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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 computationWed, 03 Dec 2008 05:47:31 -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/2008/Dec/03/t1228308483ibes727rb55uyko.htm/, Retrieved Fri, 17 May 2024 05:03:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28669, Retrieved Fri, 17 May 2024 05:03:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact179

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] [NonStationaryTime...] [2008-12-03 12:47:31] [a413cf7744efd6bb212437a3916e2f23] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1846,5
2796,3
2895,6
2472,2
2584,4
2630,4
2663,1
3176,2
2856,7
2551,4
3088,7
2628,3
2226,2
3023,6
3077,9
3084,1
2990,3
2949,6
3014,7
3517,7
3121,2
3067,4
3174,6
2676,3
2424
3195,1
3146,6
3506,7
3528,5
3365,1
3153
3843,3
3123,2
3361,1
3481,9
2970,5
2537
3257,6
3301,3
3391,6
2933,6
3283,2
3139,7
3486,4
3202,2
3294,4
3550,3
3279,3
2678,6
3451,4
3977,1
3814,8
3310,5
3971,8
4051,9
4057,6
4391,4
3628,9
4092,2
3822,5

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28669&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]1 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=28669&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28669&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 time1 seconds
R Server'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
12682.48333333333340.2415100359081329.7
22993.63333333333307.0891026553971291.5
33258.25353.37376169511419.3
43221.38333333333267.2824649328981013.3
53770.725453.693146450731712.8

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 2682.48333333333 & 340.241510035908 & 1329.7 \tabularnewline
2 & 2993.63333333333 & 307.089102655397 & 1291.5 \tabularnewline
3 & 3258.25 & 353.3737616951 & 1419.3 \tabularnewline
4 & 3221.38333333333 & 267.282464932898 & 1013.3 \tabularnewline
5 & 3770.725 & 453.69314645073 & 1712.8 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28669&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]2682.48333333333[/C][C]340.241510035908[/C][C]1329.7[/C][/ROW]
[ROW][C]2[/C][C]2993.63333333333[/C][C]307.089102655397[/C][C]1291.5[/C][/ROW]
[ROW][C]3[/C][C]3258.25[/C][C]353.3737616951[/C][C]1419.3[/C][/ROW]
[ROW][C]4[/C][C]3221.38333333333[/C][C]267.282464932898[/C][C]1013.3[/C][/ROW]
[ROW][C]5[/C][C]3770.725[/C][C]453.69314645073[/C][C]1712.8[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28669&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28669&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
12682.48333333333340.2415100359081329.7
22993.63333333333307.0891026553971291.5
33258.25353.37376169511419.3
43221.38333333333267.2824649328981013.3
53770.725453.693146450731712.8






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-10.1215156948041
beta0.111279336089377
S.D.0.0773587222583547
T-STAT1.4384846703871
p-value0.245879924162916

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -10.1215156948041 \tabularnewline
beta & 0.111279336089377 \tabularnewline
S.D. & 0.0773587222583547 \tabularnewline
T-STAT & 1.4384846703871 \tabularnewline
p-value & 0.245879924162916 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28669&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-10.1215156948041[/C][/ROW]
[ROW][C]beta[/C][C]0.111279336089377[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0773587222583547[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.4384846703871[/C][/ROW]
[ROW][C]p-value[/C][C]0.245879924162916[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28669&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28669&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-10.1215156948041
beta0.111279336089377
S.D.0.0773587222583547
T-STAT1.4384846703871
p-value0.245879924162916






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.02529666795177
beta0.850032161771266
S.D.0.760067791065591
T-STAT1.1183636140923
p-value0.344894045788348
Lambda0.149967838228734

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.02529666795177 \tabularnewline
beta & 0.850032161771266 \tabularnewline
S.D. & 0.760067791065591 \tabularnewline
T-STAT & 1.1183636140923 \tabularnewline
p-value & 0.344894045788348 \tabularnewline
Lambda & 0.149967838228734 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28669&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.02529666795177[/C][/ROW]
[ROW][C]beta[/C][C]0.850032161771266[/C][/ROW]
[ROW][C]S.D.[/C][C]0.760067791065591[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.1183636140923[/C][/ROW]
[ROW][C]p-value[/C][C]0.344894045788348[/C][/ROW]
[ROW][C]Lambda[/C][C]0.149967838228734[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28669&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28669&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-1.02529666795177
beta0.850032161771266
S.D.0.760067791065591
T-STAT1.1183636140923
p-value0.344894045788348
Lambda0.149967838228734


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')