1. Chi Square Two-way Tables
Chapter 13 Section 2

2. 13.2 Two-Way Tables
Also called Contingency Tables or Test of Independence, allows you to do multiple comparisons of proportions.
This test is conducted when comparing categorical data and responses are counts of yes or no, success or failure, A,B, C, or D. Etc.

3. Chi Square distributions are all right skewed and their actual shape depends on their degrees of freedom = (rows-1)(columns -1)
Again the larger the sample size, the closer the distribution comes to being normal.

4. Use Chi Square statistics to evaluate if proportions are equal, same as for Goodness of Fit test – which compares your observed values to some standard values.
Instead, two-way tables use chi square to compare multiple categories to each other.
Done almost the same as goodness of fit.
Chi Square values and p values are still interpreted the same way.

5. To perform Chi square Test of Independence
State the null and alternative hypotheses.
Ho: p1 = p2 = p3 (no association)
Ha: Not all of p1, p2, and p3 are equal. (is an association)
Calculate expected values
((row total x column total)/table total)
Calculate 2 value using
Check assumptions
Find P-value using table E page 842 and
degrees of freedom = (r-1)(c-1)
5. Interpret as usual

6. Remember, these observations only show association not causation.
Only a comparative experiment can show probable cause.
Remember your assumptions: same as goodness of fit test
SRSs
All expected counts are at least 5
n ≤ (1/10)N
Let’s do #14 page 723