Two-way Tables
There's a relationship if
conditional distributions are different or conditional distribution is different from marginal distribution
There's no relationship if
conditional distributions are the same or conditional distribution is the same as marginal distribution
Marginal distributions
distribution of each variable separately, totals add up to all in the table, i.e. marginal distributions of gender splits up gender into males and females
Conditional distributions
distribution of other variable when looking at one variable, totals add up to a marginal distribution, i.e. conditional distributions of majors for gender
Simpson's paradox
original two-way table shows one relationship but if we add a third variable, the relationship reverses
Two-way tables
show relationships between two categorical variables