Paradoxes in Film Ratings

I selected a simple random sample of 100 movies from the Movie and Video Guide (1996), by Leonard Maltin. My intent was to obtain some basic information on the population of roughly 19,000 movies through a small sample. In exploring the data, I discovered that it exhibited two paradoxes about a three-variable relationship: (1) A non-transitivity paradox for positive correlation, and (2) Simpson?s paradox. Giving concrete examples of these two paradoxes in an introductory course gives to students a sense of the nuances involved in describing associations in observational studies.