#	August 28, 2005

#	Examine effects of pre-testing

library("MASS")		# venables-ripley code

#	assume R^2 = 80%   so re-test difference about 20 pts

Sig <- 100^2 * matrix( c(1, .9, .9, 1), 2, 2)



###	suppose the SAT class does "nothing"   (i.e.   no change in mean)


set.seed(468)
x <- mvrnorm(10000,c(500,500), Sig)	# no change in mean for second test




#	select 100 at random and do t-test

i<- 1:100
t.test( x[i,1], x[i,2], pair=T)

#	select from initial SAT in (450,550)

i <- seq(10000)[ x[,1]>450 & x[,1]<550 ][1:100]
t.test( x[i,1], x[i,2], pair=T)

#	select from initial SAT in (200,300)

i <- seq(10000)[ x[,1]>200 & x[,1]<300 ][1:100]
t.test( x[i,1], x[i,2], pair=T)

#	select from initial SAT in (700,800)

i <- seq(10000)[ x[,1]>700 & x[,1]<800 ][1:100]
t.test( x[i,1], x[i,2], pair=T)




###   now suppose the SAT class improves average by 20 pts

set.seed(864)
x <- mvrnorm(10000,c(500,520), Sig)	# no change in mean for second test


#	select 100 at random and do t-test

i<- 1:100
t.test( x[i,1], x[i,2], pair=T)

#	select from initial SAT in (450,550)

i <- seq(10000)[ x[,1]>450 & x[,1]<550 ][1:100]
t.test( x[i,1], x[i,2], pair=T)

#	select from initial SAT in (200,300)

i <- seq(10000)[ x[,1]>200 & x[,1]<300 ][1:100]
t.test( x[i,1], x[i,2], pair=T)

#	select from initial SAT in (700,800)

i <- seq(10000)[ x[,1]>700 & x[,1]<800 ][1:100]
t.test( x[i,1], x[i,2], pair=T)