Difference between one-way and two-way tables

A one-way table describes counts for each outcome in a single variable. A two-way table describes counts for combinations of outcomes for two variables. when we consider a two-way table, we often would like to know if the variables are related in any way; that is, are they dependent or independent?

Computing expected counts in a two-way table

To identify the expected count for the \(i^{th}\) row and \(j^{th}\) column, compute \(\(\text{Expected Count}_{\text{row }i, \text{col }j}=\frac{(\text{row } i \text{ total}) \times (\text{column } j \text{ total})}{\text{table total}}\)\)

Chi-square test for two-way tables

Computed the same way as a one-way table. Compute (observed count - expected count)\(^2\) / expected count for each cell and take the sum to find \(X^2\).

Degrees of freedom for two-way tables

\(df =\) (number of rows minus 1) \(\times\) (number of columns minus 1)