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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 computationMon, 12 May 2008 05:49:18 -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/2008/May/12/t1210593005hxbic60qoen78qb.htm/, Retrieved Tue, 14 May 2024 02:35:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=12337, Retrieved Tue, 14 May 2024 02:35:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact186

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] [Elke Van Buggenho...] [2008-05-12 11:49:18] [ef244335fc0c3f0884149746f4e30bed] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
10.893
10.756
10.940
10.997
10.827
10.166
10.186
10.457
10.368
10.244
10.511
10.812
10.738
10.171
9.721
9.897
9.828
9.924
10.371
10.846
10.413
10.709
10.662
10.570
10.297
10.635
10.872
10.296
10.383
10.431
10.574
10.653
10.805
10.872
10.625
10.407
10.463
10.556
10.646
10.702
11.353
11.346
11.451
11.964
12.574
13.031
13.812
14.544
14.931
14.886
16.005
17.064
15.168
16.050
15.839
15.137
14.954
15.648
15.305
15.579
16.348
15.928
16.171
15.937
15.713
15.594
15.683
16.438
17.032
17.696
17.745
19.394

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12337&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]3 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=12337&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12337&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
110.59641666666670.3087209561851590.831
210.32083333333330.3991169419272171.125
310.57083333333330.2093808332520750.576
411.87016666666671.350423626014064.081
515.54716666666670.6323751523686982.178
616.63991666666671.139809270993363.8

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 10.5964166666667 & 0.308720956185159 & 0.831 \tabularnewline
2 & 10.3208333333333 & 0.399116941927217 & 1.125 \tabularnewline
3 & 10.5708333333333 & 0.209380833252075 & 0.576 \tabularnewline
4 & 11.8701666666667 & 1.35042362601406 & 4.081 \tabularnewline
5 & 15.5471666666667 & 0.632375152368698 & 2.178 \tabularnewline
6 & 16.6399166666667 & 1.13980927099336 & 3.8 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12337&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]10.5964166666667[/C][C]0.308720956185159[/C][C]0.831[/C][/ROW]
[ROW][C]2[/C][C]10.3208333333333[/C][C]0.399116941927217[/C][C]1.125[/C][/ROW]
[ROW][C]3[/C][C]10.5708333333333[/C][C]0.209380833252075[/C][C]0.576[/C][/ROW]
[ROW][C]4[/C][C]11.8701666666667[/C][C]1.35042362601406[/C][C]4.081[/C][/ROW]
[ROW][C]5[/C][C]15.5471666666667[/C][C]0.632375152368698[/C][C]2.178[/C][/ROW]
[ROW][C]6[/C][C]16.6399166666667[/C][C]1.13980927099336[/C][C]3.8[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12337&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12337&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
110.59641666666670.3087209561851590.831
210.32083333333330.3991169419272171.125
310.57083333333330.2093808332520750.576
411.87016666666671.350423626014064.081
515.54716666666670.6323751523686982.178
616.63991666666671.139809270993363.8






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.482138551726106
beta0.0917681845483138
S.D.0.0705517581428492
T-STAT1.30072144144880
p-value0.263227490873514

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.482138551726106 \tabularnewline
beta & 0.0917681845483138 \tabularnewline
S.D. & 0.0705517581428492 \tabularnewline
T-STAT & 1.30072144144880 \tabularnewline
p-value & 0.263227490873514 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12337&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.482138551726106[/C][/ROW]
[ROW][C]beta[/C][C]0.0917681845483138[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0705517581428492[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.30072144144880[/C][/ROW]
[ROW][C]p-value[/C][C]0.263227490873514[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12337&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12337&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-0.482138551726106
beta0.0917681845483138
S.D.0.0705517581428492
T-STAT1.30072144144880
p-value0.263227490873514






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-6.35475639296075
beta2.28371615603772
S.D.1.32147200816386
T-STAT1.72816082514746
p-value0.159024293604263
Lambda-1.28371615603772

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -6.35475639296075 \tabularnewline
beta & 2.28371615603772 \tabularnewline
S.D. & 1.32147200816386 \tabularnewline
T-STAT & 1.72816082514746 \tabularnewline
p-value & 0.159024293604263 \tabularnewline
Lambda & -1.28371615603772 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12337&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-6.35475639296075[/C][/ROW]
[ROW][C]beta[/C][C]2.28371615603772[/C][/ROW]
[ROW][C]S.D.[/C][C]1.32147200816386[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.72816082514746[/C][/ROW]
[ROW][C]p-value[/C][C]0.159024293604263[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.28371615603772[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12337&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12337&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-6.35475639296075
beta2.28371615603772
S.D.1.32147200816386
T-STAT1.72816082514746
p-value0.159024293604263
Lambda-1.28371615603772


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')