# 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 (Ai - Bi) 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, σ2, 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).