# Is a one-sample t-test on difference scores compared to 0 identical to a paired t-test?

If I want to determine the difference between two correlated measurements (i.e., pre-post scores), is a one-sample t-test on the difference scores compared to 0 an identical test to a paired sample t-test?

• compare the formulas.... – Glen_b Nov 22 '17 at 1:38

Yes. We can test this easily enough in R or whatever you like e.g. (R code):

set.seed(123)

x1 <- rnorm(100)
x2 <- rnorm(100)
diff <- x1-x2
t.test(x1,x2, paired = TRUE)
t.test(diff)


but it also follows from the definition of a paired t-test.

• More relevant is your point that it follows by the definition. There is nothing magic about two functions in R that do exactly the same computations. – Michael R. Chernick Nov 22 '17 at 5:18
• They do the same computations because of the definitions and because R implemented the definitions. – Peter Flom - Reinstate Monica Nov 22 '17 at 13:06