## Free Statistics

of Irreproducible Research!

Author's title
Author*Unverified author*
R Software Modulerwasp_boxcoxnorm.wasp
Title produced by softwareBox-Cox Normality Plot
Date of computationMon, 24 Feb 2020 22:56:15 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2020/Feb/24/t1582581523l8uymiw9o3tn7rw.htm/, Retrieved Wed, 21 Apr 2021 08:32:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=319083, Retrieved Wed, 21 Apr 2021 08:32:42 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact45
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Box-Cox Normality Plot] [] [2020-02-24 21:56:15] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
202485.00
231302.13
227730.77
40384.62
1456659.16
33035.47
53823.15
58371.02
64177.03
22558.09

 Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 2 seconds R Server Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319083&T=0

[TABLE]
[ROW]
 Summary of computational transaction[/C][/ROW] [ROW] Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW] Raw Output[/C] view raw output of R engine [/C][/ROW] [ROW] Computing time[/C] 2 seconds[/C][/ROW] [ROW] R Server[/C] Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=319083&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319083&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

 Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 2 seconds R Server Big Analytics Cloud Computing Center

 Box-Cox Normality Plot # observations x 10 maximum correlation 0.981668841261037 optimal lambda -0.5 transformation formula for all lambda <> 0 : T(Y) = (Y^lambda - 1) / lambda

\begin{tabular}{lllllllll}
\hline
Box-Cox Normality Plot \tabularnewline
# observations x & 10 \tabularnewline
maximum correlation & 0.981668841261037 \tabularnewline
optimal lambda & -0.5 \tabularnewline
transformation formula & for all lambda <> 0 : T(Y) = (Y^lambda - 1) / lambda \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319083&T=1

[TABLE]
[ROW][C]Box-Cox Normality Plot[/C][/ROW]
[ROW][C]# observations x[/C][C]10[/C][/ROW]
[ROW][C]maximum correlation[/C][C]0.981668841261037[/C][/ROW]
[ROW][C]optimal lambda[/C][C]-0.5[/C][/ROW]
[ROW][C]transformation formula[/C][C]for all lambda <> 0 : T(Y) = (Y^lambda - 1) / lambda[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319083&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319083&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

 Box-Cox Normality Plot # observations x 10 maximum correlation 0.981668841261037 optimal lambda -0.5 transformation formula for all lambda <> 0 : T(Y) = (Y^lambda - 1) / lambda

 Obs. Original Transformed 1 202485 1.99555539093736 2 231302.13 1.9958414667372 3 227730.77 1.99580898574151 4 40384.62 1.99004773353814 5 1456659.16 1.99834289120019 6 33035.47 1.98899627442939 7 53823.15 1.99137924227414 8 58371.02 1.99172188692317 9 64177.03 1.99210521716409 10 22558.09 1.98668384526218

\begin{tabular}{lllllllll}
\hline
Obs. & Original & Transformed \tabularnewline
1 & 202485 & 1.99555539093736 \tabularnewline
2 & 231302.13 & 1.9958414667372 \tabularnewline
3 & 227730.77 & 1.99580898574151 \tabularnewline
4 & 40384.62 & 1.99004773353814 \tabularnewline
5 & 1456659.16 & 1.99834289120019 \tabularnewline
6 & 33035.47 & 1.98899627442939 \tabularnewline
7 & 53823.15 & 1.99137924227414 \tabularnewline
8 & 58371.02 & 1.99172188692317 \tabularnewline
9 & 64177.03 & 1.99210521716409 \tabularnewline
10 & 22558.09 & 1.98668384526218 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319083&T=2

[TABLE]
[ROW][C]Obs.[/C][C]Original[/C][C]Transformed[/C][/ROW]
[ROW][C]1[/C][C]202485[/C][C]1.99555539093736[/C][/ROW]
[ROW][C]2[/C][C]231302.13[/C][C]1.9958414667372[/C][/ROW]
[ROW][C]3[/C][C]227730.77[/C][C]1.99580898574151[/C][/ROW]
[ROW][C]4[/C][C]40384.62[/C][C]1.99004773353814[/C][/ROW]
[ROW][C]5[/C][C]1456659.16[/C][C]1.99834289120019[/C][/ROW]
[ROW][C]6[/C][C]33035.47[/C][C]1.98899627442939[/C][/ROW]
[ROW][C]7[/C][C]53823.15[/C][C]1.99137924227414[/C][/ROW]
[ROW][C]8[/C][C]58371.02[/C][C]1.99172188692317[/C][/ROW]
[ROW][C]9[/C][C]64177.03[/C][C]1.99210521716409[/C][/ROW]
[ROW][C]10[/C][C]22558.09[/C][C]1.98668384526218[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319083&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319083&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

 Obs. Original Transformed 1 202485 1.99555539093736 2 231302.13 1.9958414667372 3 227730.77 1.99580898574151 4 40384.62 1.99004773353814 5 1456659.16 1.99834289120019 6 33035.47 1.98899627442939 7 53823.15 1.99137924227414 8 58371.02 1.99172188692317 9 64177.03 1.99210521716409 10 22558.09 1.98668384526218

 Maximum Likelihood Estimation of Lambda > summary(mypT) bcPower Transformation to Normality Est Power Rounded Pwr Wald Lwr Bnd Wald Upr Bnd x -0.382 0 -0.9516 0.1876 Likelihood ratio test that transformation parameter is equal to 0 (log transformation) LRT df pval LR test, lambda = (0) 1.935387 1 0.16417 Likelihood ratio test that no transformation is needed LRT df pval LR test, lambda = (1) 26.94696 1 2.0912e-07 

\begin{tabular}{lllllllll}
\hline
Maximum Likelihood Estimation of Lambda \tabularnewline
> summary(mypT)
bcPower Transformation to Normality
Est Power Rounded Pwr Wald Lwr Bnd Wald Upr Bnd
x    -0.382           0      -0.9516       0.1876
Likelihood ratio test that transformation parameter is equal to 0
(log transformation)
LRT df    pval
LR test, lambda = (0) 1.935387  1 0.16417
Likelihood ratio test that no transformation is needed
LRT df       pval
LR test, lambda = (1) 26.94696  1 2.0912e-07
\tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319083&T=3

[TABLE]
[ROW][C]Maximum Likelihood Estimation of Lambda[/C][/ROW]
[ROW][C]> summary(mypT)
bcPower Transformation to Normality
Est Power Rounded Pwr Wald Lwr Bnd Wald Upr Bnd
x    -0.382           0      -0.9516       0.1876
Likelihood ratio test that transformation parameter is equal to 0
(log transformation)
LRT df    pval
LR test, lambda = (0) 1.935387  1 0.16417
Likelihood ratio test that no transformation is needed
LRT df       pval
LR test, lambda = (1) 26.94696  1 2.0912e-07
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319083&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319083&T=3

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

 Maximum Likelihood Estimation of Lambda > summary(mypT) bcPower Transformation to Normality Est Power Rounded Pwr Wald Lwr Bnd Wald Upr Bnd x -0.382 0 -0.9516 0.1876 Likelihood ratio test that transformation parameter is equal to 0 (log transformation) LRT df pval LR test, lambda = (0) 1.935387 1 0.16417 Likelihood ratio test that no transformation is needed LRT df pval LR test, lambda = (1) 26.94696 1 2.0912e-07 

par5 <- 'No'par4 <- '0'par3 <- '2'par2 <- '-2'par1 <- 'Full Box-Cox transform'library(car)par2 <- abs(as.numeric(par2)*100)par3 <- as.numeric(par3)*100if(par4=='') par4 <- 0par4 <- as.numeric(par4)numlam <- par2 + par3 + 1x <- x + par4n <- length(x)c <- array(NA,dim=c(numlam))l <- array(NA,dim=c(numlam))mx <- -1mxli <- -999for (i in 1:numlam){l[i] <- (i-par2-1)/100if (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),sort(x1))if (mx < c[i]){mx <- c[i]mxli <- l[i]x1.best <- x1}}print(c)print(mx)print(mxli)print(x1.best)if (mxli != 0){if (par1 == 'Full Box-Cox transform') x1 <- (x^mxli - 1) / mxliif (par1 == 'Simple Box-Cox transform') x1 <- x^mxli} else {x1 <- log(x)}mypT <- powerTransform(x)summary(mypT)bitmap(file='test1.png')plot(l,c,main='Box-Cox Normality Plot', xlab='Lambda',ylab='correlation')mtext(paste('Optimal Lambda =',mxli))grid()dev.off()bitmap(file='test2.png')hist(x,main='Histogram of Original Data',xlab='X',ylab='frequency')grid()dev.off()bitmap(file='test3.png')hist(x1,main='Histogram of Transformed Data', xlab='X',ylab='frequency')grid()dev.off()bitmap(file='test4.png')qqPlot(x)grid()mtext('Original Data')dev.off()bitmap(file='test5.png')qqPlot(x1)grid()mtext('Transformed Data')dev.off()load(file='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)a<-table.row.start(a)a<-table.element(a,'transformation formula',header=TRUE)if (par1 == 'Full Box-Cox transform') {a<-table.element(a,'for all lambda <> 0 : T(Y) = (Y^lambda - 1) / lambda')} else {a<-table.element(a,'for all lambda <> 0 : T(Y) = Y^lambda')}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='mytable.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='mytable1.tab')}a<-table.start()a<-table.row.start(a)a<-table.element(a,'Maximum Likelihood Estimation of Lambda',1,TRUE)a<-table.row.end(a)a<-table.row.start(a)a<-table.element(a,paste('',RC.texteval('summary(mypT)'),'',sep=''))a<-table.row.end(a)a<-table.end(a)table.save(a,file='mytable3.tab')