#### Quant 1
#### Week 6 Code: Probability testing


## ILLUSTRATE SOME T-TESTING COMPUTATIONS

# same population variances
# note that sd(x) uses a sample statistic with N-1 in denominator!
x1 <- runif(20)
x2 <- runif(20)
sp <- sqrt(((length(x1)-1)*sd(x1)^2 + ((length(x2)-1)*sd(x1)^2 )) /
           (length(x1) + length(x2) - 2))
sdiff <- sp * sqrt(1/length(x1) + 1/length(x2))
(Tsame <- (mean(x1)-mean(x2)) / sdiff)
t.test(x1, x2, var.equal=TRUE)$statistic

# different population variances
# note that sd(x) uses a sample statistic with N-1 in denominator!
sdiff <- sqrt(var(x1)/length(x1) + var(x2)/length(x2))
(Tdiff <- (mean(x1)-mean(x2)) / sdiff)
t.test(x1, x2, var.equal=FALSE)$statistic