R version 3.0.2 (2013-09-25) -- "Frisbee Sailing"
Copyright (C) 2013 The R Foundation for Statistical Computing
Platform: i686-pc-linux-gnu (32-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> x <- c(23,24,22,20,24,27,28,27,24,23,24,27,27,28,27,23,24,28,27,25,19,24,20,28,26,23,23,20,11,24,25,23,18,20,20,24,23,25,28,26,26,23,22,24,21,20,22,20,25,20,22,23,25,23,23,22,24,25,21,12,17,20,23,23,20,28,24,24,24,24,28,25,21,25,25,18,17,26,28,21,27,22,21,25,22,23,26,19,25,21,13,24,25,26,25,25,22,21,23,25,24,21,21,25,22,20,20,23,28,23,28,24,18,20,28,21,21,25,19,18,21,22,24,15,28,26,23,26,20,22,20,23,22,24,23,22,26,23,27,23,21,26,23,21,27,19,23,25,23,22,22,25,25,28,28,20,25,19,25,22,18,20)
> par5 = 'No'
> par4 = '0'
> par3 = '2'
> par2 = '-2'
> par1 = 'Full Box-Cox transform'
> par5 <- 'No'
> par4 <- '0'
> par3 <- '2'
> par2 <- '-2'
> par1 <- 'Full Box-Cox transform'
> #'GNU S' R Code compiled by R2WASP v. 1.2.327 ()
> #Author: root
> #To cite this work: Wessa P., (2013), Box-Cox Normality Plot (v1.1.5) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_boxcoxnorm.wasp/
> #Source of accompanying publication: Office for Research, Development, and Education
> #
> par2 <- abs(as.numeric(par2)*100)
> par3 <- as.numeric(par3)*100
> if(par4=='') par4 <- 0
> par4 <- as.numeric(par4)
> numlam <- par2 + par3 + 1
> x <- x + par4
> n <- length(x)
> c <- array(NA,dim=c(numlam))
> l <- array(NA,dim=c(numlam))
> mx <- -1
> mxli <- -999
> for (i in 1:numlam)
+ {
+ l[i] <- (i-par2-1)/100
+ if (l[i] != 0)
+ {
+ if (par1 == 'Full Box-Cox transform') x1 <- (x^l[i] - 1) / l[i]
+ if (par1 == 'Simple Box-Cox transform') x1 <- x^l[i]
+ } else {
+ x1 <- log(x)
+ }
+ c[i] <- cor(qnorm(ppoints(x), mean=0, sd=1),x1)
+ if (mx < c[i])
+ {
+ mx <- c[i]
+ mxli <- l[i]
+ x1.best <- x1
+ }
+ }
> c
  [1] -0.03781299 -0.03809307 -0.03837308 -0.03865302 -0.03893288 -0.03921267
  [7] -0.03949236 -0.03977196 -0.04005147 -0.04033087 -0.04061017 -0.04088936
 [13] -0.04116844 -0.04144739 -0.04172622 -0.04200492 -0.04228348 -0.04256191
 [19] -0.04284019 -0.04311832 -0.04339630 -0.04367412 -0.04395178 -0.04422927
 [25] -0.04450659 -0.04478373 -0.04506069 -0.04533747 -0.04561405 -0.04589043
 [31] -0.04616662 -0.04644260 -0.04671837 -0.04699393 -0.04726926 -0.04754437
 [37] -0.04781926 -0.04809391 -0.04836832 -0.04864249 -0.04891642 -0.04919009
 [43] -0.04946351 -0.04973666 -0.05000955 -0.05028218 -0.05055452 -0.05082659
 [49] -0.05109838 -0.05136988 -0.05164108 -0.05191199 -0.05218260 -0.05245290
 [55] -0.05272290 -0.05299258 -0.05326194 -0.05353098 -0.05379969 -0.05406807
 [61] -0.05433612 -0.05460382 -0.05487118 -0.05513820 -0.05540486 -0.05567116
 [67] -0.05593710 -0.05620268 -0.05646789 -0.05673273 -0.05699719 -0.05726126
 [73] -0.05752495 -0.05778826 -0.05805116 -0.05831368 -0.05857579 -0.05883749
 [79] -0.05909879 -0.05935967 -0.05962014 -0.05988018 -0.06013980 -0.06039899
 [85] -0.06065775 -0.06091608 -0.06117396 -0.06143140 -0.06168840 -0.06194494
 [91] -0.06220103 -0.06245666 -0.06271183 -0.06296654 -0.06322077 -0.06347454
 [97] -0.06372783 -0.06398064 -0.06423297 -0.06448481 -0.06473617 -0.06498703
[103] -0.06523740 -0.06548727 -0.06573663 -0.06598549 -0.06623385 -0.06648169
[109] -0.06672901 -0.06697582 -0.06722211 -0.06746787 -0.06771311 -0.06795782
[115] -0.06820199 -0.06844563 -0.06868873 -0.06893129 -0.06917330 -0.06941477
[121] -0.06965569 -0.06989605 -0.07013586 -0.07037512 -0.07061381 -0.07085193
[127] -0.07108950 -0.07132649 -0.07156291 -0.07179876 -0.07203403 -0.07226873
[133] -0.07250284 -0.07273637 -0.07296932 -0.07320168 -0.07343344 -0.07366462
[139] -0.07389520 -0.07412518 -0.07435457 -0.07458335 -0.07481153 -0.07503911
[145] -0.07526607 -0.07549243 -0.07571818 -0.07594331 -0.07616783 -0.07639173
[151] -0.07661502 -0.07683768 -0.07705972 -0.07728114 -0.07750192 -0.07772209
[157] -0.07794162 -0.07816052 -0.07837879 -0.07859642 -0.07881342 -0.07902978
[163] -0.07924551 -0.07946059 -0.07967503 -0.07988883 -0.08010198 -0.08031449
[169] -0.08052635 -0.08073756 -0.08094812 -0.08115804 -0.08136729 -0.08157590
[175] -0.08178385 -0.08199115 -0.08219779 -0.08240377 -0.08260910 -0.08281376
[181] -0.08301776 -0.08322111 -0.08342379 -0.08362580 -0.08382716 -0.08402784
[187] -0.08422787 -0.08442722 -0.08462591 -0.08482393 -0.08502128 -0.08521796
[193] -0.08541398 -0.08560932 -0.08580399 -0.08599799 -0.08619132 -0.08638397
[199] -0.08657595 -0.08676726 -0.08695789 -0.08714785 -0.08733714 -0.08752575
[205] -0.08771368 -0.08790094 -0.08808753 -0.08827343 -0.08845866 -0.08864322
[211] -0.08882709 -0.08901029 -0.08919282 -0.08937466 -0.08955583 -0.08973632
[217] -0.08991614 -0.09009528 -0.09027374 -0.09045152 -0.09062863 -0.09080506
[223] -0.09098081 -0.09115588 -0.09133028 -0.09150401 -0.09167705 -0.09184942
[229] -0.09202112 -0.09219214 -0.09236248 -0.09253215 -0.09270115 -0.09286947
[235] -0.09303712 -0.09320409 -0.09337039 -0.09353602 -0.09370098 -0.09386526
[241] -0.09402887 -0.09419182 -0.09435409 -0.09451569 -0.09467663 -0.09483689
[247] -0.09499649 -0.09515542 -0.09531369 -0.09547129 -0.09562822 -0.09578449
[253] -0.09594010 -0.09609504 -0.09624932 -0.09640294 -0.09655589 -0.09670819
[259] -0.09685983 -0.09701081 -0.09716113 -0.09731080 -0.09745981 -0.09760816
[265] -0.09775586 -0.09790291 -0.09804931 -0.09819505 -0.09834014 -0.09848459
[271] -0.09862839 -0.09877153 -0.09891404 -0.09905589 -0.09919711 -0.09933768
[277] -0.09947760 -0.09961689 -0.09975554 -0.09989355 -0.10003091 -0.10016765
[283] -0.10030375 -0.10043921 -0.10057404 -0.10070824 -0.10084180 -0.10097474
[289] -0.10110705 -0.10123873 -0.10136979 -0.10150022 -0.10163003 -0.10175921
[295] -0.10188778 -0.10201572 -0.10214305 -0.10226976 -0.10239585 -0.10252133
[301] -0.10264619 -0.10277045 -0.10289409 -0.10301712 -0.10313955 -0.10326137
[307] -0.10338258 -0.10350319 -0.10362320 -0.10374261 -0.10386142 -0.10397963
[313] -0.10409724 -0.10421426 -0.10433068 -0.10444651 -0.10456175 -0.10467641
[319] -0.10479047 -0.10490395 -0.10501684 -0.10512914 -0.10524087 -0.10535202
[325] -0.10546258 -0.10557257 -0.10568198 -0.10579082 -0.10589908 -0.10600678
[331] -0.10611390 -0.10622045 -0.10632644 -0.10643186 -0.10653672 -0.10664101
[337] -0.10674475 -0.10684792 -0.10695054 -0.10705260 -0.10715411 -0.10725506
[343] -0.10735546 -0.10745532 -0.10755462 -0.10765338 -0.10775159 -0.10784926
[349] -0.10794639 -0.10804297 -0.10813902 -0.10823453 -0.10832950 -0.10842395
[355] -0.10851785 -0.10861123 -0.10870408 -0.10879640 -0.10888820 -0.10897947
[361] -0.10907022 -0.10916044 -0.10925015 -0.10933934 -0.10942801 -0.10951617
[367] -0.10960382 -0.10969095 -0.10977758 -0.10986370 -0.10994931 -0.11003441
[373] -0.11011902 -0.11020312 -0.11028672 -0.11036982 -0.11045243 -0.11053454
[379] -0.11061616 -0.11069728 -0.11077792 -0.11085807 -0.11093773 -0.11101690
[385] -0.11109559 -0.11117380 -0.11125153 -0.11132878 -0.11140555 -0.11148185
[391] -0.11155768 -0.11163303 -0.11170791 -0.11178232 -0.11185626 -0.11192974
[397] -0.11200276 -0.11207531 -0.11214740 -0.11221903 -0.11229021
> mx
[1] -0.03781299
> mxli
[1] -2
> x1.best
  [1] 0.4990548 0.4991319 0.4989669 0.4987500 0.4991319 0.4993141 0.4993622
  [8] 0.4993141 0.4991319 0.4990548 0.4991319 0.4993141 0.4993141 0.4993622
 [15] 0.4993141 0.4990548 0.4991319 0.4993622 0.4993141 0.4992000 0.4986150
 [22] 0.4991319 0.4987500 0.4993622 0.4992604 0.4990548 0.4990548 0.4987500
 [29] 0.4958678 0.4991319 0.4992000 0.4990548 0.4984568 0.4987500 0.4987500
 [36] 0.4991319 0.4990548 0.4992000 0.4993622 0.4992604 0.4992604 0.4990548
 [43] 0.4989669 0.4991319 0.4988662 0.4987500 0.4989669 0.4987500 0.4992000
 [50] 0.4987500 0.4989669 0.4990548 0.4992000 0.4990548 0.4990548 0.4989669
 [57] 0.4991319 0.4992000 0.4988662 0.4965278 0.4982699 0.4987500 0.4990548
 [64] 0.4990548 0.4987500 0.4993622 0.4991319 0.4991319 0.4991319 0.4991319
 [71] 0.4993622 0.4992000 0.4988662 0.4992000 0.4992000 0.4984568 0.4982699
 [78] 0.4992604 0.4993622 0.4988662 0.4993141 0.4989669 0.4988662 0.4992000
 [85] 0.4989669 0.4990548 0.4992604 0.4986150 0.4992000 0.4988662 0.4970414
 [92] 0.4991319 0.4992000 0.4992604 0.4992000 0.4992000 0.4989669 0.4988662
 [99] 0.4990548 0.4992000 0.4991319 0.4988662 0.4988662 0.4992000 0.4989669
[106] 0.4987500 0.4987500 0.4990548 0.4993622 0.4990548 0.4993622 0.4991319
[113] 0.4984568 0.4987500 0.4993622 0.4988662 0.4988662 0.4992000 0.4986150
[120] 0.4984568 0.4988662 0.4989669 0.4991319 0.4977778 0.4993622 0.4992604
[127] 0.4990548 0.4992604 0.4987500 0.4989669 0.4987500 0.4990548 0.4989669
[134] 0.4991319 0.4990548 0.4989669 0.4992604 0.4990548 0.4993141 0.4990548
[141] 0.4988662 0.4992604 0.4990548 0.4988662 0.4993141 0.4986150 0.4990548
[148] 0.4992000 0.4990548 0.4989669 0.4989669 0.4992000 0.4992000 0.4993622
[155] 0.4993622 0.4987500 0.4992000 0.4986150 0.4992000 0.4989669 0.4984568
[162] 0.4987500
> if (mxli != 0)
+ {
+ if (par1 == 'Full Box-Cox transform') x1 <- (x^mxli - 1) / mxli
+ if (par1 == 'Simple Box-Cox transform') x1 <- x^mxli
+ } else {
+ x1 <- log(x)
+ }
> postscript(file="/var/wessaorg/rcomp/tmp/1a35o1382562509.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> plot(l,c,main='Box-Cox Normality Plot', xlab='Lambda',ylab='correlation')
> mtext(paste('Optimal Lambda =',mxli))
> grid()
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/2ieda1382562509.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> hist(x,main='Histogram of Original Data',xlab='X',ylab='frequency')
> grid()
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/3ntrr1382562509.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> hist(x1,main='Histogram of Transformed Data', xlab='X',ylab='frequency')
> grid()
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/4b9xe1382562509.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> qqnorm(x)
> qqline(x)
> grid()
> mtext('Original Data')
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/5anmr1382562509.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> qqnorm(x1)
> qqline(x1)
> grid()
> mtext('Transformed Data')
> dev.off()
null device 
          1 
> 
> #Note: the /var/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/wessaorg/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Box-Cox Normality Plot',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'# observations x',header=TRUE)
> a<-table.element(a,n)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'maximum correlation',header=TRUE)
> a<-table.element(a,mx)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'optimal lambda',header=TRUE)
> a<-table.element(a,mxli)
> a<-table.row.end(a)
> if(mx<0) {
+ a<-table.row.start(a)
+ a<-table.element(a,'Warning: maximum correlation is negative! The Box-Cox transformation must not be used.',2)
+ a<-table.row.end(a)
+ }
> a<-table.end(a)
> table.save(a,file="/var/wessaorg/rcomp/tmp/6ttc41382562509.tab") 
> if(par5=='Yes') {
+ a<-table.start()
+ a<-table.row.start(a)
+ a<-table.element(a,'Obs.',header=T)
+ a<-table.element(a,'Original',header=T)
+ a<-table.element(a,'Transformed',header=T)
+ a<-table.row.end(a)
+ for (i in 1:n) {
+ a<-table.row.start(a)
+ a<-table.element(a,i)
+ a<-table.element(a,x[i])
+ a<-table.element(a,x1.best[i])
+ a<-table.row.end(a)
+ }
+ a<-table.end(a)
+ table.save(a,file="/var/wessaorg/rcomp/tmp/7lre31382562509.tab") 
+ }
> 
> try(system("convert tmp/1a35o1382562509.ps tmp/1a35o1382562509.png",intern=TRUE))
character(0)
> try(system("convert tmp/2ieda1382562509.ps tmp/2ieda1382562509.png",intern=TRUE))
character(0)
> try(system("convert tmp/3ntrr1382562509.ps tmp/3ntrr1382562509.png",intern=TRUE))
character(0)
> try(system("convert tmp/4b9xe1382562509.ps tmp/4b9xe1382562509.png",intern=TRUE))
character(0)
> try(system("convert tmp/5anmr1382562509.ps tmp/5anmr1382562509.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  3.172   0.645   3.794