Performance and weight of high school children

Association

Joint Probabilities
Athletic performance
Poor Satisfactory Above average Marginal
Underweight 0.0450 0.0900 0.0150 0.1500
Normal 0.0825 0.3025 0.1650 0.5500
Overweight 0.0500 0.1200 0.0300 0.2000
Obese 0.0300 0.0650 0.0050 0.1000
Marginal 0.1700 0.5400 0.2900 1.0000

Conditional probabilities

Use this diagram to explain the interpretation of association and why independence is important.

In the first example, athletic performance is associated with weight — children with normal weight are better athletes.

In the second example (select from the pop-up menu), maths performance is independent of weight — the conditional probabilities for performance are the same for each weight category.

The probabilities are artificial and are only used to illustrate the idea of independence.