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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 computationMon, 13 Aug 2012 08:55:58 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Aug/13/t1344862611cz6ppz65f7c62jk.htm/, Retrieved Sat, 27 Apr 2024 20:02:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=169281, Retrieved Sat, 27 Apr 2024 20:02:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsVerbraken Frederik
Estimated Impact138

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] [TIJDREEKS B - STA...] [2012-08-13 12:55:58] [31886bd2f92a612f059dd2285dd41f3c] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
500
510
590
490
540
530
550
510
390
480
530
690
570
460
540
510
520
520
580
480
410
530
540
670
570
400
510
570
470
640
650
500
340
450
600
680
630
480
400
520
470
610
670
500
290
470
660
650
570
500
400
500
340
530
680
480
340
460
630
650
550
470
240
430
390
570
700
620
280
480
560
560
560
550
140
380
390
500
750
680
280
360
590
580
490
610
170
320
440
510
770
660
300
350
580
620
490
640
150
290
370
560
780
690
310
280
590
590

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'AstonUniversity' @ aston.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 & 1 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169281&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169281&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169281&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'AstonUniversity' @ aston.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1525.83333333333370.6410044885512300
2527.564.8249390842192260
3531.666666666667105.039675043925340
4529.166666666667117.740726971931380
5506.666666666667112.92260691073340
6487.5135.319487274981460
7480174.460206455122610
8485174.850585565869600
9478.333333333333194.554658519181630

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 525.833333333333 & 70.6410044885512 & 300 \tabularnewline
2 & 527.5 & 64.8249390842192 & 260 \tabularnewline
3 & 531.666666666667 & 105.039675043925 & 340 \tabularnewline
4 & 529.166666666667 & 117.740726971931 & 380 \tabularnewline
5 & 506.666666666667 & 112.92260691073 & 340 \tabularnewline
6 & 487.5 & 135.319487274981 & 460 \tabularnewline
7 & 480 & 174.460206455122 & 610 \tabularnewline
8 & 485 & 174.850585565869 & 600 \tabularnewline
9 & 478.333333333333 & 194.554658519181 & 630 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169281&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]525.833333333333[/C][C]70.6410044885512[/C][C]300[/C][/ROW]
[ROW][C]2[/C][C]527.5[/C][C]64.8249390842192[/C][C]260[/C][/ROW]
[ROW][C]3[/C][C]531.666666666667[/C][C]105.039675043925[/C][C]340[/C][/ROW]
[ROW][C]4[/C][C]529.166666666667[/C][C]117.740726971931[/C][C]380[/C][/ROW]
[ROW][C]5[/C][C]506.666666666667[/C][C]112.92260691073[/C][C]340[/C][/ROW]
[ROW][C]6[/C][C]487.5[/C][C]135.319487274981[/C][C]460[/C][/ROW]
[ROW][C]7[/C][C]480[/C][C]174.460206455122[/C][C]610[/C][/ROW]
[ROW][C]8[/C][C]485[/C][C]174.850585565869[/C][C]600[/C][/ROW]
[ROW][C]9[/C][C]478.333333333333[/C][C]194.554658519181[/C][C]630[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169281&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169281&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
1525.83333333333370.6410044885512300
2527.564.8249390842192260
3531.666666666667105.039675043925340
4529.166666666667117.740726971931380
5506.666666666667112.92260691073340
6487.5135.319487274981460
7480174.460206455122610
8485174.850585565869600
9478.333333333333194.554658519181630






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha1015.18223983039
beta-1.75458504609865
S.D.0.356999097345115
T-STAT-4.91481647753993
p-value0.00172377885013264

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1015.18223983039 \tabularnewline
beta & -1.75458504609865 \tabularnewline
S.D. & 0.356999097345115 \tabularnewline
T-STAT & -4.91481647753993 \tabularnewline
p-value & 0.00172377885013264 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169281&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1015.18223983039[/C][/ROW]
[ROW][C]beta[/C][C]-1.75458504609865[/C][/ROW]
[ROW][C]S.D.[/C][C]0.356999097345115[/C][/ROW]
[ROW][C]T-STAT[/C][C]-4.91481647753993[/C][/ROW]
[ROW][C]p-value[/C][C]0.00172377885013264[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169281&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169281&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)
alpha1015.18223983039
beta-1.75458504609865
S.D.0.356999097345115
T-STAT-4.91481647753993
p-value0.00172377885013264






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha49.6435622137106
beta-7.20576887884312
S.D.1.70297356287278
T-STAT-4.23128640158546
p-value0.0038819410423839
Lambda8.20576887884312

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 49.6435622137106 \tabularnewline
beta & -7.20576887884312 \tabularnewline
S.D. & 1.70297356287278 \tabularnewline
T-STAT & -4.23128640158546 \tabularnewline
p-value & 0.0038819410423839 \tabularnewline
Lambda & 8.20576887884312 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169281&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]49.6435622137106[/C][/ROW]
[ROW][C]beta[/C][C]-7.20576887884312[/C][/ROW]
[ROW][C]S.D.[/C][C]1.70297356287278[/C][/ROW]
[ROW][C]T-STAT[/C][C]-4.23128640158546[/C][/ROW]
[ROW][C]p-value[/C][C]0.0038819410423839[/C][/ROW]
[ROW][C]Lambda[/C][C]8.20576887884312[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169281&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169281&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)
alpha49.6435622137106
beta-7.20576887884312
S.D.1.70297356287278
T-STAT-4.23128640158546
p-value0.0038819410423839
Lambda8.20576887884312


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')