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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, 26 Jan 2010 17:48:11 -0700
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/Jan/27/t1264553326xf1xvy9tap37v5a.htm/, Retrieved Mon, 06 May 2024 05:55:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72683, Retrieved Mon, 06 May 2024 05:55:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W83
Estimated Impact185

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] [] [2010-01-27 00:48:11] [93f7fd88d04bfc03ecae616214d88989] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2.46
2.46
2.45
2.45
2.46
2.43
2.44
2.44
2.43
2.43
2.42
2.43
2.43
2.42
2.41
2.42
2.39
2.4
2.39
2.4
2.41
2.41
2.41
2.41
2.42
2.43
2.43
2.43
2.44
2.42
2.44
2.42
2.42
2.42
2.43
2.44
2.43
2.44
2.44
2.45
2.45
2.43
2.44
2.45
2.46
2.44
2.43
2.42
2.41
2.43
2.41
2.43
2.43
2.44
2.43
2.44
2.43
2.44
2.44
2.43
2.43
2.43
2.43
2.44
2.47
2.48
2.49
2.5
2.51
2.49
2.49
2.48
2.48
2.48
2.5
2.5
2.5
2.5
2.5
2.48
2.49
2.48
2.5
2.5
2.49
2.48
2.47
2.46
2.43
2.42
2.43
2.45
2.45
2.46
2.44
2.45
2.45
2.42
2.41
2.39
2.39
2.38
2.37
2.37
2.38
2.39
2.41
2.42
2.48
2.53
2.56
2.56
2.53
2.57
2.56
2.57
2.58
2.57
2.6
2.63
2.72
2.83
2.9
2.92
2.94
2.95
2.98
3.02
3.16
3.2
3.18
3.17

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time13 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 13 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72683&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]13 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72683&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72683&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 time13 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
12.441666666666670.01403458930534470.04
22.408333333333330.01193416282879710.04
32.428333333333330.008348471099367240.02
42.440.01128152149635530.04
52.430.01044465935734180.0299999999999998
62.470.02954195783503980.0799999999999996
72.49250.009653072991634230.02
82.45250.02094364733365140.0700000000000003
92.398333333333330.02405801069888950.08
102.561666666666670.03737605780402340.15
112.99750.1529780138688980.48

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 2.44166666666667 & 0.0140345893053447 & 0.04 \tabularnewline
2 & 2.40833333333333 & 0.0119341628287971 & 0.04 \tabularnewline
3 & 2.42833333333333 & 0.00834847109936724 & 0.02 \tabularnewline
4 & 2.44 & 0.0112815214963553 & 0.04 \tabularnewline
5 & 2.43 & 0.0104446593573418 & 0.0299999999999998 \tabularnewline
6 & 2.47 & 0.0295419578350398 & 0.0799999999999996 \tabularnewline
7 & 2.4925 & 0.00965307299163423 & 0.02 \tabularnewline
8 & 2.4525 & 0.0209436473336514 & 0.0700000000000003 \tabularnewline
9 & 2.39833333333333 & 0.0240580106988895 & 0.08 \tabularnewline
10 & 2.56166666666667 & 0.0373760578040234 & 0.15 \tabularnewline
11 & 2.9975 & 0.152978013868898 & 0.48 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72683&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]2.44166666666667[/C][C]0.0140345893053447[/C][C]0.04[/C][/ROW]
[ROW][C]2[/C][C]2.40833333333333[/C][C]0.0119341628287971[/C][C]0.04[/C][/ROW]
[ROW][C]3[/C][C]2.42833333333333[/C][C]0.00834847109936724[/C][C]0.02[/C][/ROW]
[ROW][C]4[/C][C]2.44[/C][C]0.0112815214963553[/C][C]0.04[/C][/ROW]
[ROW][C]5[/C][C]2.43[/C][C]0.0104446593573418[/C][C]0.0299999999999998[/C][/ROW]
[ROW][C]6[/C][C]2.47[/C][C]0.0295419578350398[/C][C]0.0799999999999996[/C][/ROW]
[ROW][C]7[/C][C]2.4925[/C][C]0.00965307299163423[/C][C]0.02[/C][/ROW]
[ROW][C]8[/C][C]2.4525[/C][C]0.0209436473336514[/C][C]0.0700000000000003[/C][/ROW]
[ROW][C]9[/C][C]2.39833333333333[/C][C]0.0240580106988895[/C][C]0.08[/C][/ROW]
[ROW][C]10[/C][C]2.56166666666667[/C][C]0.0373760578040234[/C][C]0.15[/C][/ROW]
[ROW][C]11[/C][C]2.9975[/C][C]0.152978013868898[/C][C]0.48[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72683&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72683&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
12.441666666666670.01403458930534470.04
22.408333333333330.01193416282879710.04
32.428333333333330.008348471099367240.02
42.440.01128152149635530.04
52.430.01044465935734180.0299999999999998
62.470.02954195783503980.0799999999999996
72.49250.009653072991634230.02
82.45250.02094364733365140.0700000000000003
92.398333333333330.02405801069888950.08
102.561666666666670.03737605780402340.15
112.99750.1529780138688980.48






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.568716093028495
beta0.239326735064931
S.D.0.0182182988067788
T-STAT13.1366126773528
p-value3.54948967847602e-07

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.568716093028495 \tabularnewline
beta & 0.239326735064931 \tabularnewline
S.D. & 0.0182182988067788 \tabularnewline
T-STAT & 13.1366126773528 \tabularnewline
p-value & 3.54948967847602e-07 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72683&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.568716093028495[/C][/ROW]
[ROW][C]beta[/C][C]0.239326735064931[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0182182988067788[/C][/ROW]
[ROW][C]T-STAT[/C][C]13.1366126773528[/C][/ROW]
[ROW][C]p-value[/C][C]3.54948967847602e-07[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72683&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72683&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-0.568716093028495
beta0.239326735064931
S.D.0.0182182988067788
T-STAT13.1366126773528
p-value3.54948967847602e-07






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-14.4468815225932
beta11.4706191798726
S.D.2.28730836924548
T-STAT5.01489844312355
p-value0.000724104687995969
Lambda-10.4706191798726

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -14.4468815225932 \tabularnewline
beta & 11.4706191798726 \tabularnewline
S.D. & 2.28730836924548 \tabularnewline
T-STAT & 5.01489844312355 \tabularnewline
p-value & 0.000724104687995969 \tabularnewline
Lambda & -10.4706191798726 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72683&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-14.4468815225932[/C][/ROW]
[ROW][C]beta[/C][C]11.4706191798726[/C][/ROW]
[ROW][C]S.D.[/C][C]2.28730836924548[/C][/ROW]
[ROW][C]T-STAT[/C][C]5.01489844312355[/C][/ROW]
[ROW][C]p-value[/C][C]0.000724104687995969[/C][/ROW]
[ROW][C]Lambda[/C][C]-10.4706191798726[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72683&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72683&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-14.4468815225932
beta11.4706191798726
S.D.2.28730836924548
T-STAT5.01489844312355
p-value0.000724104687995969
Lambda-10.4706191798726


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')