Subjective Statistical Inference Based on Pure Associations

• Activity Number: 80
• Type: Topic Contributed
• Date/Time: Monday, August 4, 2003 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Education
• Author(s): Robyn M. Dawes*+
• Companies: Carnegie Mellon University
• Keywords: Bayes theorem ; irrationality ; association

Abstract

The "fourth axiom of probability theory" quickly yields Bayes theorem--and hence how to deal with inverse probabilities (e.g., P(h/e) versus P(e/h)) --and shows in odds form the importance of likelihood ratios as opposed to simple likelihoods. This paper discusses a problem more basic than ignoring Bayes theorem. The problem is making no comparisons at all, just associating! Thus, if P(A/B) or P(B/A) is high (low), people tend to think that A and B "go together" (or don't). A distressing number of examples ranging from Nazi ideology to unjustified inferences in the mental health field will be presented, as well as some experimental research. In fact, A and B are often thought to "go together" simply on the basis that P(A) and P(B) are both high (or low). Criminal behaviors are unusual, minority group membership is unusual, so would you believe? This "Von Rostoff effect" was originally found in paired associates learning of words or nonsense syllables. If a few stimuli were printed in red rather than black and so were a few to-be-learned responses, people tended to believe that they were paired, even though statistically independent.