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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 computationSat, 29 Nov 2008 14:08:55 -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/Nov/29/t1227992972pte8dwgbkilewu4.htm/, Retrieved Sun, 19 May 2024 10:56:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26381, Retrieved Sun, 19 May 2024 10:56:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact213

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [Airline data] [2007-10-18 09:58:47] [42daae401fd3def69a25014f2252b4c2]
- RMPD  [Standard Deviation-Mean Plot] [Q5] [2008-11-29 20:10:39] [57fa5e3679c393aa19449b2f1be9928b]
-   P     [Standard Deviation-Mean Plot] [Q5] [2008-11-29 20:18:39] [57fa5e3679c393aa19449b2f1be9928b]
- RM        [Variance Reduction Matrix] [Q6 Variance] [2008-11-29 20:25:29] [57fa5e3679c393aa19449b2f1be9928b]
- RM          [(Partial) Autocorrelation Function] [Q6 ACF] [2008-11-29 20:35:57] [57fa5e3679c393aa19449b2f1be9928b]
-               [(Partial) Autocorrelation Function] [Q6 aangepaste ACF] [2008-11-29 20:44:03] [57fa5e3679c393aa19449b2f1be9928b]
- RM D            [Cross Correlation Function] [Q7] [2008-11-29 20:55:14] [57fa5e3679c393aa19449b2f1be9928b]
F RM D              [Standard Deviation-Mean Plot] [Q8 Mean plot insc...] [2008-11-29 21:03:17] [57fa5e3679c393aa19449b2f1be9928b]
-    D                  [Standard Deviation-Mean Plot] [Q8 Mean plot bouw...] [2008-11-29 21:08:55] [270782e2502ae87124d0ebdcd1862d6a] [Current]
- RM                      [Variance Reduction Matrix] [Q8 VRM Bouwvergun...] [2008-11-29 21:11:38] [57fa5e3679c393aa19449b2f1be9928b]
-                           [Variance Reduction Matrix] [] [2008-11-30 11:21:50] [ffbe22449df335faef31f462015daa42]
-                             [Variance Reduction Matrix] [] [2008-11-30 11:22:57] [ffbe22449df335faef31f462015daa42]
-   P                       [Variance Reduction Matrix] [] [2008-11-30 11:25:19] [a4ee3bef49b119f4bd2e925060c84f5e]
-                         [Standard Deviation-Mean Plot] [] [2008-11-30 11:20:10] [ffbe22449df335faef31f462015daa42]
-   P                     [Standard Deviation-Mean Plot] [] [2008-11-30 11:23:30] [a4ee3bef49b119f4bd2e925060c84f5e]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2218
1855
2187
1852
1570
1851
1954
1828
2251
2277
2085
2282
2266
1878
2267
2069
1746
2299
2360
2214
2825
2355
2333
3016
2155
2172
2150
2533
2058
2160
2259
2498
2695
2799
2945
2930
2318
2540
2570
2669
2450
2842
3439
2677
2979
2257
2842
2546
2455
2293
2379
2478
2054
2272
2351
2271
2542
2304
2194
2722
2395
2146
1894
2548
2087
2063
2481
2476
2212
2834
2148
2598

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'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26381&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26381&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26381&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
12017.5231.011019020935712
22302.33333333333349.5364029249271270
32446.16666666667329.5757143892887
42677.41666666667320.5887930705381182
52359.58333333333173.739333659958668
62323.5273.452172982938940

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 2017.5 & 231.011019020935 & 712 \tabularnewline
2 & 2302.33333333333 & 349.536402924927 & 1270 \tabularnewline
3 & 2446.16666666667 & 329.5757143892 & 887 \tabularnewline
4 & 2677.41666666667 & 320.588793070538 & 1182 \tabularnewline
5 & 2359.58333333333 & 173.739333659958 & 668 \tabularnewline
6 & 2323.5 & 273.452172982938 & 940 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26381&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]2017.5[/C][C]231.011019020935[/C][C]712[/C][/ROW]
[ROW][C]2[/C][C]2302.33333333333[/C][C]349.536402924927[/C][C]1270[/C][/ROW]
[ROW][C]3[/C][C]2446.16666666667[/C][C]329.5757143892[/C][C]887[/C][/ROW]
[ROW][C]4[/C][C]2677.41666666667[/C][C]320.588793070538[/C][C]1182[/C][/ROW]
[ROW][C]5[/C][C]2359.58333333333[/C][C]173.739333659958[/C][C]668[/C][/ROW]
[ROW][C]6[/C][C]2323.5[/C][C]273.452172982938[/C][C]940[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26381&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26381&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
12017.5231.011019020935712
22302.33333333333349.5364029249271270
32446.16666666667329.5757143892887
42677.41666666667320.5887930705381182
52359.58333333333173.739333659958668
62323.5273.452172982938940






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-29.5108119742131
beta0.131311245382351
S.D.0.142617312517423
T-STAT0.92072444126521
p-value0.409298032986998

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -29.5108119742131 \tabularnewline
beta & 0.131311245382351 \tabularnewline
S.D. & 0.142617312517423 \tabularnewline
T-STAT & 0.92072444126521 \tabularnewline
p-value & 0.409298032986998 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26381&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-29.5108119742131[/C][/ROW]
[ROW][C]beta[/C][C]0.131311245382351[/C][/ROW]
[ROW][C]S.D.[/C][C]0.142617312517423[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.92072444126521[/C][/ROW]
[ROW][C]p-value[/C][C]0.409298032986998[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26381&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26381&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-29.5108119742131
beta0.131311245382351
S.D.0.142617312517423
T-STAT0.92072444126521
p-value0.409298032986998






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.99368536797137
beta1.10812358600228
S.D.1.33435608974938
T-STAT0.830455674100018
p-value0.452973059390836
Lambda-0.108123586002284

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.99368536797137 \tabularnewline
beta & 1.10812358600228 \tabularnewline
S.D. & 1.33435608974938 \tabularnewline
T-STAT & 0.830455674100018 \tabularnewline
p-value & 0.452973059390836 \tabularnewline
Lambda & -0.108123586002284 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26381&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.99368536797137[/C][/ROW]
[ROW][C]beta[/C][C]1.10812358600228[/C][/ROW]
[ROW][C]S.D.[/C][C]1.33435608974938[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.830455674100018[/C][/ROW]
[ROW][C]p-value[/C][C]0.452973059390836[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.108123586002284[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26381&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26381&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-2.99368536797137
beta1.10812358600228
S.D.1.33435608974938
T-STAT0.830455674100018
p-value0.452973059390836
Lambda-0.108123586002284


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')