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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 computationSat, 04 Dec 2010 10:17:50 +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/2010/Dec/04/t1291457769g9ngar5mpvovtk5.htm/, Retrieved Sun, 05 May 2024 08:31:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=105072, Retrieved Sun, 05 May 2024 08:31:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W83
Estimated Impact154

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] [Opgave 8 Stap 5] [2010-12-04 10:17:50] [cf38f7df7be58a8c28b053c2e6c1601e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
361.58
363.19
363.61
364.14
365.51
365.51
365.5
365.5
364.59
364.63
364.54
363.67
365.22
369.05
370.45
370.46
370.46
370.58
370.58
370.22
370.21
370.29
370.29
370.2
370.2
372.55
374.51
375.58
375.75
375.75
375.75
375.69
375.76
377.5
377.51
377.74
369.82
373.1
374.55
375.01
374.81
375.31
375.31
375.39
375.59
376.26
377.18
377.26
377.26
381.87
387.09
387.14
388.78
389.16
389.16
389.42
389.49
388.97
388.97
389.09
389.09
391.76
390.96
391.76
392.8
393.06
393.06
393.26
393.87
394.47
394.57
394.57
394.57
399.57
406.13
407.03
409.46
409.9
409.9
410.14
410.54
410.69
410.79
410.97

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=105072&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=105072&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105072&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
1364.3308333333331.189976763205783.93000000000001
2369.8341666666671.508162387768235.35999999999996
3375.35752.150776286916817.54000000000002
4374.9658333333331.972702153868847.44
5387.23.7829545932439512.2300000000000
6392.7691666666671.647253683246675.48000000000002
7407.4741666666675.1941706107263516.4000000000000

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 364.330833333333 & 1.18997676320578 & 3.93000000000001 \tabularnewline
2 & 369.834166666667 & 1.50816238776823 & 5.35999999999996 \tabularnewline
3 & 375.3575 & 2.15077628691681 & 7.54000000000002 \tabularnewline
4 & 374.965833333333 & 1.97270215386884 & 7.44 \tabularnewline
5 & 387.2 & 3.78295459324395 & 12.2300000000000 \tabularnewline
6 & 392.769166666667 & 1.64725368324667 & 5.48000000000002 \tabularnewline
7 & 407.474166666667 & 5.19417061072635 & 16.4000000000000 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105072&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]364.330833333333[/C][C]1.18997676320578[/C][C]3.93000000000001[/C][/ROW]
[ROW][C]2[/C][C]369.834166666667[/C][C]1.50816238776823[/C][C]5.35999999999996[/C][/ROW]
[ROW][C]3[/C][C]375.3575[/C][C]2.15077628691681[/C][C]7.54000000000002[/C][/ROW]
[ROW][C]4[/C][C]374.965833333333[/C][C]1.97270215386884[/C][C]7.44[/C][/ROW]
[ROW][C]5[/C][C]387.2[/C][C]3.78295459324395[/C][C]12.2300000000000[/C][/ROW]
[ROW][C]6[/C][C]392.769166666667[/C][C]1.64725368324667[/C][C]5.48000000000002[/C][/ROW]
[ROW][C]7[/C][C]407.474166666667[/C][C]5.19417061072635[/C][C]16.4000000000000[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105072&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105072&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
1364.3308333333331.189976763205783.93000000000001
2369.8341666666671.508162387768235.35999999999996
3375.35752.150776286916817.54000000000002
4374.9658333333331.972702153868847.44
5387.23.7829545932439512.2300000000000
6392.7691666666671.647253683246675.48000000000002
7407.4741666666675.1941706107263516.4000000000000






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-27.9687264445374
beta0.079802595347338
S.D.0.0248840744593794
T-STAT3.20697462457794
p-value0.0238089965500525

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -27.9687264445374 \tabularnewline
beta & 0.079802595347338 \tabularnewline
S.D. & 0.0248840744593794 \tabularnewline
T-STAT & 3.20697462457794 \tabularnewline
p-value & 0.0238089965500525 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105072&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-27.9687264445374[/C][/ROW]
[ROW][C]beta[/C][C]0.079802595347338[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0248840744593794[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.20697462457794[/C][/ROW]
[ROW][C]p-value[/C][C]0.0238089965500525[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105072&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105072&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-27.9687264445374
beta0.079802595347338
S.D.0.0248840744593794
T-STAT3.20697462457794
p-value0.0238089965500525






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-63.871685581071
beta10.8779397256105
S.D.3.57021281620253
T-STAT3.04686030934730
p-value0.0285263627609211
Lambda-9.87793972561053

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -63.871685581071 \tabularnewline
beta & 10.8779397256105 \tabularnewline
S.D. & 3.57021281620253 \tabularnewline
T-STAT & 3.04686030934730 \tabularnewline
p-value & 0.0285263627609211 \tabularnewline
Lambda & -9.87793972561053 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105072&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-63.871685581071[/C][/ROW]
[ROW][C]beta[/C][C]10.8779397256105[/C][/ROW]
[ROW][C]S.D.[/C][C]3.57021281620253[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.04686030934730[/C][/ROW]
[ROW][C]p-value[/C][C]0.0285263627609211[/C][/ROW]
[ROW][C]Lambda[/C][C]-9.87793972561053[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105072&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105072&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-63.871685581071
beta10.8779397256105
S.D.3.57021281620253
T-STAT3.04686030934730
p-value0.0285263627609211
Lambda-9.87793972561053


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')