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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 computationTue, 21 Dec 2010 20:05:46 +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/21/t1292962459afyawrm5nxwsgqe.htm/, Retrieved Sun, 19 May 2024 21:34:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=113929, Retrieved Sun, 19 May 2024 21:34:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact91

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...] [2010-12-21 20:05:46] [194b0dcd1d575718d8c1582a0112d12c] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4940
3924
3927
4535
3446
3016
4934
2743
3242
6662
3262
3381
7144
3803
3684
6759
3386
3066
5538
2940
3215
7023
3443
3712
7475
4137
3491
7019
3908
3402
5604
3222
3636
7123
4368
4092
8377
4595
4188
6988
4218
3655
6211
3622
3841
8510
4627
4582
8967
4928
4809
7917
4790
4065
7290
4670
3561
5149
6880
6981
8454
4960
4670
7638
4560
3980
6825
3939
4079
8117
5121
5167
7960
4670
4397
7191
4293
3747
6425
3709
3840
7642
4821
4865

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'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113929&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113929&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113929&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'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
140011107.704752261103919
24476.083333333331645.985775832354204
34789.751582.778232039534253
45284.51783.039973038904888
55833.916666666671699.348723285875406
65625.833333333331667.781805727344515
75296.666666666671570.224380800594251

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 4001 & 1107.70475226110 & 3919 \tabularnewline
2 & 4476.08333333333 & 1645.98577583235 & 4204 \tabularnewline
3 & 4789.75 & 1582.77823203953 & 4253 \tabularnewline
4 & 5284.5 & 1783.03997303890 & 4888 \tabularnewline
5 & 5833.91666666667 & 1699.34872328587 & 5406 \tabularnewline
6 & 5625.83333333333 & 1667.78180572734 & 4515 \tabularnewline
7 & 5296.66666666667 & 1570.22438080059 & 4251 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113929&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]4001[/C][C]1107.70475226110[/C][C]3919[/C][/ROW]
[ROW][C]2[/C][C]4476.08333333333[/C][C]1645.98577583235[/C][C]4204[/C][/ROW]
[ROW][C]3[/C][C]4789.75[/C][C]1582.77823203953[/C][C]4253[/C][/ROW]
[ROW][C]4[/C][C]5284.5[/C][C]1783.03997303890[/C][C]4888[/C][/ROW]
[ROW][C]5[/C][C]5833.91666666667[/C][C]1699.34872328587[/C][C]5406[/C][/ROW]
[ROW][C]6[/C][C]5625.83333333333[/C][C]1667.78180572734[/C][C]4515[/C][/ROW]
[ROW][C]7[/C][C]5296.66666666667[/C][C]1570.22438080059[/C][C]4251[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113929&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113929&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
140011107.704752261103919
24476.083333333331645.985775832354204
34789.751582.778232039534253
45284.51783.039973038904888
55833.916666666671699.348723285875406
65625.833333333331667.781805727344515
75296.666666666671570.224380800594251






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha306.077114235083
beta0.252474990429583
S.D.0.0998439965373905
T-STAT2.52869475567350
p-value0.0526136324312272

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 306.077114235083 \tabularnewline
beta & 0.252474990429583 \tabularnewline
S.D. & 0.0998439965373905 \tabularnewline
T-STAT & 2.52869475567350 \tabularnewline
p-value & 0.0526136324312272 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113929&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]306.077114235083[/C][/ROW]
[ROW][C]beta[/C][C]0.252474990429583[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0998439965373905[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.52869475567350[/C][/ROW]
[ROW][C]p-value[/C][C]0.0526136324312272[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113929&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113929&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)
alpha306.077114235083
beta0.252474990429583
S.D.0.0998439965373905
T-STAT2.52869475567350
p-value0.0526136324312272






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-0.431012648765939
beta0.914026577805861
S.D.0.333151678204844
T-STAT2.74357488676330
p-value0.0406190817124599
Lambda0.085973422194139

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -0.431012648765939 \tabularnewline
beta & 0.914026577805861 \tabularnewline
S.D. & 0.333151678204844 \tabularnewline
T-STAT & 2.74357488676330 \tabularnewline
p-value & 0.0406190817124599 \tabularnewline
Lambda & 0.085973422194139 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113929&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.431012648765939[/C][/ROW]
[ROW][C]beta[/C][C]0.914026577805861[/C][/ROW]
[ROW][C]S.D.[/C][C]0.333151678204844[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.74357488676330[/C][/ROW]
[ROW][C]p-value[/C][C]0.0406190817124599[/C][/ROW]
[ROW][C]Lambda[/C][C]0.085973422194139[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113929&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113929&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-0.431012648765939
beta0.914026577805861
S.D.0.333151678204844
T-STAT2.74357488676330
p-value0.0406190817124599
Lambda0.085973422194139


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')