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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationWed, 22 Dec 2010 20:22:11 +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/22/t1293049186lm9k6hr9854vmj1.htm/, Retrieved Mon, 06 May 2024 00:38:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114556, Retrieved Mon, 06 May 2024 00:38:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
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] [mean plot bel20] [2008-12-10 18:16:19] [74be16979710d4c4e7c6647856088456]
-  M D  [Standard Deviation-Mean Plot] [] [2009-12-15 12:36:38] [2f674a53c3d7aaa1bcf80e66074d3c9b]
-    D    [Standard Deviation-Mean Plot] [] [2010-12-22 19:40:05] [82643889efeee0b265cd2ff213e5137b]
-             [Standard Deviation-Mean Plot] [] [2010-12-22 20:22:11] [4afc4ea409ad669ec2851bc39795365d] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1,000
2547,000
10,550
0,023
160,000
3,300
52,160
0,425
465,000
0,550
0,075
3,000
0,785
0,200
1,410
60,000
27,660
0,120
85,000
0,101
1,040
521,000
0,005
0,010
62,000
0,122
1,350
0,023
0,048
1,700
3,500
0,480
10,000
1,620
192,000
2,500
0,280
4,235
6,800
0,750
3,600
55,500
0,060
0,900
2,000
0,104
4,190
3,500

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=114556&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=114556&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114556&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
1270.256916666667729.5965096174062546.977
258.1109166666667148.480878052886520.995
322.9452556.0164513548151191.977
46.8265833333333315.472643779841955.44

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 270.256916666667 & 729.596509617406 & 2546.977 \tabularnewline
2 & 58.1109166666667 & 148.480878052886 & 520.995 \tabularnewline
3 & 22.94525 & 56.0164513548151 & 191.977 \tabularnewline
4 & 6.82658333333333 & 15.4726437798419 & 55.44 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114556&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]270.256916666667[/C][C]729.596509617406[/C][C]2546.977[/C][/ROW]
[ROW][C]2[/C][C]58.1109166666667[/C][C]148.480878052886[/C][C]520.995[/C][/ROW]
[ROW][C]3[/C][C]22.94525[/C][C]56.0164513548151[/C][C]191.977[/C][/ROW]
[ROW][C]4[/C][C]6.82658333333333[/C][C]15.4726437798419[/C][C]55.44[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114556&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114556&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
1270.256916666667729.5965096174062546.977
258.1109166666667148.480878052886520.995
322.9452556.0164513548151191.977
46.8265833333333315.472643779841955.44






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-6.12049894403713
beta2.71974475111041
S.D.0.0154965284347489
T-STAT175.506711878239
p-value3.24632048417571e-05

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -6.12049894403713 \tabularnewline
beta & 2.71974475111041 \tabularnewline
S.D. & 0.0154965284347489 \tabularnewline
T-STAT & 175.506711878239 \tabularnewline
p-value & 3.24632048417571e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114556&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-6.12049894403713[/C][/ROW]
[ROW][C]beta[/C][C]2.71974475111041[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0154965284347489[/C][/ROW]
[ROW][C]T-STAT[/C][C]175.506711878239[/C][/ROW]
[ROW][C]p-value[/C][C]3.24632048417571e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114556&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114556&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-6.12049894403713
beta2.71974475111041
S.D.0.0154965284347489
T-STAT175.506711878239
p-value3.24632048417571e-05






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha0.736719446067473
beta1.04723723550714
S.D.0.00456778915576368
T-STAT229.265668750433
p-value1.902433801838e-05
Lambda-0.0472372355071387

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.736719446067473 \tabularnewline
beta & 1.04723723550714 \tabularnewline
S.D. & 0.00456778915576368 \tabularnewline
T-STAT & 229.265668750433 \tabularnewline
p-value & 1.902433801838e-05 \tabularnewline
Lambda & -0.0472372355071387 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114556&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.736719446067473[/C][/ROW]
[ROW][C]beta[/C][C]1.04723723550714[/C][/ROW]
[ROW][C]S.D.[/C][C]0.00456778915576368[/C][/ROW]
[ROW][C]T-STAT[/C][C]229.265668750433[/C][/ROW]
[ROW][C]p-value[/C][C]1.902433801838e-05[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.0472372355071387[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114556&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114556&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)
alpha0.736719446067473
beta1.04723723550714
S.D.0.00456778915576368
T-STAT229.265668750433
p-value1.902433801838e-05
Lambda-0.0472372355071387


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = ; par3 = ; par4 = ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;
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')