__Assumptions for the t-test__

- Bivariate independent variable (A, B groups)
- Continuous dependent variable
- Each observation of the dependent variable is
*independent* of the other observations of the dependent variable (its probability distribution isn't affected by their values). Exception: For the paired t-test, we only require that the pair-differences (A_{i} - B_{i}) be independent from each other (across i). [Note: "independent" and "dependent" are used in two different senses here. Just think of a "dependent variable" as one thing, and "observations that are dependent" as another thing.]
- Dependent variable has a
*normal distribution*,
with the same variance, σ^{2}, in each group
(as though the distribution for group A were merely shifted over to become the distribution for group B, without changing shape):

Note: σ, "sigma", the scale parameter of the normal distribution, also known as the population standard deviation, is easy to see on a picture of a normal curve. Located one
σ to the left or right of the normal mean are the two places where the curve changes from convex to concave (the second derivative is zero).