n2.power <- function(J, K, prop=1.0, n.sims, effect.size , mu.a.true, sigma.item.true, sigma.id.true, sigma.y.true ){
	signif.f   <- rep(NA, n.sims)
	signif.x1  <- rep(NA, n.sims)
	signif.x2  <- rep(NA, n.sims)
	signif.x3  <- rep(NA, n.sims)

	N <- J*K
	
	for (s in 1:n.sims){

		x1.true <- effect.size
		x2.true <- effect.size
		x3.true <- effect.size
		f.true <- effect.size
		
		# simulate fixation times
		fake <- ffd.fake(J,K,mu.a.true, x1.true, x2.true, x3.true, f.true, sigma.item.true, sigma.id.true, sigma.y.true)
		fake$ix <- 1:N
		fake <- fake[sample(fake$ix, prop*N), ]
		lme.power <- lmer(y ~ f + x1 + x2 + x3 + (1|id) + (1|item), data=fake)
		
		               
		theta.f.hat <- fixef(lme.power)["f"]
		theta.f.se  <- sqrt(vcov(lme.power)[2,2])#["f","f"])
		signif.f[s] <- (theta.f.hat - 2*theta.f.se) > 0        # returns TRUE or FALSE
		
		theta.x1.hat <- fixef(lme.power)["x1"]
		theta.x1.se  <- sqrt(vcov(lme.power)[3,3])#["x1","x1"])
		signif.x1[s] <- (theta.x1.hat - 2*theta.x1.se) > 0        # returns TRUE or FALSE

		theta.x2.hat <- fixef(lme.power)["x2"]
		theta.x2.se  <- sqrt(vcov(lme.power)[4,4])#["x2","x2"])
		signif.x2[s] <- (theta.x2.hat - 2*theta.x2.se) > 0  # returns TRUE or FALSE

		theta.x3.hat <- fixef(lme.power)["x3"]
		theta.x3.se  <- sqrt(vcov(lme.power)[5,5])#["x3","x3"])
		signif.x3[s] <- (theta.x3.hat - 2*theta.x3.se) > 0  # returns TRUE or FALSE


	}
	signif<-cbind(signif.f, signif.x1, signif.x2, signif.x3)
}