R/Brown_Forsythe.R

In homnormal: Tests of Homogeneity of Variances

#' Brown-Forsythe Test for Homogeniety
#'
#' Tests the homogeniety of variances for more than two normal groups.
#'
#' @export
#' @import huxtable
#' @importFrom stats integrate median pchisq pf rchisq rnorm var
#' @importFrom graphics boxplot par
#' 
#' @param x1 a numeric matrix containing the values of groups.
#'
#' @param x2  numeric matrix containing the values of group numbers.
#' 
#' @param alfa significance level of the test. Default number is 0.05.
#'
#' @param table a logical variable that indicates table will appear or not. Default is TRUE.
#'
#' @param graph box plot of groups of raw or centered data.
#' 
#'@return if table is TRUE, then it gives a detailed table,
#'else it gives a vector of r value(r=1 when null hypothesis was rejected and r=0 when null hypothesis was accepted)
#' p-value and test statistic value.
#'
#' @examples
#'     data(FH_data)
#'    x1=FH_data$SurvivalTime
#'    x2=FH_data$HospitalNo
#'    Brown_Forsythe(x1,x2)
#'    readline(prompt = "Pause. Press <Enter> to continue...")
#'    Brown_Forsythe(x1,x2,alfa=0.10)
#'    readline(prompt = "Pause. Press <Enter> to continue...")
#'     Brown_Forsythe(x1,x2,alfa=0.10,table=FALSE)
#'     readline(prompt = "Pause. Press <Enter> to continue...")
#'     Brown_Forsythe(x1,x2,alfa=0.10,table=FALSE,graph="raw")
#'     readline(prompt = "Pause. Press <Enter> to continue...")
#'     Brown_Forsythe(x1,x2,alfa=0.10,table=FALSE,graph="none")
#' # ---THIS VERSION IS ESPECIALLY USEFUL FOR COMPARISON STUDIES BY SIMULATION---
#' #    #first value of the vector is r value(r=1 when rejected and r=0 when accepted null hypothesis)
#' # second value of the vector is the p-value and third value is the tests statistic value
#'@seealso \code{\link[homnormal]{bdai}}, \code{\link[homnormal]{Cat_GG}}, \code{\link[homnormal]{Cat_LR}}, \code{\link[homnormal]{genp}}, \code{\link[homnormal]{slrt}}, \code{\link[homnormal]{levene}},
#' @references Brown, M. B., & Forsythe, A. B. (1974). Robust tests for the equality of variances. Journal of the American Statistical Association, 69(346), 364-367.
Brown_Forsythe<-function(x1,x2,alfa=0.05,table=TRUE,graph="none"){
  ne=c()
  for (i in factor(x2)) { 
    ne[as.numeric(i)]=(sum(x2==i))
  }
    xm=c()
  xmed=c()
  s2t=c()
  mut=c()
  s2tt=c()
  k=length(ne)
  for (i in 1:k) {
    xmed[i]=median(x1[x2==i])
    mut[i]=mean(x1[x2==i])
    s2tt[i]=var(x1[x2==i])
  }
x1b=abs(x1-rep(xmed,ne))
for (i in 1:k) {
s2t[i]=var(x1b[x2==i])
xm[i]=mean(x1b[x2==i])
}
gm=mean(x1b)
down=sum(s2t*(ne-1))/sum(ne-1)
up=sum(ne*(xm-gm)^2)/(k-1)
Fh=up/down
p=1-pf(Fh,k-1,sum(ne-1))
r=(p<alfa) 
if(graph=="raw") {
  boxplot(x1~x2,xlab = "", ylab = "")
}
else if(graph=="centered") {
  boxplot(x1-rep(mut,ne)~x2,xlab = "", ylab = "")
}
else if (graph=="none")
{}
if (table==FALSE) {
  return(c(r,p,Fh))
}
else if (table==TRUE)
{
  C1=1:length(ne)
  C2=c(ne)
  C3=c(mut)
  C4=c(s2t)
  C5=c(rep(NA,ifelse(k%%2==0,ceiling(k/2),floor(k/2))),Fh,rep(NA,floor(k/2-1)))
  C6=c(rep(NA,ifelse(k%%2==0,ceiling(k/2),floor(k/2))),p,rep(NA,floor(k/2-1)))
  HT<-hux(Group_No=C1,Sample_Size=C2,Sample_Mean=C3,Sample_Var=C4,Test_Stat=C5,p_value=C6)
  align(HT)[,1:5]          <- 'center'
  number_format(HT)[,3:6]      <- 2
  number_format(HT)[,2]      <- 0
  
  print_md(HT, header = TRUE)
  return(HT)
}
}