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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 computationTue, 25 May 2010 15:42:36 +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/May/25/t1274802230w5lpu2pjs3wm3p8.htm/, Retrieved Wed, 01 May 2024 23:59:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=76413, Retrieved Wed, 01 May 2024 23:59:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W81
Estimated Impact153

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...] [2010-05-25 15:42:36] [a99e434d1cfd87bdfab8a9b2b38ccb03] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2851
2672
2755
2721
2946
3036
2282
2212
2922
4301
5764
7132
2541
2475
3031
3266
3776
3230
3028
1759
3595
4474
6838
8357
3113
3006
4047
3523
3937
3986
3260
1573
3528
5211
7614
9254
5375
3088
3718
4514
4520
4539
3663
1643
4739
5428
8314
10651
3633
4292
4154
4121
4647
4753
3965
1723
5048
6922
9858
11331
4016
3975
4510
4276
4968
4677
3523
1821
5222
6873
10803
13916
2639
2899
3370
3740
2927
3986
4217
1738
5221
6424
9842
13076
3934
3162
4286
4676
5010
4874
4633
1659
5951
6981
9851
12670

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'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76413&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76413&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76413&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'RServer@AstonUniversity' @ vre.aston.ac.uk






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
13466.166666666671513.947269006864920
23864.166666666671900.883757783756598
34337.666666666672119.889119455997681
450162380.616001259879008
55370.583333333332723.367082336049608
657153381.3480098381412095
75006.583333333333324.2239957984811338
85640.583333333332995.5727471275611011

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 3466.16666666667 & 1513.94726900686 & 4920 \tabularnewline
2 & 3864.16666666667 & 1900.88375778375 & 6598 \tabularnewline
3 & 4337.66666666667 & 2119.88911945599 & 7681 \tabularnewline
4 & 5016 & 2380.61600125987 & 9008 \tabularnewline
5 & 5370.58333333333 & 2723.36708233604 & 9608 \tabularnewline
6 & 5715 & 3381.34800983814 & 12095 \tabularnewline
7 & 5006.58333333333 & 3324.22399579848 & 11338 \tabularnewline
8 & 5640.58333333333 & 2995.57274712756 & 11011 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76413&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]3466.16666666667[/C][C]1513.94726900686[/C][C]4920[/C][/ROW]
[ROW][C]2[/C][C]3864.16666666667[/C][C]1900.88375778375[/C][C]6598[/C][/ROW]
[ROW][C]3[/C][C]4337.66666666667[/C][C]2119.88911945599[/C][C]7681[/C][/ROW]
[ROW][C]4[/C][C]5016[/C][C]2380.61600125987[/C][C]9008[/C][/ROW]
[ROW][C]5[/C][C]5370.58333333333[/C][C]2723.36708233604[/C][C]9608[/C][/ROW]
[ROW][C]6[/C][C]5715[/C][C]3381.34800983814[/C][C]12095[/C][/ROW]
[ROW][C]7[/C][C]5006.58333333333[/C][C]3324.22399579848[/C][C]11338[/C][/ROW]
[ROW][C]8[/C][C]5640.58333333333[/C][C]2995.57274712756[/C][C]11011[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76413&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76413&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
13466.166666666671513.947269006864920
23864.166666666671900.883757783756598
34337.666666666672119.889119455997681
450162380.616001259879008
55370.583333333332723.367082336049608
657153381.3480098381412095
75006.583333333333324.2239957984811338
85640.583333333332995.5727471275611011






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-984.858834068418
beta0.734542059262015
S.D.0.146609109906723
T-STAT5.01020748116779
p-value0.00242756134456555

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -984.858834068418 \tabularnewline
beta & 0.734542059262015 \tabularnewline
S.D. & 0.146609109906723 \tabularnewline
T-STAT & 5.01020748116779 \tabularnewline
p-value & 0.00242756134456555 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76413&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-984.858834068418[/C][/ROW]
[ROW][C]beta[/C][C]0.734542059262015[/C][/ROW]
[ROW][C]S.D.[/C][C]0.146609109906723[/C][/ROW]
[ROW][C]T-STAT[/C][C]5.01020748116779[/C][/ROW]
[ROW][C]p-value[/C][C]0.00242756134456555[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76413&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76413&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-984.858834068418
beta0.734542059262015
S.D.0.146609109906723
T-STAT5.01020748116779
p-value0.00242756134456555






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-4.41776493302761
beta1.44455182102591
S.D.0.233558174458706
T-STAT6.18497650263711
p-value0.000821997381942209
Lambda-0.444551821025914

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -4.41776493302761 \tabularnewline
beta & 1.44455182102591 \tabularnewline
S.D. & 0.233558174458706 \tabularnewline
T-STAT & 6.18497650263711 \tabularnewline
p-value & 0.000821997381942209 \tabularnewline
Lambda & -0.444551821025914 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76413&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.41776493302761[/C][/ROW]
[ROW][C]beta[/C][C]1.44455182102591[/C][/ROW]
[ROW][C]S.D.[/C][C]0.233558174458706[/C][/ROW]
[ROW][C]T-STAT[/C][C]6.18497650263711[/C][/ROW]
[ROW][C]p-value[/C][C]0.000821997381942209[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.444551821025914[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76413&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76413&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-4.41776493302761
beta1.44455182102591
S.D.0.233558174458706
T-STAT6.18497650263711
p-value0.000821997381942209
Lambda-0.444551821025914


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')