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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 computationThu, 25 Dec 2014 13:49:58 +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/2014/Dec/25/t1419515414fu4ftwlfml18cvp.htm/, Retrieved Thu, 16 May 2024 11:26:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=271484, Retrieved Thu, 16 May 2024 11:26:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact146

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] [] [2014-12-25 13:49:58] [0837030ca90013de3b1661dab7c6b0da] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1196
1141
6081
-3508
1782
-891
-2043
35
5042
-1837
406
-3621
1987
1627
6692
-3999
679
-215
-2820
799
9957
5154
1302
6287
1891
2191
7336
-2351
881
388
-1936
1120
4438
-3495
1012
-3704
2879
1907
6451
-2814
1613
-40
-3086
292
5283
-1671
3529
-3191
2090
3278
5686
-1817
2322
-705
-1980
646
6077
2632
2356
-1717
1733
2232
6167
-4668
1694
589
-4163
174
5421
-38
3158
-4322
1920
2527
7755
-2567
-388
-2084
-2024
-131
5615
187
2054
-7172

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'Gwilym Jenkins' @ jenkins.wessa.net

\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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271484&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271484&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271484&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'Gwilym Jenkins' @ jenkins.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1315.253030.775782024979702
22287.54051.9747486424913956
3647.5833333333333237.169343123811040
4929.3333333333333256.406869076679642
51572.333333333332757.82006576788057
6664.753581.8132818955910835
7474.3333333333333930.4032717760514927

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 315.25 & 3030.77578202497 & 9702 \tabularnewline
2 & 2287.5 & 4051.97474864249 & 13956 \tabularnewline
3 & 647.583333333333 & 3237.1693431238 & 11040 \tabularnewline
4 & 929.333333333333 & 3256.40686907667 & 9642 \tabularnewline
5 & 1572.33333333333 & 2757.8200657678 & 8057 \tabularnewline
6 & 664.75 & 3581.81328189559 & 10835 \tabularnewline
7 & 474.333333333333 & 3930.40327177605 & 14927 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271484&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]315.25[/C][C]3030.77578202497[/C][C]9702[/C][/ROW]
[ROW][C]2[/C][C]2287.5[/C][C]4051.97474864249[/C][C]13956[/C][/ROW]
[ROW][C]3[/C][C]647.583333333333[/C][C]3237.1693431238[/C][C]11040[/C][/ROW]
[ROW][C]4[/C][C]929.333333333333[/C][C]3256.40686907667[/C][C]9642[/C][/ROW]
[ROW][C]5[/C][C]1572.33333333333[/C][C]2757.8200657678[/C][C]8057[/C][/ROW]
[ROW][C]6[/C][C]664.75[/C][C]3581.81328189559[/C][C]10835[/C][/ROW]
[ROW][C]7[/C][C]474.333333333333[/C][C]3930.40327177605[/C][C]14927[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271484&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271484&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
1315.253030.775782024979702
22287.54051.9747486424913956
3647.5833333333333237.169343123811040
4929.3333333333333256.406869076679642
51572.333333333332757.82006576788057
6664.753581.8132818955910835
7474.3333333333333930.4032717760514927






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha3256.42529986395
beta0.152571985042464
S.D.0.291948348706327
T-STAT0.522599239620764
p-value0.623574030393662

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 3256.42529986395 \tabularnewline
beta & 0.152571985042464 \tabularnewline
S.D. & 0.291948348706327 \tabularnewline
T-STAT & 0.522599239620764 \tabularnewline
p-value & 0.623574030393662 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271484&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3256.42529986395[/C][/ROW]
[ROW][C]beta[/C][C]0.152571985042464[/C][/ROW]
[ROW][C]S.D.[/C][C]0.291948348706327[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.522599239620764[/C][/ROW]
[ROW][C]p-value[/C][C]0.623574030393662[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271484&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271484&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)
alpha3256.42529986395
beta0.152571985042464
S.D.0.291948348706327
T-STAT0.522599239620764
p-value0.623574030393662






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha7.96160545347535
beta0.024465992260417
S.D.0.0901470332994705
T-STAT0.271400969781672
p-value0.796931500880559
Lambda0.975534007739583

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 7.96160545347535 \tabularnewline
beta & 0.024465992260417 \tabularnewline
S.D. & 0.0901470332994705 \tabularnewline
T-STAT & 0.271400969781672 \tabularnewline
p-value & 0.796931500880559 \tabularnewline
Lambda & 0.975534007739583 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271484&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]7.96160545347535[/C][/ROW]
[ROW][C]beta[/C][C]0.024465992260417[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0901470332994705[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.271400969781672[/C][/ROW]
[ROW][C]p-value[/C][C]0.796931500880559[/C][/ROW]
[ROW][C]Lambda[/C][C]0.975534007739583[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271484&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271484&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)
alpha7.96160545347535
beta0.024465992260417
S.D.0.0901470332994705
T-STAT0.271400969781672
p-value0.796931500880559
Lambda0.975534007739583


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 750 ; par2 = 5 ; par3 = 0 ; par4 = P1 P5 Q1 Q3 P95 P99 ;
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')