Beer fridge statistics

In this month's video tip Darryl uses the contents of his beer fridge to explain the relationship between probabilities, odds and odds ratios.

Here's a quick summary. Let S_j=number of Speight's beers and Cj=number of citrus beers on shelf j in the beer fridge. The probability of selecting a Speight's from shelf j, P_j, is therefore:

P_j = S_j/(S_j+C_j),

which makes the probability of selecting a citrus beer 1-P_j=C_j/(S_j+C_j).

The odds compares the probabilities of two outcomes, indicating how much greater the probability of the focal outcome is, and can be calculated as:

O_j = S_j/C_j.

An odds ratio then compares to sets of odds. That is:

OR = O₂/O₁

Watch the video for more details and further explanations.