#------- shade.tails -------------------
# draw probability density functions of t with critical regions shaded.  
#   by default the function draws the 95% confidence interval on the normal
#   distribution.
#
# Input parameters
#	crit - the critical value of t (always a positive number)
#	df - degrees of freedom of the t distribution
#	tail - "upper", "lower" or "both"
#	xlim - the x axis range is -xlim to +xlim

shade.tails <- function(crit=1.96, df = 10000, tail = "both",xlim=3.5) 
{

curve(dt(x,df),-xlim,xlim,ylab="density",xlab="t")

ylow = dt(xlim,df)
pcrit = pt(crit,df)
caption = paste(signif(1-pcrit,3))

if (tail == "both" | tail == "lower") {
	xx <- seq(-xlim,-crit,0.05)
	yy <- dt(xx,df)
	polygon(c(xx,-crit,-xlim),c(yy,ylow,ylow),density=20,angle = -45)
	text(-crit-0.7,dt(crit,df)+0.02,caption)
}
if (tail =="both" | tail == "upper") {		
	xx2 <- seq(crit,xlim,0.05)
	yy2 <- dt(xx2,df)
	polygon(c(xx2,xlim,crit),c(yy2,ylow,ylow),density=20,angle = 45)
	text(crit+0.7,dt(crit,df)+0.02,caption)
}
}