#' Title
#' @title P value
#' @param t0 t calc
#' @param xmax the limit of the plot
#' @param n sample size
#' @param alpha for a 100(1-alpha)% confidence interval
#'
#' @return p value and the quantile defining the rejection regions. Creates a plot showing the distribution of T along with the rejection regions and a shaded area representing the pvalue.
#' @export
#'
#' @examples
#' \dontrun{mypvalue(tcalc,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))
}
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