## question about two sample t-test (unpaired)

I have read that the statistic computed for the unpaired two sample t-test is:

$t = \frac{\bar{x} - \bar{y}}{\sqrt{SEM_x + SEM_y}}$

where:

$SEM_x = \frac{\sigma^2_x}{n_x}$

(and likewise for y).

Part of this makes sense: it is satisfactorily proven to me that that $Var(\bar{x} - \bar{y}) = Var(\bar{x}) + Var(\bar{y})$ when the two variables are independent. Then the denominator is the standard deviation of the term $\bar{x} - \bar{y})$. What doesn't make sense is that the numerator isn't normalized. In the one sample t-test, one computes:

$t = \frac{\bar{x} - \mu_x}{\sqrt{SEM_x}}$

so, here, $\bar{x}$ is normalized with $\mu_x$. I don't see why this shouldn't also apply to the two-sample case. Can someone enlighten me?
 PhysOrg.com science news on PhysOrg.com >> City-life changes blackbird personalities, study shows>> Origins of 'The Hoff' crab revealed (w/ Video)>> Older males make better fathers: Mature male beetles work harder, care less about female infidelity
 In the two-sample t-test, you're testing whether the two samples are different from each other; that is, whether the mean of the difference between them is zero. You can think of the numerator as having an implicit 0 subtracted from it, if you like.

 Quote by pmsrw3 In the two-sample t-test, you're testing whether the two samples are different from each other; that is, whether the mean of the difference between them is zero. You can think of the numerator as having an implicit 0 subtracted from it, if you like.
That clarifies matters a bit. Thank you.

 Similar discussions for: question about two sample t-test (unpaired) Thread Forum Replies Set Theory, Logic, Probability, Statistics 6 Calculus & Beyond Homework 4 Other Science Learning Materials 0 Biology, Chemistry & Other Homework 0