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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 computationThu, 09 Dec 2010 18:52:13 +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/09/t12919206160v1iajiu7uw9ul0.htm/, Retrieved Mon, 29 Apr 2024 02:42:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=107318, Retrieved Mon, 29 Apr 2024 02:42:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact190

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Standard Deviation-Mean Plot] [Identifying Integ...] [2009-11-22 12:50:05] [b98453cac15ba1066b407e146608df68]
-   PD        [Standard Deviation-Mean Plot] [WS8.10] [2009-11-25 19:32:05] [626f1d98f4a7f05bcb9f17666b672c60]
-   PD          [Standard Deviation-Mean Plot] [Paper SMP] [2009-12-11 20:41:37] [626f1d98f4a7f05bcb9f17666b672c60]
-    D              [Standard Deviation-Mean Plot] [Paper - Standard ...] [2010-12-09 18:52:13] [cfd788255f1b1b5389e58d7f218c70bf] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
376.974
377.632
378.205
370.861
369.167
371.551
382.842
381.903
384.502
392.058
384.359
388.884
386.586
387.495
385.705
378.67
377.367
376.911
389.827
387.82
387.267
380.575
372.402
376.74
377.795
376.126
370.804
367.98
367.866
366.121
379.421
378.519
372.423
355.072
344.693
342.892
344.178
337.606
327.103
323.953
316.532
306.307
327.225
329.573
313.761
307.836
300.074
304.198
306.122
300.414
292.133
290.616
280.244
285.179
305.486
305.957
293.886
289.441
288.776
299.149
306.532
309.914
313.468
314.901
309.16
316.15
336.544
339.196
326.738
320.838
318.62
331.533
335.378

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=107318&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=107318&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107318&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
1379.91157.1696394419296222.891
2382.2804166666675.7773602096826417.425
3366.64266666666712.622813750099336.529
4319.86216666666713.939488335681744.104
5294.7835833333338.5927393606286625.878
6320.299510.897208445702532.664

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 379.9115 & 7.16963944192962 & 22.891 \tabularnewline
2 & 382.280416666667 & 5.77736020968264 & 17.425 \tabularnewline
3 & 366.642666666667 & 12.6228137500993 & 36.529 \tabularnewline
4 & 319.862166666667 & 13.9394883356817 & 44.104 \tabularnewline
5 & 294.783583333333 & 8.59273936062866 & 25.878 \tabularnewline
6 & 320.2995 & 10.8972084457025 & 32.664 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107318&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]379.9115[/C][C]7.16963944192962[/C][C]22.891[/C][/ROW]
[ROW][C]2[/C][C]382.280416666667[/C][C]5.77736020968264[/C][C]17.425[/C][/ROW]
[ROW][C]3[/C][C]366.642666666667[/C][C]12.6228137500993[/C][C]36.529[/C][/ROW]
[ROW][C]4[/C][C]319.862166666667[/C][C]13.9394883356817[/C][C]44.104[/C][/ROW]
[ROW][C]5[/C][C]294.783583333333[/C][C]8.59273936062866[/C][C]25.878[/C][/ROW]
[ROW][C]6[/C][C]320.2995[/C][C]10.8972084457025[/C][C]32.664[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107318&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107318&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
1379.91157.1696394419296222.891
2382.2804166666675.7773602096826417.425
3366.64266666666712.622813750099336.529
4319.86216666666713.939488335681744.104
5294.7835833333338.5927393606286625.878
6320.299510.897208445702532.664






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha22.4673073924083
beta-0.0367309504562261
S.D.0.0390273024972722
T-STAT-0.94116036994341
p-value0.399910933722019

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 22.4673073924083 \tabularnewline
beta & -0.0367309504562261 \tabularnewline
S.D. & 0.0390273024972722 \tabularnewline
T-STAT & -0.94116036994341 \tabularnewline
p-value & 0.399910933722019 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107318&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]22.4673073924083[/C][/ROW]
[ROW][C]beta[/C][C]-0.0367309504562261[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0390273024972722[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.94116036994341[/C][/ROW]
[ROW][C]p-value[/C][C]0.399910933722019[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107318&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107318&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)
alpha22.4673073924083
beta-0.0367309504562261
S.D.0.0390273024972722
T-STAT-0.94116036994341
p-value0.399910933722019






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha10.6140719201973
beta-1.43517342039747
S.D.1.39534925631338
T-STAT-1.02854064235452
p-value0.361821925844958
Lambda2.43517342039747

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 10.6140719201973 \tabularnewline
beta & -1.43517342039747 \tabularnewline
S.D. & 1.39534925631338 \tabularnewline
T-STAT & -1.02854064235452 \tabularnewline
p-value & 0.361821925844958 \tabularnewline
Lambda & 2.43517342039747 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107318&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]10.6140719201973[/C][/ROW]
[ROW][C]beta[/C][C]-1.43517342039747[/C][/ROW]
[ROW][C]S.D.[/C][C]1.39534925631338[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.02854064235452[/C][/ROW]
[ROW][C]p-value[/C][C]0.361821925844958[/C][/ROW]
[ROW][C]Lambda[/C][C]2.43517342039747[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107318&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107318&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)
alpha10.6140719201973
beta-1.43517342039747
S.D.1.39534925631338
T-STAT-1.02854064235452
p-value0.361821925844958
Lambda2.43517342039747


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')