Concepts

1. Contingency X is used when we have no prior knowledge of the expected ratios in each class.
   
   
2. Contingency X test uses the concept that if two events are independent, the product of the probability of each separate event will be the probability of both events occurring.
   
   
3. P(A) x P(B) = P(AB), if events A and B are independent.
   
   
4. Binomial distribution is an exact test used when the number of each class are small.
   
   
5. X test is an approximation to the binomial distribution and is used for larger class sizes.