 0.230000000000000 \tabularnewline
4 & 21.5 & 0.0491750121319939 & 0.109999999999999 \tabularnewline
5 & 21.62 & 0.0966718911858798 & 0.300000000000001 \tabularnewline
6 & 21.9808333333333 & 0.0625893301004587 & 0.209999999999997 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40701&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]20.7716666666667[/C][C]0.0406388379695482[/C][C]0.120000000000001[/C][/ROW]
[ROW][C]2[/C][C]20.9458333333333[/C][C]0.100494987060263[/C][C]0.32[/C][/ROW]
[ROW][C]3[/C][C]21.24[/C][C]0.0831209414593634[/C][C]0.230000000000000[/C][/ROW]
[ROW][C]4[/C][C]21.5[/C][C]0.0491750121319939[/C][C]0.109999999999999[/C][/ROW]
[ROW][C]5[/C][C]21.62[/C][C]0.0966718911858798[/C][C]0.300000000000001[/C][/ROW]
[ROW][C]6[/C][C]21.9808333333333[/C][C]0.0625893301004587[/C][C]0.209999999999997[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40701&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40701&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
120.77166666666670.04063883796954820.120000000000001
220.94583333333330.1004949870602630.32
321.240.08312094145936340.230000000000000
421.50.04917501213199390.109999999999999
521.620.09667189118587980.300000000000001
621.98083333333330.06258933010045870.209999999999997






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.0145947898282921
beta0.00269503945549102
S.D.0.0279317749792997
T-STAT0.0964865089128179
p-value0.927775128565487

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.0145947898282921 \tabularnewline
beta & 0.00269503945549102 \tabularnewline
S.D. & 0.0279317749792997 \tabularnewline
T-STAT & 0.0964865089128179 \tabularnewline
p-value & 0.927775128565487 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40701&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.0145947898282921[/C][/ROW]
[ROW][C]beta[/C][C]0.00269503945549102[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0279317749792997[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.0964865089128179[/C][/ROW]
[ROW][C]p-value[/C][C]0.927775128565487[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40701&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40701&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)
alpha0.0145947898282921
beta0.00269503945549102
S.D.0.0279317749792997
T-STAT0.0964865089128179
p-value0.927775128565487






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-10.1754441870683
beta2.44752669966689
S.D.8.79383000211787
T-STAT0.278323176485949
p-value0.794559254285853
Lambda-1.44752669966689

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -10.1754441870683 \tabularnewline
beta & 2.44752669966689 \tabularnewline
S.D. & 8.79383000211787 \tabularnewline
T-STAT & 0.278323176485949 \tabularnewline
p-value & 0.794559254285853 \tabularnewline
Lambda & -1.44752669966689 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40701&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-10.1754441870683[/C][/ROW]
[ROW][C]beta[/C][C]2.44752669966689[/C][/ROW]
[ROW][C]S.D.[/C][C]8.79383000211787[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.278323176485949[/C][/ROW]
[ROW][C]p-value[/C][C]0.794559254285853[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.44752669966689[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40701&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40701&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-10.1754441870683
beta2.44752669966689
S.D.8.79383000211787
T-STAT0.278323176485949
p-value0.794559254285853
Lambda-1.44752669966689


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')