R/mypvalue from Lab 12.R

In sammcdonald9914/math4753d: Functions from the MATH4753 course

#' My p-value function
#'
#' Plots the p-value corresponding to a given t-statistic, sample size, and alpha
#'
#' Plots rejection region for t values as well
#'
#' @param t0 value of the t statistic
#' @param xmax the maximum value of x shown on the graph
#' @param n the number of data points in the sample
#' @param alpha value that determines the quantiles
#'
#' @return plot of p-value and rejection region for t distribution
#' @export
#'
#' @examples mypvalue(t0=2,xmax=5,n=30, alpha=0.05)
mypvalue=function(t0,xmax=4,n=20, alpha=0.05){
  #calculate alpha/2
  va=round(pt(-t0,df=n-1),4)
  pv=2*va

  # plot the t dist
  curve(dt(x,df=n-1),xlim=c(-xmax,xmax),ylab="T Density",xlab=expression(t),
        main=substitute(paste("P-value=", pv, " alpha=", alpha)))


  # set up points on the polygon to the right
  xcurve=seq(t0,xmax,length=1000)
  ycurve=dt(xcurve,df=n-1)

  # set up points to the left
  xlcurve=seq(-t0,-xmax,length=1000)
  ylcurve=dt(xcurve,df=n-1)

  # Shade in the polygon defined by the line segments
  polygon(c(t0,xcurve,xmax),c(0,ycurve,0),col="green")
  polygon(c(-t0,xlcurve,-xmax),c(0,ylcurve,0),col="green")

  # make quantiles
  q=qt(1-alpha/2,n-1)
  abline( v=c(q,-q),lwd=2) # plot the cut off t value
  axis(3,c(q,-q),c(expression(abs(t[alpha/2])),expression(-abs(t[alpha/2]))))


  # Annotation
  text(0.5*(t0+xmax),max(ycurve),substitute(paste(area, "=",va)))
  text(-0.5*(t0+xmax),max(ycurve),expression(area))

  return(list(q=q,pvalue=pv))
}